On the Black Holes in Alternative Theories of Gravity: The Case of Non-linear Massive Gravity

Arraut, Ivan

doi:10.1007/978-3-319-20046-0_7

Cited by 1 publication

(4 citation statements)

References 26 publications

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“…[26,27], the Schwarzschild(-de Sitter) solutions in ref. [76][77][78][79], the LTB solution in ref. [27], and the RN solution in ref.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…In the case of dRGT massive gravity, f µν is not a dynamical but a fixed metric, and hence we need not consider the equations of motion for f µν . The class of solutions with C(t, r) = 0 includes the cosmological solutions [26,27], the black hole solutions [76][77][78][79], the Lemaître-Tolman-Bondi (LTB) solution [27], and the Reissner-Nordström (RN) solution [77]. Since the equations of motion for g µν (and, in fact, those for f µν as well) reduce to the Einstein equations with a cosmological constant, any spherically symmetric solution in GR is also a solution of the one-parameter subclass (3.11) of bi-gravity and massive gravity with a suitable fiducial metric.…”

Section: Bi-spherically Symmetric Background Solutionsmentioning

confidence: 99%

“…[69,75]. The last class is a solution with a off-diagonal metric tensor and a special choice of the parameters α 3 and α 4 [76][77][78], where linear perturbations have been studied only in massive gravity with a flat fiducial metric [79] and not in bi-gravity.…”

Section: Introductionmentioning

confidence: 99%

“…In the present article, we will give a unified and general treatment for solutions with an off-diagonal metric tensor in massive gravity and bi-gravity belonging to a one parameter family of α 3 and α 4 , which include both cosmological [26,27] and spherically symmetric black hole solutions [64,[76][77][78][79]. We will find that the equations of motion for this class of solutions exactly reduce to those of general relativity (GR) with a cosmological constant not only at the background and linear (first-order) perturbation level but also at the level of quadratic (second-order) perturbations.…”

Section: Introductionmentioning

confidence: 99%

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Perturbations of cosmological and black hole solutions in massive gravity and bi-gravity

Kobayashi

Siino

Yamaguchi

et al. 2016

Prog. Theor. Exp. Phys.

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We investigate perturbations of a class of spherically symmetric solutions in massive gravity and bi-gravity. The background equations of motion for the particular class of solutions we are interested in reduce to a set of the Einstein equations with a cosmological constant. Thus, the solutions in this class include all the spherically symmetric solutions in general relativity, such as the Friedmann-Lemaître-Robertson-Walker solution and the Schwarzschild (-de Sitter) solution, though the one-parameter family of two parameters of the theory admits such a class of solutions. We find that the equations of motion for the perturbations of this class of solutions also reduce to the perturbed Einstein equations at first and second order. Therefore, the stability of the solutions coincides with that of the corresponding solutions in general relativity. In particular, these solutions do not suffer from non-linear instabilities which often appear in the other cosmological solutions in massive gravity and bi-gravity.

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“…[26,27], the Schwarzschild(-de Sitter) solutions in ref. [76][77][78][79], the LTB solution in ref. [27], and the RN solution in ref.…”

Section: Conclusion and Discussionmentioning

confidence: 99%