Emerging hyperbolic spaces and some considerations in \(AdS\) cosmology. (English) Zbl 1536.53149
Summary: Recently, PNDP-manifolds have been introduced, and these have shown to be useful in applicative aspects especially in the field of cosmology, introducing a new geometric/topological approach to the concept of “emerging space”. However, the applications considered so far concern only trivial and flat PNDP-manifolds. Therefore, we show the existence of non-Ricci-flat solutions for PNDP-manifolds with positive “virtual” dimension which have hyperbolic \(\widetilde{B}\)-manifold. Based on this, we have advanced an applicative hypothesis, accompanied by some open considerations, in the context of \(AdS\) cosmology.
MSC:
| 53C80 | Applications of global differential geometry to the sciences |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 53Z05 | Applications of differential geometry to physics |
Keywords:
Einstein warped product manifolds; virtual dimension; hyperbolic manifolds; anti de Sitter (AdS) spacetimeReferences:
| [1] | Pigazzini, A., Özel, C., Linker, P. and Jafari, S., On PNDP-manifold, Poincare J. Anal. Appl.8(1(I)) (2021) 111-125. · Zbl 1490.53066 |
| [2] | Pincak, R., Pigazzini, A., Jafari, S. and Özel, C., The “emerging” reality from “hidden” spaces, Universe7(3) (2021) 75. |
| [3] | Pincak, R., Pigazzini, A., Jafari, S., Özel, C. and DeBenedictis, A., A topological approach for emerging D-branes and its implications for gravity, Int. J. Geom. Methods Mod. Phys.18(14) (2021) 2150227. · Zbl 1520.53039 |
| [4] | R. Abbasi et al., Search for quantum gravity using astrophysical neutrino flavour with icecube, preprint (2021), arXiv:2111.04654v1. |
| [5] | IceCube Collaboration, Neutrino interferometry for high-precision tests of Lorentz symmetry with icecube, preprint (2017), arXiv:1709.03434v3. |
| [6] | Pincak, R. and Kanjamapornkul, K., GARCH(1,1) model of the financial market with the Minkowski metric, Z. Naturforsch.73(8) (2018) 669-684. |
| [7] | Joyce, D., Kuranishis and Symplectic Geometry, Vol. II (The Mathematical Institute, Radcliffe Observatory Quarter, Oxford, 2017). |
| [8] | Margolis, H. R., Spectra and the Steenrod Algebra (North-Holland, Amsterdam, 1983). · Zbl 0552.55002 |
| [9] | Wolcott, L. and McTernan, E., Imagining negative-dimensional space, inProc. Bridges 2012: Mathematics, Music, Art, Architecture, Culture (Tessellations Publishing, 2012), pp. 637-642. |
| [10] | Hughston, L. P., The twistor particle programme, Surveys in High Energy Physics, Vol. 1, Issue 4 (Taylor \(\operatorname{\&\#38;}\) Francis, 1980), pp. 313-332. |
| [11] | Claus, P., Rahmfeld, J. and Zunger, Y., A simple particle action from a twistor parametrization of AdS5, Phys. Lett. B466 (1999) 181. · Zbl 0987.81556 |
| [12] | Cederwall, M., Geometric construction of AdS twistors, Phys. Lett. B483 (2000) 257. · Zbl 1006.83029 |
| [13] | Cederwall, M., AdS twistors for higher spin theory, AIP Conf. Proc.767 (2005) 96. · Zbl 1096.81015 |
| [14] | Arvanitakis, A. S., Barns-Graham, A. E. and Townsend, P. K., Twistor description of spinning particles in AdS, J. High Energy Phys.59 (2018) 59. · Zbl 1384.83031 |
| [15] | Boskoff, W. G. and Capozziello, S., Recovering the cosmological constant from affine geometry, Int. J. Geom. Methods Mod. Phys.16(10) (2019) 1950161. · Zbl 07801953 |
| [16] | Kolekar, K. S. and Narayan, K., \(Ad S_2\) dilaton gravity from reductions of some nonrelativistic theories, Phys. Rev. D98 (2018) 046012. |
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.
