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We investigate how the quasi-universal relations connecting tidal deformability with gravitational waveform characteristics and/or properties of individual neutron stars that were proposed in the literature within general relativity would be influenced in the massive Damour-Esposito-Farese-type scalar-tensor gravity. For this purpose, we systematically perform numerical relativity simulations of ~120 binary neutron star mergers with varying scalar coupling constants. Although only three neutron-star equations of state are adopted, a clear breach of universality can be observed in the data sets. In addition to presenting difficulties in constructing quasi-universal relations in alternative gravity theories, we also briefly compare the impacts of non-general-relativity physics on the waveform features and those due to the first order or cross-over quantum chromodynamical phase transition.

The recent discovery of gravitational waves (GWs) has opened a new avenue for investigating the equation of state (EOS) of dense matter in compact stars, which is an outstanding problem in astronomy and nuclear physics. In the future, next-generation (XG) GW detectors will be constructed, deemed to provide a large number of high-precision observations. We investigate the potential of constraining the EOS of quark stars (QSs) with high-precision measurements of mass $m$ and tidal deformability $\Lambda$ from the XG GW observatories. We adopt the widely-used bag model for QSs, consisting of four microscopic parameters: the effective bag constant $B_{\rm eff}$, the perturbative quantum chromodynamics correction parameter $a_4$, the strange quark mass $m_s$, and the pairing energy gap $\Delta$. With the help of hierarchical Bayesian inference, for the first time we are able to infer the EOS of QSs combining multiple GW observations. Using the top 25 loudest GW events in our simulation, we find that, the constraints on $B_{\rm eff}$ and $\Delta$ are tightened by several times, while $a_4$ and $m_s$ are still poorly constrained. We also study a simplified 2-dimensional (2-d) EOS model which was recently proposed in literature. The 2-d model is found to exhibit significant parameter-estimation biases as more GW events are analyzed, while the predicted $m$-$\Lambda$ relation remains consistent with the full model.

We explore the new physics phenomena of gravidynamics governed by the inhomogeneous spin gauge symmetry based on the gravitational quantum field theory. Such a gravidynamics enables us to derive the generalized Einstein equation and an equation beyond it. To simplify the analyses, we linearize the dynamic equations of gravitational interaction by keeping terms up to the leading order in the dual gravigauge field. We then apply the linearized dynamic equations into two particular gravitational phenomena. First, we consider the linearized equations in the absence of source fields, which is shown to have five physical propagating polarizations as gravitational waves, i.e., two tensor modes, two vector modes, and one scalar, instead of two tensor polarizations in the general relativity. Second, we examine the Newtonian limit in which the gravitational fields and the matter source distribution are weak and static. By deriving the associated Poisson equation, we obtain the exact relation of the fundamental interaction coupling in the gravidynamics with the experimentally measured Newtonian constant. We also make use of nonrelativistic objects and relativistic photons to probe the Newtonian field configurations. In particular, the experiments from the gravitational deflection of light rays and the Shapiro time delay can place stringent constraints on the linearized gravidynamics in the gravitational quantum field theory.

It is commonly believed that black holes are the smallest self-gravitating objects of the same mass in the Universe. Here, we demonstrate, in a subclass of higher-order pure gravities known as quasi-topological gravity, that by modifying general relativity (GR) to reduce the strength of gravity in strong-field regimes while keeping GR unchanged in weak-field regimes, it is possible for stars to collapse to radii less than $2M$ while still maintaining equilibrium between gravity and pressure gradients, leading to physically-reasonable neutron stars smaller in size than a black hole of the same mass. We present concrete solutions for such objects and discuss some of their observational consequences. These objects may furnish new avenues for understanding the nature of gravity in strong-field regimes and leave imprints on gravitational wave echoes from compact binary mergers. An observation of these imprints may constitute evidence for new physics beyond GR when effects of gravity in strong-field regimes are concerned.

Under the local gravitational field, perturbations from high-frequency gravitational waves can cause a vertical shift of the Mössbauer resonance height. Considering a stationary scheme with the $^{109}$Ag isotope, we demonstrate that the extremely high precision of Mössbauer resonance allows for competitive gravitational wave sensitivity from KHz up to above MHz frequencies. Mössbauer resonance can offer a novel and small-sized alternative in the quest of multi-band gravitational wave searches. The presence of the static gravitational field plays essential role in the detection mechanism, isotope selection and sensitivity forecast. The proposed stationary scheme's sensitivity has the potential of significant improvement in a low-gravity environment.

Based on different neutron star-white dwarf (NS-WD) population models, we investigate the prospects of gravitational-wave (GW) detections for NS-WD mergers, with the help of early warnings from two space-borne decihertz GW observatories, DO-Optimal and DECIGO. We not only give quick assessments of the GW detection rates for NS-WD mergers with the two decihertz GW detectors, but also report systematic analyses on the characteristics of GW-detectable merger events using the method of Fisher matrix. With a sufficient one-day early-warning time, the yearly GW detection number for DO-Optimal is in the range of $ (1.5$-$1.9) \times 10^{3}$, while it is $ (3.3$-$4.6) \times 10^{4}$ for DECIGO. More importantly, our results show that most NS-WD mergers can be localized with an uncertainty of $O(10^{-2})\,\mathrm{deg}^2$. Given the NS-WD merger as a possible origin for a peculiar long-duration gamma-ray burst, GRB 211211A, followed with kilonova-like emissions, we further suggest that the GW early-warning detection would allow future electromagnetic telescopes to get prepared to follow-up transients after some special NS-WD mergers. Based on our analyses, we emphasize that such a feasible "wait-for" pattern can help to firmly identify the origin of GRB 211211A-like events in the future and bring excellent opportunities for the multimessenger astronomy.

Several pulsar timing array (PTA) experiments such as NANOGrav and PPTA reported evidence of a gravitational wave background at the nano-Hz frequency band recently. This signal can originate from scalar-induced gravitational waves (SIGW) generated by the enhanced curvature perturbation. Here we perform a joint likelihood inference on PTA datasets, and our results show that if the PTA signals were indeed of SIGW origin, the curvature perturbations amplitude required will produce primordial black holes (PBHs) in $[2 \times 10^{-5}, 2 \times 10^{-2}]\ m_\odot$ mass range. Mergers of these PBHs can leave a strong gravitational wave signature in the $[10^{-3}, 10^8]$ Hz frequency range, to be detectable at upcoming interferometers such as the Einstein Telescope, DECIGO and BBO, etc. This offers a multi-frequency opportunity to further scrutinize the source of the observed PTA signal.

It was conjectured that the basic units of the ground state of bulk strong matter may be strange-clusters called strangeons, and they can form self-bound strangeon stars that are highly compact. Strangeon stars can develop a strange quark matter (SQM) core at high densities, particularly in the color-flavor-locking phase, yielding a branch of hybrid strangeon stars. We explore the stellar structure and astrophysical implications of hybrid strangeon stars. We find that hybrid strangeon stars can meet various astrophysical constraints on pulsar masses, radii, and tidal deformabilities. Finally, we show that the strangeon-SQM mixed phase is not preferred if the charge-neutrality condition is imposed at the strangeon-SQM transition region.

Gravitational waves from isolated sources have eluded detection so far. The upper limit of long-lasting continuous gravitational wave emission can now probe physically-motivated models with the most optimistic being strongly constrained. Naturally, one might want to relax the assumption of the gravitational wave being quasi-infinite in duration, leading to the idea of transient continuous gravitational waves. In this paper, we outline how to get transient continuous waves from magnetars (or strongly-magnetised neutron stars) that exhibit glitches and/or antiglitches and apply the model to magnetar SGR J1935+2154. The toy model hypothesizes that at a glitch or antiglitch, mass is ejected from the magnetar but becomes trapped on its outward journey through the magnetosphere. Depending on the height of the trapped ejecta and the magnetic inclination angle, we are able to reproduce both glitches and antiglitches from simple angular momentum arguments. The trapped ejecta causes the magnetar to precess leading to gravitational wave emission at once and twice the magnetar's spin frequency, for a duration equal to however long the ejecta is trapped for. We find that the gravitational waves are more detectable when the magnetar is: closer, rotating faster, or has larger glitches/antiglitches. The detectability also improves when the ejecta height and magnetic inclination angle have values near their critical values, though this requires more mass to be ejected to remain consistent with the observed glitch/antiglitch. We find it unlikely that gravitational waves will be detected from SGR J1935+2154 when using the trapped ejecta model.

Solid states of strange-cluster matter called strangeon matter can form strangeon stars that are highly compact. We show that strangeon matter and strangeon stars can be recast into dimensionless forms by a simple reparametrization and rescaling, through which we manage to maximally reduce the number of degrees of freedom. With this dimensionless scheme, we find that strangeon stars are generally compact enough to feature a photon sphere that is essential to foster gravitational-wave (GW) echoes. Rescaling the dimension back, we illustrate its implications on the expanded dimensional parameter space, and calculate the GW echo frequencies associated with strangeon stars, showing that the minimum echo frequency is $\sim 8$ kHz for empirical parameter space that satisfies the GW170817 constraint, and can reduce to $\mathcal O(100)$ Hertz at the extended limit.

Gravitational waves can generate electromagnetic effects inside a strong electric or magnetic field within the Standard Model and general relativity. Here we propose using a quarterly split cavity and LC(inductor and capacitor)-resonance circuit to detect a high-frequency gravitational wave from 0.1 MHz to GHz. We perform a full 3D simulation of the cavity's signal for sensitivity estimate. Our sensitivity depends on the coherence time scale of the high-frequency gravitational wave sources and the volume size of the split cavity. We discuss the resonant measurement schemes for narrow-band gravitational wave sources and also a non-resonance scheme for broadband signals. For a meter-sized split cavity under a 14 Tesla magnetic field, the LC resonance enhanced sensitivity to the gravitational wave strain is expected to reach $h\sim 10^{-20}$ around $10$ MHz.

It is well-known that the mass of a non-asymptotically flat spacetime cannot be uniquely defined. Some mass formulas for the Kerr-AdS black hole have been found and used in studying black hole thermodynamics. However, the derivations usually need a background subtraction to eliminate the divergence at infinity. It is also unknown whether the mass depends on the choice of coordinates. In this paper, we provide a more straightforward derivation for the mass formula, only demanding that the first law of black hole thermodynamics and Smarr formula are satisfied. We first make use of the Iyer-Wald formalism to derive a first law which avoids the divergence at infinity. Then we apply this formula to charged Kerr-AdS black hole expressed in the coordinates rotating at infinity. However, the first law associated with the timelike Killing vector field $\frac{\partial}{\partial t}$ is not integrable. Then, by making use of the gauge freedom of $t$, we find a favorite parameter $t'$ which just makes the mass integrable. Applying the scaling argument, we show that the mass satisfies the Smarr formula and takes the form $M/\Xi^{3/2}$. Moreover, applying the conformal method with $\ppn{}{t'}$, we obtain the same mass. By applying the first law to the coordinates which is not rotating at infinity, we find a preferred time $T$ that makes the first law integrable and the mass is just the familiar mass $M/\Xi^2$ in the literature. This mass is also confirmed by the conformal method. We find that the two mass formulas correspond to different families of observers and the preferred Killing times. So our work clarifies the ambiguities of mass in Kerr-AdS spacetimes.

Universal relations that are insensitive to the equation of state (EoS) are useful in reducing the parameter space when measuring global quantities of neutron stars (NSs). In this paper, we reveal a new universal relation that connects the eccentricity to the radius and moment of inertia of rotating NSs. We demonstrate that the universality of this relation holds for both conventional NSs and bare quark stars (QSs) in the slow rotation approximation, albeit with different relations. The maximum relative deviation is approximately $1\%$ for conventional NSs and $0.1\%$ for QSs. Additionally, we show that the universality still exists for fast-rotating NSs if we use the dimensionless spin to characterize their rotation. The new universal relation will be a valuable tool to reduce the number of parameters used to describe the shape and multipoles of rotating NSs, and it may also be used to infer the eccentricity or moment of inertia of NSs in future X-ray observations.

The equation of state (EOS) of nuclear dense matter plays a crucial role in many astrophysical phenomena associated with neutron stars (NSs). Fluid oscillations are one of the most fundamental properties therein. NSs support a family of gravity $g$-modes, which are related to buoyancy. We study the gravity $g$-modes caused by composition gradient and density discontinuity in the framework of pseudo-Newtonian gravity. The mode frequencies are calculated in detail and compared with Newtonian and general-relativistic (GR) solutions. We find that the $g$-mode frequencies in one of the pseudo-Newtonian treatments can approximate remarkably well the GR solutions, with relative errors in the order of $1\%$. Our findings suggest that, with much less computational cost, pseudo-Newtonian gravity can be utilized to accurately analyze oscillation of NSs constructed from an EOS with a first-order phase transition between nuclear and quark matter, as well as to provide an excellent approximation of GR effects in core-collapse supernova (CCSN) simulations.

Sufficiently large scalar perturbations in the early Universe can create over-dense regions that collapse into primordial black holes (PBH). This process is accompanied by the emission of scalar-induced gravitational waves (SIGW) that behave like an extra radiation component, thus contributing to the relativistic degrees of freedom ($N_{\rm{eff}}$). We show that the cosmological constraints on $N_{\rm{eff}}$ can be used to pose stringent limits on PBHs created from this particular scenario as well as the relevant small-scale curvature perturbation ($\mathcal{P}_{\mathcal{R}}(k)$). We show that the combination of cosmic microwave background (CMB), baryon acoustic oscillation (BAO) and Big-Bang nucleosynthesis (BBN) datasets can exclude supermassive PBHs with peak mass $M_{\bullet} \in [5 \times 10^{5}, 5 \times 10^{10}]\,{\rm M}_{\odot}$ as the major component of dark matter, while the detailed constraints depend on the shape of the PBHs mass distribution. The future CMB mission like CMB-S4 can broaden this constraint window to a much larger range $M_{\bullet} \in [8 \times 10^{-5}, 5 \times 10^{10}]\,{\rm M}_{\odot}$, covering sub-stellar masses. These limits on PBH correspond to a tightened constraint on $\mathcal{P}_{\mathcal{R}}$ on scales of $k \in [10, 10^{22}]\ {\rm{Mpc^{-1}}}$, much smaller than those probed by direct CMB and large-scale structure power spectra.

We test the weak cosmic censorship conjecture for magnetized Kerr-Newman spacetime via the method of injecting a test particle. Hence, we need to know how the black hole's parameters change when a test particle enters the horizon. This was an unresolved issue for non-asymptotically flat spacetimes since there are ambiguities on the energies of black holes and particles. We find a novel approach to solve the problem. We start with the "physical process version" of the first law, which relates the particle's parameters with the change in the area of the black hole. By comparing this first law with the usual first law of black hole thermodynamics, we redefine the particle's energy such that the energy can match the mass parameter of the black hole. Then, we show that the horizon of the extremal magnetized Kerr-Newman black hole could be destroyed after a charged test particle falls in, which leads to a possible violation of the weak cosmic censorship conjecture. We also find that the allowed parameter range for this process is very small, which indicates that after the self-force and radiation effects are taken into account, the weak cosmic censorship conjecture could still be valid. In contrast to the case where the magnetic field is absent, the particle cannot be released at infinity to destroy the horizon. And in the case of a weak magnetic field, the releasing point becomes closer to the horizon as the magnetic field increases. This indicates that the magnetic field makes the violation of the cosmic censorship more difficult. Finally, by applying our new method to Kerr-Newman-dS (AdS) black holes, which are well-known non-asymptotically flat spacetimes, we obtain the expression of the particle's energy which matches the black hole's mass parameter.

The strong interaction at low energy scales determines the equation of state (EOS) of supranuclear matters in neutron stars (NSs). It is conjectured that the bulk dense matter may be composed of strangeons, which are quark clusters with nearly equal numbers of $u$, $d$, and $s$ quarks. To characterize the strong-repulsive interaction at short distance and the nonrelativistic nature of strangeons, a phenomenological Lennard-Jones model with two parameters is used to describe the EOS of strangeon stars (SSs). For the first time, we investigate the oscillation modes of non-rotating SSs and obtain their frequencies for various parameterizations of the EOS. We find that the properties of radial oscillations of SSs are different from those of NSs, especially for stars with relatively low central energy densities. Moreover, we calculate the $f$-mode frequency of nonradial oscillations of SSs within the relativistic Cowling approximation. The frequencies of the $f$-mode of SSs are found to be in the range from $6.7\,$kHz to $ 8.7\,\rm{kHz}$. Finally, we study the universal relations between the $f$-mode frequency and global properties of SSs, such as the compactness and the tidal deformability. The results we obtained are relevant to pulsar timing and gravitational waves, and will help to probe NSs' EOSs and infer nonperturbative behaviours in quantum chromodynamics.

Based on the GW dispersion relation raised in [1], we investigate the possible reflection of gravitational wave (GW) by superfluidity (SF) in the neutron star, provided its high density and dissipationless properties. Following this scenario, an experimental proposal is raised to probe the expected SF in neutron star by means of GW detection. Two types of binary systems are considered, neutron star-black hole and binary neutron star systems, with weak gravitational field condition imposed. Non-negligible modulation on the total signal caused by the GW reflection is found, which contributes amplitude and phase variations distinguishable from the primitive sine signal. Furthermore, we show that it is possible for such modulations to be detected by the Cosmic Explorer and Einstein Telescope at $100\,\mbox{Mpc}$. Identification of those signals can evince the existence of the long-sought SF in neutron stars as well as the exotic superfluidity-induced GW reflection.

The class of scalar-tensor theories with the scalar field coupling to the Gauss-Bonnet invariant has drawn great interest since solutions of spontaneous scalarization were found for black holes in these theories. We contribute to the existing literature a detailed study of the spontaneously scalarized neutron stars (NSs) in a typical theory where the coupling function of the scalar field takes the quadratic form and the scalar field is massive. The investigation here includes the spherical solutions of the NSs as well as their perturbative properties, namely the tidal deformability and the moment of inertia, treated in a unified and extendable way under the framework of spherical decomposition. We find that while the mass, the radius, and the moment of inertia of the spontaneously scalarized NSs show very moderate deviations from those of the NSs in general relativity (GR), the tidal deformability exhibits significant differences between the solutions in GR and the solutions of spontaneous scalarization for certain values of the parameters in the scalar-Gauss-Bonnet theory. As a result, the celebrated universal relation between the moment of inertia and the tidal deformability of neutron stars breaks down. With the mass and the tidal deformability of NSs attainable in the gravitational waves from binary NS mergers, the radius measurable using the X-ray satellites, and the moment of inertia accessible via the high-precision pulsar timing techniques, future multi-messenger observations can be contrasted with the theoretical results and provide us necessary information for building up theories beyond GR.

The strong interactions at low energy scales determine the state of the supranuclear matter in the pulsar-like compact objects. It is proposed that the bulk strong matter could be composed of strangeons, which are quark clusters with a nearly equal number of three light-flavor quarks. In this work, to characterize the strong-repulsive interactions at short distances and the non-relativistic nature of the strangeons, the Lennard-Jones model is used to describe the equation of state (EoS) of strangeon stars (SSs). We investigate the static, the slowly rotating, and the tidally deformed SSs in detail. The corrections resulted from the finite surface densities are considered crucially in the perturbative approaches. We also study the universal relations between the moments of inertia, the tidal deformabilities, and the quadrupole moments. Those results are ready to be used for various purposes in astrophysics, and possible constraints from contemporary observations on the parameter space of the Lennard-Jones model are discussed. Future observations of the pulsars' radio signals, the X-ray emissions from the hot spots on the surface of the stars, and the gravitational waves (GWs) from binary mergers can give tighter constraints or even verify or falsify the existence of SSs.

Neutron stars (NSs) in scalar-tensor theories of gravitation with the phenomenon of spontaneous scalarization can develop significant deviations from general relativity. Cases with a massless scalar were studied widely. Here we compare the NS scalarizations in the Damour--Esposito-Farèse theory, the Mendes-Ortiz theory, and the $\xi$-theory with a massive scalar field. Numerical solutions for slowly rotating NSs are obtained. They are used to construct the X-ray pulse profiles of a pair of extended hot spots on the surface of NSs. We also calculate the tidal deformability for NSs with spontaneous scalarization which is done for the first time with a massive scalar field. We show the universal relation between the moment of inertia and the tidal deformability. The X-ray pulse profiles, the tidal deformability, and the universal relation may help to constrain the massive scalar-tensor theories in X-ray and gravitational-wave observations of NSs, including the Neutron star Interior Composition Explorer (NICER) satellite, Square Kilometre Array (SKA) telescope, and LIGO/Virgo/KAGRA laser interferometers.

The $T\bar{T}$ deformed 2D CFTs correspond to AdS$_3$ gravity with Dirichlet boundary condition at finite cutoff or equivalently a mixed boundary condition at spatial infinity. In this work, we use the latter perspective and Chern-Simons formalism of AdS$_3$ gravity to construct the surface charges and associated algebra in $T\bar{T}$ deformed theories. Starting from the Bañados geometry, we obtain the Chern-Simons gauge fields for the $T\bar{T}$ deformed geometry, which are parametrized by two independent charges. With help of the mixed boundary condition, the residual gauge symmetries of the deformed gauge fields and the associated surface charges were obtained respectively. The charge algebra turns out to be a non-linear deformed Virasoro algebra, which was obtained in different way by applying the cutoff perspective. Finally, we propose a way to construct the time-independent charges from these surface charges and they satisfy the field-dependent Virasoro algebra.

Atom-interferometer gravitational-wave (GW) observatory, as a new design of ground-based GW detector for the near future, is sensitive at a relatively low frequency for GW observations. Taking the proposed atom interferometer Zhaoshan Long-baseline Atom Interferometer Gravitation Antenna (ZAIGA), and its illustrative upgrade (Z+) as examples, we investigate how the atom interferometer will complement ground-based laser interferometers in testing the gravitational dipole radiation from binary neutron star (BNS) mergers. A test of such kind is important for a better understanding of the strong equivalence principle laying at the heart of Einstein's general relativity. To obtain a statistically sound result, we sample BNS systems according to their merger rate and population, from which we study the expected bounds on the parameterized dipole radiation parameter $B$. Extracting BNS parameters and the dipole radiation from the combination of ground-based laser interferometers and the atom-interferometer ZAIGA/Z+, we are entitled to obtain tighter bounds on $B$ by a few times to a few orders of magnitude, compared to ground-based laser interferometers alone, ultimately reaching the levels of $|B| \lesssim 10^{-9}$ (with ZAIGA) and $|B| \lesssim 10^{-10}$ (with Z+).

We study effects of Lorentz-invariance violation on the rotation of neutron stars (NSs) in the minimal gravitational Standard-Model Extension framework, and calculate the quadrupole radiation generated by them. Aiming at testing Lorentz invariance with observations of continuous gravitational waves (GWs) from rotating NSs in the future, we compare the GW spectra of a rotating ellipsoidal NS under Lorentz-violating gravity with those of a Lorentz-invariant one. The former are found to possess frequency components higher than the second harmonic, which does not happen for the latter, indicating those higher frequency components to be potential signatures of Lorentz violation in continuous GW spectra of rotating NSs.

In this work we consider AdS$_3$ gravitational theory with certain mixed boundary conditions at spatial infinity. Using the Chern-Simons formalism of AdS$_3$ gravity, we find that these boundary conditions lead to non-trivial boundary terms, which, in turn, produce exactly the spectrum of the $T\bar{T}/J\bar{T}$-deformed CFTs. We then follow the procedure for constructing asymptotic boundary dynamics of AdS$_3$ to derive the constrained $T\bar{T}$-deformed WZW model from Chern-Simons gravity. The resulting theory turns out to be the $T\bar{T}$-deformed Alekseev-Shatashvili action after disentangling the constraints. Furthermore, by adding a $U(1)$ gauge field associated to the current $J$, we obtain one type of the $J\bar T$-deformed WZW model, and show that its action can be constructed from the gravity side. These results provide a check on the correspondence between the $T\bar{T}/J\bar{T}$-deformed CFTs and the deformations of boundary conditions of AdS$_3$, the latter of which may be regarded as coordinate transformations.

The Standard-Model Extension (SME) is an effective-field-theoretic framework that catalogs all Lorentz-violating field operators. The anisotropic correction from the minimal gravitational SME to Newtonian gravitational energy for spheroids is studied, and the rotation of rigid spheroids is solved with perturbation method and numerical approach. The well-known forced precession solution given by Nordtvedt in the parameterized post-Newtonian formalism is recovered and applied to two observed solitary millisecond pulsars to set bounds on the coefficients for Lorentz violation in the SME framework. A different solution, which describes the rotation of an otherwise free-precessing star in the presence of Lorentz violation, is found, and its consequences on pulsar signals and continuous gravitational waves (GWs) emitted by neutron stars (NSs) are investigated. The study provides new possible tests of Lorentz violation once free-precessing NSs are firmly identified in the future.

A deformed neutron star (NS) will precess if the instantaneous spin axis and the angular momentum are not aligned. Such a precession can produce continuous gravitational waves (GWs) and modulate electromagnetic pulse signals of pulsars. In this contribution we extend our previous work in a more convenient parameterization. We treat NSs as rigid triaxial bodies and give analytical solutions for angular velocities and Euler angles. We summarize the general GW waveforms from freely precessing triaxial NSs and use Taylor expansions to obtain waveforms with a small wobble angle. For pulsar signals, we adopt a simple cone model to study the timing residuals and pulse profile modulations. In reality, the electromagnetic torque acts on pulsars and affects the precession behavior. Thereof, as an additional extension to our previous work, we consider a vacuum torque and display an illustrative example for the residuals of body-frame angular velocities. Detailed investigations concerning continuous GWs and modulated pulsar signals from forced precession of triaixal NSs will be given in future studies.

The new version of the gedanken experiments proposed by Sorce and Wald are designed to test the validity of the weak cosmic censorship conjecture (WCCC) by overspinning or overcharging the Kerr-Newman black hole in Einstein-Maxwell gravity. Following their setup, in this paper, we investigate the WCCC in the higher-dimensional charged black hole with a nonlinear electrodynamics source. We derive the first and seconder order perturbation inequalities of the charged collision matter based on the Iyer-Wald formalism as well as the null energy conditions, and show that they share the similar form as that in Einstein-Maxwell gravity. As a result, we find that the static higher-dimensional nonlinear electrodynamics (HDNL) black holes cannot be overcharged after considering these two inequalities. Our result might indicate the validity of WCCC for more general HNDL and related systems.

Neutron stars (NSs) in scalar-tensor (ST) theories of gravitation can acquire scalar charges and generate distinct spacetimes from those in General Relativity (GR) through the celebrated phenomenon of spontaneous scalarization. Taking on an ST theory with the mass term of the scalar field, we determine the theory parameter space for spontaneous scalarization by investigating the linearized scalar field equation. Then the full numerical solutions for slowly rotating NSs are obtained and studied in great detail. The resulted spacetime is used to calculate test-particle geodesics. The lightlike geodesics are used to construct the profile of X-ray radiation from a pair of hot spots on the surface of scalarized NSs, which potentially can be compared with the data from the Neutron star Interior Composition Explorer (NICER) mission for testing the ST theory.

The basic equations of the thermodynamic system give the relationship between the internal energy, entropy and volume of two neighboring equilibrium states. By using the functional relationship between the state parameters in the basic equation, we give the differential equation satisfied by the entropy of spacetime. We can obtain the expression of the entropy by solving the differential equationy. This expression is the sum of entropy corresponding to the two event horizons and the interaction term. The interaction term is a function of the ratio of the locations of the black hole horizon and the cosmological horizon. The entropic force, which is strikingly similar to the Lennard-Jones force between particles, varies with the ratio of the two event horizons. The discovery of this phenomenon makes us realize that the entropic force between the two horizons may be one of the candidates to promote the expansion of the universe.

The shape of a neutron star (NS) is closely linked to its internal structure and the equation of state of supranuclear matters. A rapidly rotating, asymmetric NS in the Milky Way undergoes free precession, making it a potential source for multimessenger observation. The free precession could manifest in (i) the spectra of continuous gravitational waves (GWs) in the kilohertz band for ground-based GW detectors, and (ii) the timing behavior and pulse-profile characteristics if the NS is monitored as a pulsar with radio and/or X-ray telescopes. We extend previous work and investigate in great detail the free precession of a triaxially deformed NS with analytical and numerical approaches. In particular, its associated continuous GWs and pulse signals are derived. Explicit examples are illustrated for the continuous GWs, as well as timing residuals in both time and frequency domains. These results are ready to be used for future multimessenger observation of triaxially-deformed freely-precessing NSs, in order to extract scientific implication as much as possible.

The Advanced LIGO and Virgo detectors opened a new era to study black holes (BHs) in our Universe. A population of stellar-mass binary BHs (BBHs) are discovered to be heavier than previously expected. These heavy BBHs provide us an opportunity to achieve multiband observation with ground-based and space-based gravitational-wave (GW) detectors. In this work, we use BBHs discovered by the LIGO/Virgo Collaboration as indubitable examples, and study in great detail the prospects for multiband observation with GW detectors in the near future. We apply the Fisher matrix to spinning, non-precessing inspiral-merger-ringdown waveforms, while taking the motion of space-based GW detectors fully into account. Our analysis shows that, detectors with decihertz sensitivity are expected to log stellar-mass BBH signals with very large signal-to-noise ratio, and provide accurate parameter estimation, including the sky location and time to coalescence. Furthermore, the combination of multiple detectors will achieve unprecedented measurement of BBH properties. As an explicit example, we present the multiband sensitivity to the generic dipole radiation for BHs, which is vastly important for the equivalence principle in the foundation of gravitation, in particular for those theories that predict curvature-induced scalarization of BHs.

We investigate the strong gravitational lensing of spherically symmetric black holes in the novel Einstein-Gauss-Bonnet(EGB) gravity surrounded by unmagnetised plasma medium. The deflection angle in the strong deflection limit in EGB spacetime with homogeneous plasma is derived. We find that both the coupling constant $\alpha$ in the novel EGB gravity and the presence of plasma can affect the radius of photon sphere, strong field limit coefficient and other lensing observables significantly. While plasma has little effect on the angular image separation and the relative magnifications as $\alpha/M^2\to -8$ and $\alpha/M^2\to 1$, respectively.

Recently, Li and Bambi proposed a hypothesis that the event horizon of a regular black hole can be destroyed because these objects have no gravitational singularity and therefore they are not protected by the weak cosmic censorship conjecture (WCCC). In this paper, to test their hypothesis, we perform the new version of the gedanken experiments proposed by Sorce and Wald to overcharge a near extremal static electrically regular black hole. After introducing the stability condition of the spacetime and the null energy condition of matter fields, we derive the first-order and second-order perturbation inequalities of the perturbation matter fields based on the Iyer-Wald formalism. As a result, we find that these regular black holes cannot be destroyed under the second-order approximation after these two perturbation inequalities are taken into account, even though they are not protected by the WCCC. Our results indicate that there might be some deeper mechanisms to protect the event horizon of the black holes.

We propose a symmetry of $T\bar T$ deformed 2D CFT, which preserves the trace relation. The deformed conformal killing equation is obtained. Once we consider the background metric runs with the deformation parameter $\mu$, the deformation contributes an additional term in conformal killing equation, which plays the role of renormalization group flow of metric. The conformal symmetry coincides with the fixed point. On the gravity side, this deformed conformal killing equation can be described by a new boundary condition of AdS$_3$. In addition, based on the deformed conformal killing equation, we derive that the stress tensor of the deformed CFT equals to Brown-York's quasilocal stress tensor on a finite boundary with a counterterm. For a specific example, BTZ black hole, we get $T\bar T$ deformed conformal killing vectors and the associated conserved charges are also studied.

It is recently shown that, besides the Schwarzshcild black hole solution, there exist also scalarized black hole solutions in some Einstein-scalar-Gauss-Bonnet theories. In this paper, we construct analytical expressions for the metric functions and scalar field configurations for these scalarized black hole solutions approximately by employing the continued fraction parametrization method and investigate their thermodynamic stability. It is found that the horizon entropy of a scalarized black hole is always smaller than that of a Schwarzschild black hole, which indicates that these scalarized black holes may decay to Schwarzschild black holes by emission of scalar waves. This fact also implies the possibility to extract the energy of scalar charges.

We study the scalar perturbation on the background of a Kerr black hole in the dynamical Chern-Simons modified gravity with a quadratic coupling between the scalar field and Chern-Simons term. In particular, the late-time tails of scalar perturbations are investigated numerically in time domain by using the hyperboloidal foliation method. It is found that the Kerr black hole becomes unstable under linear perturbations in a certain region of the parameter space, which depends on the harmonic azimuthal index $m$ of the perturbation's mode. This may indicate that some Kerr black holes in this theory will get spontaneously scalarized into a non-Kerr black hole.

Relic gravitational waves (RGWs) , a background originated during inflation, would give imprints on the pulsar timing residuals. This makes RGWs be one of important sources for detection using the method of pulsar timing. In this paper, we discuss the effects of RGWs on the single pulsar timing, and give quantitively the timing residuals caused by RGWs with different model parameters. In principle, if the RGWs are strong enough today, they can be detected by timing a single millisecond pulsar with high precision after the intrinsic red noise in pulsar timing residuals were understood, even though observing simultaneously multiple millisecond pulsars is a more powerful technique in extracting gravitational wave signals. We corrected the normalization of RGWs using observations of the cosmic microwave background (CMB), which leads to the amplitudes of RGWs being reduced by two orders of magnitude or so compared to our previous works. We made new constraints on RGWs using the recent observations from the Parkes Pulsar Timing Array, employing the tensor-to-scalar ratio $r=0.2$ due to the tensor-type polarization observations of CMB by BICEP2 as a referenced value even though it has been denied. Moreover, the constraints on RGWs from CMB and BBN (Big Bang nucleosynthesis) will also be discussed for comparison.

Type Ia supernovae luminosities can be corrected to render them useful as standard candles able to probe the expansion history of the universe. This technique was successful applied to discover the present acceleration of the universe. As the number of SNe Ia observed at high redshift increases and analysis techniques are perfected, people aim to use this technique to probe the equation of state of the dark energy. Nevertheless, the nature of SNe Ia progenitors remains controversial and concerns persist about possible evolution effects that may be larger and harder to characterize than the more obvious statistical uncertainties.

The pulsar timing residuals induced by gravitational waves from non-evolving single binary sources are affected by many parameters related to the relative positions of the pulsar and the gravitational wave sources. We will fully analyze the effects due to different parameters one by one. The standard deviations of the timing residuals will be calculated with a variable parameter fixing a set of other parameters. The orbits of the binary sources will be generally assumed to be elliptical. The influences of different eccentricities on the pulsar timing residuals will also studied in detail. We find that effects of the related parameters are quite different, and some of them present certain regularities.

The pulsar timing residuals induced by gravitational waves from non-evolving single binary sources with general elliptical orbits will be analyzed. For different orbital eccentricities, the timing residuals present different properties. The standard deviations of the timing residuals induced by a fixed gravitational wave source will be calculated for different values of the eccentricity. We will also analyze the timing residuals of PSR J0437-4715 induced by one of the best known single gravitational wave sources, the supermassive black hole binary in the blazar OJ287.

Three-dimensional neutral hydrogen mapping using the redshifted 21 cm line has recently emerged as a promising cosmological probe. Within the framework of slow-roll reconstruction, we analyze how well the inflationary potential can be reconstructed by combining data from 21 cm experiments and cosmic microwave background data from the Planck satellite. We consider inflationary models classified according to the amplitude of their tensor component, and show that 21 cm measurements can significantly improve constraints on the slow-roll parameters and determine the shape of the inflationary potential.

We test if the latest Gold set of 182 SNIa or the combined "Platinum" set of 192 SNIa from the ESSENCE and Gold sets, in conjunction with the CMB shift parameter show a preference between the LambdaCDM model, three wCDM models, and the DGP model of modified gravity as an explanation for the current accelerating phase of the universe's expansion. We consider flat wCDM models with an equation of state w(a) that is (i) constant with scale factor $a$, (ii) varies as w(a)=w_0+w_a(1-a) for redshifts probed by supernovae but is fixed at -1 at earlier epochs and (iii) varies as w_0+w_a(1-a) since recombination. We find that all five models explain the data with comparable success.

We ask if the conventional variable separation techniques in the studying of standard cosmology and the collapsing of extremely dense stars introduce Newton's absolute space-time concepts. If this is the case, then a completely relative cosmology is needed. We build the basic frame-works for such a cosmology and illustrate that, the observed luminosity-distance v.s. red-shift relations of supernovaes can be explained naturally even without any conception of dark energies.

We point out that $\Lambda$CDM cosmology has an ignored assumption. That is, the $\Lambda$ component of the universe moves synchronously with ordinary matters on Hubble scales. If cosmological constant is vacuum energy, this assumption may be very difficult to be understood. We then propose a new mechanism which can explain the accelerating recession of super-novaes. That is, considering the pressures originating from the random moving (including Hubble recession) of galaxy clusters and galaxies. We provide an new analytical solution of Einstein equation which may describe a universe whose pressures originating from the random moving of galaxy clusters and galaxies are considered.

We generalize the work of Deser and Levin on the unified description of Hawking radiation and Unruh effect to general stationary motions in spherically symmetric black holes. We have also matched the chemical potential term of the thermal spectrum of the two sides for uncharged black holes.

In numerical calculations of the primordial power spectrum of perturbations produced during inflation, for very little wavenumber $k$s, to implement the initial conditions required of the perturbation mode functions consistently, we must let the universe experience more e-foldings of inflation than that required of it to solve the horizon, flatness and other pre-inflation problems. However, if the number of e-foldings of inflation has an upper bound, then for perturbations at scales greater than some critical value, the initial conditions required of the mode functions cannot be implemented physically. Because at the inflation beginning point, these perturbation modes lie outside the horizon. We propose that such perturbations do not contribute to the Cosmological Microwave Background Anisotropy (CMBA). Under this proposition, the exceptional lowness of the observed little $l$ muli-poles of CMBA is reproduced numerically. In Linde's $\phi^2$ model, the upper bound on the number of e-foldings of inflation is determined to be 65 approximately.