Regular Article - Theoretical Physics
A critical assessment of black hole solutions with a linear term in their redshift function
School of Science, Jiangsu University of Science and Technology, 212003, Zhenjiang, China
2 Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, 180 Siwangting Road, 225002, Yangzhou, Jiangsu, China
3 School of Aeronautics and Astronautics, Shanghai Jiao Tong University, 200240, Shanghai, China
Accepted: 17 July 2021
Published online: 2 August 2021
Different theories of gravity can admit the same black hole solution, but the parameters usually have different physical interpretations. In this work we study in depth the linear term in the redshift function of black holes, which arises in conformal gravity, de Rham–Gabadadze–Tolley (dRGT) massive gravity, f(R) gravity (as approximate solution) and general relativity. Geometrically we quantify the parameter in terms of the curvature invariants. Astrophysically we found that can be expressed in terms of the cosmological constant, the photon orbit radius and the innermost stable circular orbit (ISCO) radius. The metric degeneracy can be broken once black hole thermodynamics is taken into account. Notably, we show that under Hawking evaporation, different physical theories with the same black hole solution (at the level of the metric) can lead to black hole remnants with different values of their physical masses with direct consequences on their viability as dark matter candidates. In particular, the mass of the graviton in massive gravity can be expressed in terms of the cosmological constant and of the formation epoch of the remnant. Furthermore the upper bound of remnant mass can be estimated to be around kg.
© The Author(s) 2021
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3