https://doi.org/10.1140/epjc/s10052-021-09464-3
Regular Article - Theoretical Physics
A critical assessment of black hole solutions with a linear term in their redshift function
1
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
Received:
16
June
2021
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
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