Abstract
We consider a hybrid bimetric model where, in addition to the ordinary metric tensor that determines geometry, an informational metric is introduced to describe the reference frame of an observer. We note that the local information metric being Minkowskian explains one of the key aspects of the Einstein equivalence principle. Our approach has the potential to justify the three-dimensional nature of physical space and address the gravitational energy puzzle. Furthermore, it appears to be free of ghost instabilities in the matter sector, as the second metric tensor couples exclusively to the observer and is non-dynamical.
Similar content being viewed by others
Data availability
There are no data associated with this article.
References
Will, C.M.: The confrontation between general relativity and experiment. Living Rev. Rel. 17, 4 (2014). https://doi.org/10.12942/lrr-2014-4. [ar**v: 1403.7377 [gr-qc]]
Hassan, S.F., Rosen, R.A.: Bimetric gravity from ghost-free massive gravity. JHEP 02, 126 (2012). https://doi.org/10.1007/JHEP02(2012)126. [ar**v: 1109.3515 [hep-th]]
Aoki, K., Maeda, K. i.: Dark matter in ghost-free bigravity theory: From a galaxy scale to the universe. Phys. Rev. D 90 (2014) 124089, https://doi.org/10.1103/PhysRevD.90.124089[ar**v: 1409.0202 [gr-qc]]
Babichev, E., et al.: Bigravitational origin of dark matter. Phys. Rev. D 94, 084055 (2016). https://doi.org/10.1103/PhysRevD.94.084055. [ar**v: 1604.08564 [hep-ph]]
Kolb, E.W., Ling, S., Long, A.J., Rosen, R.A.: Cosmological gravitational particle production of massive spin-2 particles. JHEP 05, 181 (2023). https://doi.org/10.1007/JHEP05(2023)181. [ar**v: 2302.04390 [astro-ph.CO]]
Gialamas, I.D., Tamvakis, K.: Bimetric-affine quadratic gravity. Phys. Rev. D 107, 104012 (2023). https://doi.org/10.1103/PhysRevD.107.104012. [ar**v: 2303.11353 [gr-qc]]
Volkov, M.S.: Hairy black holes in the ghost-free bigravity theory. Phys. Rev. D 85, 124043 (2012). https://doi.org/10.1103/PhysRevD.85.124043. [ar**v: 1202.6682 [hep-th]]
Gialamas, I. D., Tamvakis, K.: On the bimetric Starobinsky model. [ar**v: 2307.05673 [gr-qc]]
Schmidt-May, A., von Strauss, M.: Recent developments in bimetric theory. J. Phys. A 49, 183001 (2016). https://doi.org/10.1088/1751-8113/49/18/183001. [ar**v: 1512.00021 [hep-th]]
Clifton, T., Ferreira, P.G., Padilla, A., Skordis, C.: Modified gravity and cosmology. Phys. Rept. 513, 1 (2012). https://doi.org/10.1016/j.physrep.2012.01.001. [ar**v: 1106.2476 [astro-ph.CO]]
Koyama, K.: Cosmological tests of modified gravity. Rept. Prog. Phys. 79, 046902 (2016). https://doi.org/10.1088/0034-4885/79/4/046902. [ar**v: 1504.04623 [astro-ph.CO]]
K. Sundermeyer, Symmetries in Fundamental Physics. In: Fundamental Theories of Physics, Vol. 176, Springer, NY (2014) https://doi.org/10.1007/978-94-007-7642-5.
C. Rovelli, Quantum Gravity, Cambridge Monographs on Mathematical Physics (Cambridge University Press, NY 2004) https://doi.org/10.1017/CBO9780511755804.
Frewer, M.: More clarity on the concept of material frame-indifference in classical continuum mechanics. Acta Mech. 202, 213 (2009). https://doi.org/10.1007/s00707-008-0028-4
Torretti, R.: Relativity and Geometry. Dover, NY (1996)
Macdonald, A.: Einstein’s hole argument. Am. J. Phys. 69, 223 (2001). https://doi.org/10.1119/1.1308265
Gogberashvili, M.: Algebraical entropy and arrow of time. Entropy 24, 1522 (2022). https://doi.org/10.3390/e24111522. [ar**v: 2211.00501 [physics.gen-ph]]
Susskind, L., Lindesay, J.: An Introduction to Black Holes, Information, and the String Theory Revolution: The Holographic Universe. World Scientific, Singapore (2005)
Poincaré, H.: Dernières pensées. Flammarion, Paris (1913)
Herrera, L.: Landauer principle and general relativity. Entropy 22, 340 (2020). https://doi.org/10.3390/e22030340. [ar**v: 2003.07436 [gr-qc]]
Ilgin, I., Yang, I.S.: Energy carries information. Int. J. Mod. Phys. A 29, 1450115 (2014). https://doi.org/10.1142/S0217751X14501152. [ar**v: 1402.0878 [hep-th]]
Gogberashvili, M., Modrekiladze, B.: Probing the information-probabilistic description. Int. J. Theor. Phys. 61, 149 (2022). https://doi.org/10.1007/s10773-022-05129-3. [ar**v: 2105.05034 [gr-qc]]
Gogberashvili, M.: Fixing cosmological constant on the event horizon. Eur. Phys. J. C 82, 1049 (2022). https://doi.org/10.1140/epjc/s10052-022-11033-1. [ar**v: 2301.04334 [gr-qc]]
Gogberashvili, M.: Information-probabilistic description of the universe. Int. J. Theor. Phys. 55, 4185 (2016). https://doi.org/10.1007/s10773-016-3045-4. [ar**v: 1504.06183 [physics.gen-ph]]
Gogberashvili, M.: Towards an information description of space-time. Found. Phys. 52, 74 (2022). https://doi.org/10.1007/s10701-022-00594-6. [ar**v: 2208.13738 [physics.gen-ph]]
Rao, C.R.: Information and the accuracy attainable in the estimation of statistical parameters. Bull. Calcutta Math. Soc. 37 (1945) 81; In: Breakthroughs in Statistics: Foundations and basic theory, S. Kotz and N. L. Johnson (eds), Springer Series in Statistics, pp. 235–247 (Springer, NY 1992) https://doi.org/10.1007/978-1-4612-0919-5_16.
Amari, Sh.-I.: Differential-Geometrical Methods in Statistics. Lecture Notes in Statistics, vol. 28. Springer-Verlag, Berlin (1985)
Amari, Sh.-I., Nagaoka, H.: Methods of Information Geometry, Translations of Mathematical Monographs, Vol. 191 (American Math. Soc., 2000)
Caticha, A.: Lectures on probability, entropy and statistical physics. [ar**v: 0808.0012 [physics.data-an]]
Gogberashvili, M.: Machian solution of hierarchy problem. Eur. Phys. J. C 54, 671 (2008). https://doi.org/10.1140/epjc/s10052-008-0559-9. [ar**v: 0707.4308 [hep-th]]
Gogberashvili, M., Kanatchikov, I.: Machian origin of the entropic gravity and cosmic acceleration. Int. J. Theor. Phys. 51, 985 (2012). https://doi.org/10.1007/s10773-011-0971-z. [ar**v: 1012.5914 [physics.gen-ph]]
Gogberashvili, M.: On the dynamics of the ensemble of particles in the thermodynamic model of gravity. J. Mod. Phys. 5, 1945 (2014). https://doi.org/10.4236/jmp.2014.517189. [ar**v: 1309.0376 [gr-qc]]
Gogberashvili, M., Kanatchikov, I.: Cosmological parameters from the thermodynamic model of gravity. Int. J. Theor. Phys. 53, 1779 (2014). https://doi.org/10.1007/s10773-013-1976-6. [ar**v: 1210.4618 [physics.gen-ph]]
Adams, C.C.: The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. American Mathematical Society, Providence (2004)
Berera, A., et al.: Knotty inflation and the dimensionality of spacetime. Eur. Phys. J. C 77, 682 (2017). https://doi.org/10.1140/epjc/s10052-017-5253-3. [ar**v: 1508.01458 [hep-ph]]
Hartman, T., Maldacena, J.: Time evolution of entanglement entropy from black hole interiors. JHEP 05, 014 (2013). https://doi.org/10.1007/JHEP05(2013)014. [ar**v: 1303.1080 [hep-th]]
Liu, H., Suh, S.J.: Entanglement tsunami: universal scaling in holographic thermalization. Phys. Rev. Lett. 112, 011601 (2014). https://doi.org/10.1103/PhysRevLett.112.011601. [ar**v: 1305.7244 [hep-th]]
Liu, H., Suh, S.J.: Entanglement growth during thermalization in holographic systems. Phys. Rev. D 89, 066012 (2014). https://doi.org/10.1103/PhysRevD.89.066012. [ar**v: 1311.1200 [hep-th]]
Aoki, S., Onogi, T., Yokoyama, S.: Conserved charges in general relativity. Int. J. Mod. Phys. A 36, 2150098 (2021). https://doi.org/10.1142/S0217751X21500986. [ar**v: 2005.13233 [gr-qc]]
Eling, C., Jacobson, T., Mattingly, D.: Einstein-Aether theory. In Deserfest: A Celebration of the Life and Works of Stanley Deser, p. 163 (World Scientific, Singapore 2006) [ar**v: gr-qc/0410001 [gr-qc]]
Author information
Authors and Affiliations
Contributions
MG wrote the paper.
Corresponding author
Ethics declarations
Conflict of interest
M.G. declares no conflicts of interest.
Ethical approval
Not applicable.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Gogberashvili, M. The bimetric model with an informational metric tensor. Gen Relativ Gravit 55, 104 (2023). https://doi.org/10.1007/s10714-023-03153-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10714-023-03153-0