×

General relativity from causality. (English) Zbl 1382.83012

Summary: We study large families of theories of interacting spin 2 particles from the point of view of causality. Although it is often stated that there is a unique Lorentz invariant effective theory of massless spin 2, namely general relativity, other theories that utilize higher derivative interactions do in fact exist. These theories are distinct from general relativity, as they permit any number of species of spin 2 particles, are described by a much larger set of parameters, and are not constrained to satisfy the equivalence principle. We consider the leading spin 2 couplings to scalars, fermions, and vectors, and systematically study signal propagation in all these other families of theories. We find that most interactions directly lead to superluminal propagation of either a spin 2 particle or a matter particle, and interactions that are subluminal generate other interactions that are superluminal. Hence, such theories of interacting multiple spin 2 species have superluminality, and by extension, acausality. This is radically different to the special case of general relativity with a single species of minimally coupled spin 2, which leads to subluminal propagation from sources satisfying the null energy condition. This pathology persists even if the spin 2 field is massive. We compare these findings to the analogous case of spin 1 theories, where higher derivative interactions can be causal. This makes the spin 2 case very special, and suggests that multiple species of spin 2 is forbidden, leading us to general relativity as essentially the unique internally consistent effective theory of spin 2.

MSC:

83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
03A05 Philosophical and critical aspects of logic and foundations
06B35 Continuous lattices and posets, applications
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
70H40 Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C40 Gravitational energy and conservation laws; groups of motions
81T10 Model quantum field theories

References:

[1] M.P. Hertzberg, Gravitation, causality and quantum consistency, arXiv:1610.03065 [INSPIRE]. · Zbl 1414.81024
[2] R.M. Wald, Spin-2 fields and general covariance, Phys. Rev.D 33 (1986) 3613 [INSPIRE].
[3] D. Bai and Y.-H. Xing, Special gravity as alternatives for interacting massless gravitons, arXiv:1610.00241 [INSPIRE]. · Zbl 1311.83042
[4] D. Bai and Y.-H. Xing, On the uniqueness of ghost-free special gravity, arXiv:1702.05756 [INSPIRE]. · Zbl 1377.83071
[5] N. Boulanger, T. Damour, L. Gualtieri and M. Henneaux, Inconsistency of interacting, multigraviton theories, Nucl. Phys.B 597 (2001) 127 [hep-th/0007220] [INSPIRE]. · Zbl 0972.83051 · doi:10.1016/S0550-3213(00)00718-5
[6] P. Benincasa and F. Cachazo, Consistency conditions on the S-matrix of massless particles, arXiv:0705.4305 [INSPIRE].
[7] S. Deser, Selfinteraction and gauge invariance, Gen. Rel. Grav.1 (1970) 9 [gr-qc/0411023] [INSPIRE]. · Zbl 1263.81275
[8] C. Deffayet, X. Gao, D.A. Steer and G. Zahariade, From k-essence to generalised Galileons, Phys. Rev.D 84 (2011) 064039 [arXiv:1103.3260] [INSPIRE].
[9] S. Ohashi, N. Tanahashi, T. Kobayashi and M. Yamaguchi, The most general second-order field equations of bi-scalar-tensor theory in four dimensions, JHEP07 (2015) 008 [arXiv:1505.06029] [INSPIRE]. · Zbl 1388.83937 · doi:10.1007/JHEP07(2015)008
[10] Y. Ohkuwa, Effect of a background gravitational field on the velocity of neutrinos, Prog. Theor. Phys.65 (1981) 1058 [INSPIRE]. · doi:10.1143/PTP.65.1058
[11] I.T. Drummond and S.J. Hathrell, QED vacuum polarization in a background gravitational field and its effect on the velocity of photons, Phys. Rev.D 22 (1980) 343 [INSPIRE].
[12] G.M. Shore, Quantum gravitational optics, Contemp. Phys.44 (2003) 503 [gr-qc/0304059] [INSPIRE].
[13] F.A.E. Pirani, Noncausal behavior of classical tachyons, Phys. Rev.D 1 (1970) 3224 [INSPIRE].
[14] T.J. Hollowood and G.M. Shore, Causality violation, gravitational shockwaves and UV completion, JHEP03 (2016) 129 [arXiv:1512.04952] [INSPIRE]. · doi:10.1007/JHEP03(2016)129
[15] G. Goon and K. Hinterbichler, Superluminality, black holes and EFT, JHEP02 (2017) 134 [arXiv:1609.00723] [INSPIRE]. · Zbl 1377.83044 · doi:10.1007/JHEP02(2017)134
[16] Y. Choquet-Bruhat, The Cauchy problem for stringy gravity, J. Math. Phys.29 (1988) 1891 [INSPIRE]. · Zbl 0658.53078 · doi:10.1063/1.527841
[17] K. Izumi, Causal structures in Gauss-Bonnet gravity, Phys. Rev.D 90 (2014) 044037 [arXiv:1406.0677] [INSPIRE].
[18] H. Reall, N. Tanahashi and B. Way, Causality and hyperbolicity of Lovelock theories, Class. Quant. Grav.31 (2014) 205005 [arXiv:1406.3379] [INSPIRE]. · Zbl 1304.83013 · doi:10.1088/0264-9381/31/20/205005
[19] B.A. Campbell, M.J. Duncan, N. Kaloper and K.A. Olive, Gravitational dynamics with Lorentz Chern-Simons terms, Nucl. Phys.B 351 (1991) 778 [INSPIRE]. · doi:10.1016/S0550-3213(05)80045-8
[20] R. Jackiw and S.Y. Pi, Chern-Simons modification of general relativity, Phys. Rev.D 68 (2003) 104012 [gr-qc/0308071] [INSPIRE].
[21] S. Dyda, E.E. Flanagan and M. Kamionkowski, Vacuum instability in Chern-Simons gravity, Phys. Rev.D 86 (2012) 124031 [arXiv:1208.4871] [INSPIRE].
[22] X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality constraints on corrections to the graviton three-point coupling, JHEP02 (2016) 020 [arXiv:1407.5597] [INSPIRE]. · Zbl 1388.83093 · doi:10.1007/JHEP02(2016)020
[23] A. Gruzinov and M. Kleban, Causality constrains higher curvature corrections to gravity, Class. Quant. Grav.24 (2007) 3521 [hep-th/0612015] [INSPIRE]. · Zbl 1120.83037 · doi:10.1088/0264-9381/24/13/N02
[24] B. Bellazzini, C. Cheung and G.N. Remmen, Quantum gravity constraints from unitarity and analyticity, Phys. Rev.D 93 (2016) 064076 [arXiv:1509.00851] [INSPIRE].
[25] M. Visser, B. Bassett and S. Liberati, Superluminal censorship, Nucl. Phys. Proc. Suppl.88 (2000) 267 [gr-qc/9810026] [INSPIRE]. · Zbl 1273.83125
[26] F.J. Tipler, Singularities and causality violation, Annals Phys.108 (1977) 1 [INSPIRE]. · Zbl 0369.53057 · doi:10.1016/0003-4916(77)90348-7
[27] K.D. Olum, Superluminal travel requires negative energies, Phys. Rev. Lett.81 (1998) 3567 [gr-qc/9805003] [INSPIRE]. · Zbl 0949.83008
[28] L.H. Ford and T.A. Roman, Averaged energy conditions and quantum inequalities, Phys. Rev.D 51 (1995) 4277 [gr-qc/9410043] [INSPIRE]. · Zbl 1304.83013
[29] M.S. Morris, K.S. Thorne and U. Yurtsever, Wormholes, time machines and the weak energy condition, Phys. Rev. Lett.61 (1988) 1446 [INSPIRE]. · doi:10.1103/PhysRevLett.61.1446
[30] R. Penrose, A remarkable property of plane waves in general relativity, Rev. Mod. Phys.37 (1965) 215 [INSPIRE]. · Zbl 0125.21101 · doi:10.1103/RevModPhys.37.215
[31] G.M. Shore, Constructing time machines, Int. J. Mod. Phys.A 18 (2003) 4169 [gr-qc/0210048] [INSPIRE]. · Zbl 1032.83004
[32] S.M. Carroll, G.B. Field and R. Jackiw, Limits on a Lorentz and parity violating modification of electrodynamics, Phys. Rev.D 41 (1990) 1231 [INSPIRE].
[33] M. Nowakowski, E.A. Paschos and J.M. Rodriguez, All electromagnetic form-factors, Eur. J. Phys.26 (2005) 545 [physics/0402058] [INSPIRE]. · Zbl 0658.53078
[34] C. Giunti and A. Studenikin, Neutrino electromagnetic properties, Phys. Atom. Nucl.72 (2009) 2089 [arXiv:0812.3646] [INSPIRE]. · Zbl 1263.81275 · doi:10.1134/S1063778809120126
[35] C. Broggini, C. Giunti and A. Studenikin, Electromagnetic properties of neutrinos, Adv. High Energy Phys.2012 (2012) 459526 [arXiv:1207.3980] [INSPIRE]. · Zbl 1263.81275 · doi:10.1155/2012/459526
[36] C. Giunti, K.A. Kouzakov, Y.-F. Li, A.V. Lokhov, A.I. Studenikin and S. Zhou, Electromagnetic neutrinos in laboratory experiments and astrophysics, Annalen Phys.528 (2016) 198 [arXiv:1506.05387] [INSPIRE]. · Zbl 1341.81048 · doi:10.1002/andp.201500211
[37] G. Velo and D. Zwanziger, Propagation and quantization of Rarita-Schwinger waves in an external electromagnetic potential, Phys. Rev.186 (1969) 1337 [INSPIRE]. · doi:10.1103/PhysRev.186.1337
[38] J.A. Madore, The characteristic surface of a classical spin-3/2 field in an Einstein-Maxwell background, Phys. Lett.B 55 (1975) 217 [INSPIRE]. · doi:10.1016/0370-2693(75)90446-3
[39] J. Madore and W. Tait, Propagation of shock waves in interacting higher spin wave equations, Commun. Math. Phys.30 (1973) 201. · doi:10.1007/BF01837358
[40] S. Deser and A. Waldron, Inconsistencies of massive charged gravitating higher spins, Nucl. Phys.B 631 (2002) 369 [hep-th/0112182] [INSPIRE]. · Zbl 0995.83023 · doi:10.1016/S0550-3213(02)00199-2
[41] R. Rahman, Helicity-1/2 mode as a probe of interactions of a massive Rarita-Schwinger field, Phys. Rev.D 87 (2013) 065030 [arXiv:1111.3366] [INSPIRE].
[42] S. Deser and A. Waldron, Acausality of massive gravity, Phys. Rev. Lett.110 (2013) 111101 [arXiv:1212.5835] [INSPIRE]. · Zbl 1311.83042 · doi:10.1103/PhysRevLett.110.111101
[43] S. Deser, M. Sandora, A. Waldron and G. Zahariade, Covariant constraints for generic massive gravity and analysis of its characteristics, Phys. Rev.D 90 (2014) 104043 [arXiv:1408.0561] [INSPIRE].
[44] G. D’Amico, G. Gabadadze, L. Hui and D. Pirtskhalava, Quasidilaton: theory and cosmology, Phys. Rev.D 87 (2013) 064037 [arXiv:1206.4253] [INSPIRE]. · Zbl 1277.83108
[45] C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of massive gravity, Phys. Rev. Lett.106 (2011) 231101 [arXiv:1011.1232] [INSPIRE]. · doi:10.1103/PhysRevLett.106.231101
[46] A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion, JHEP10 (2006) 014 [hep-th/0602178] [INSPIRE]. · doi:10.1088/1126-6708/2006/10/014
[47] C. Cheung, K. Kampf, J. Novotny, C.-H. Shen and J. Trnka, A periodic table of effective field theories, JHEP02 (2017) 020 [arXiv:1611.03137] [INSPIRE]. · Zbl 1377.81123 · doi:10.1007/JHEP02(2017)020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.