A critical assessment of black hole solutions with a linear term in their redshift function

Abstract

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 $$\beta r$$ β r 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 $$\beta $$ β in terms of the curvature invariants. Astrophysically we found that $$\beta $$ β 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 $$0.5 \times 10^{27}$$ 0.5 × 10 27 kg.

Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A ∗

“…which, although not obvious at first glance, does indeed reduce to 3 √ 3 as a → 0, as can be seen by Taylor expanding equation (116) in a (we have made the valid approximation that 52 We note that this same space-time can arise in a wide range of theories other than Rindler gravity, see e.g. [1085][1086][1087][1088][1089][1090][1091]. It is also a particular case of the Kiselev BH [1092], with equation of state of the surrounding fluid given by w = −2/3.…”

The Kiselev solution in power-Maxwell electrodynamics

“…Besides the p = 0 case where the calculations are significantly simpler, we have focused on the case corresponding to p = 1. This is important not only because one can find an analytical solution to the Klein-Gordon equation, but also because this particular value of p is close to the limit imposed in confrontation with observations [17]. In both cases under consideration, the imaginary energy spectrum can be derived by imposing that the Heun functions get a polynomial form.…”

“…In the particular case w = −2/3, one gets in the metric function an additional linear contribution, −kr. The parameter k, which is the Kiselev quintessence charge can lead to a metric that was previously used in modified Newtonian dynamics (MOND) [16], and various other modifications of General Relativity [17], [18] (see also [19] and [20]).…”

Gravitational Decoupling in Higher Order Theories

“…Moreover in this case, apart from the fact that the massive graviton behaves like a kind of dark energy on the large scale, it can also mimic the dark matter halo on the galactic scale through the linear term γr in the above metric, which can be used to fit the rotational curves of most galaxies [66]. One should mention [67] that this metric is also a solution in other theories, such as conformal Weyl gravity [68], f (R) gravity [69] and general relativity [70], and although in each case the metric represents the same manifold at a geometric level, the physical meaning of the individual parameters m, Λ, γ and η is different.…”