Horizons and Singularity in Clifton’s Spherical Solution of f (R) vacuum

Abstract

Due to the failure of Birkhoff's theorem, black holes in f (R) gravity theories in which an effective time-varying cosmological "constant" is present are, in general, dynamical. Clifton's exact spherical solution of R 1+δ gravity, which is dynamical and describes a central object embedded in a spatially flat universe, is studied. It is shown that apparent black hole horizons disappear and a naked singularity emerges at late times.

Reissner–Nordström Anti-de Sitter Black Holes in Mimetic F(R) Gravity

“…A direct comparison of the perturbation equations (54), (55), (56) and (57), to the ones corresponding to non-mimetic F (R) gravity in Ref. [50], shows that the two cases lead to the same perturbation equations.…”

“…For a similar study but for a Schwarzschild-anti de Sitter black hole in vacuum F (R) gravity, see [51] and also [52]. Moreover, there exist a large number of studies devoted on black holes solutions in the context of F (R) gravity, and for an incomplete list we refer to [53][54][55][56][57][58][59][60][61][62][63][64][65][66] and references therein.…”

A note on Schwarzschild–de Sitter black holes in mimetic F(R) gravity

“…As we demonstrated in [47], the resulting mimetic F (R) gravity was the same as an ordinary F (R) with an additional cosmological constant, and therefore the linearly perturbed equations of motion lead to anti-evaporation phenomena [53][54][55][56][57]. For some relevant works on black holes in modified gravity see [58][59][60][61][62][63][64][65][66][67][68][69][70] and references therein. As we demonstrate in the present work, the Schwarzschild de Sitter black hole is a solution of trivial mimetic F (R) gravity, which is an ordinary F (R) gravity with a cosmological constant.…”

Isotropic universe with almost scale-invariant fourth-order gravity

“…In [44], the following strict result is shown: Exact power-law cosmic expansion in f (R) gravity models with perfect fluid as source is possible for f (R) = R n only. Newer models of this kind can be found in [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], [60], [61], [62], [63], [64], [65], [66], [67], [68], [69], [70], [71], [72], [73], [74], [75], [76], [77], [78], [79], [80], and [81].…”