Black hole solutions in massive gravity

Abstract

The static vacuum spherically symmetric solutions in massive gravity are obtained both analytically and numerically. The solutions depend on two parameters (integration constants): the mass M (or, equivalently, the Schwarzschild radius), and an additional parameter, the "scalar charge" S. At zero value of S and positive mass the standard Schwarzschild black hole solutions are recovered. Depending on the parameters of the model and the signs of M and S, the solutions may or may not have horizon. Those with the horizon describe modified black holes provided they are stable against small perturbations. In the analytically solvable example, the modified black hole solutions may have both attractive and repulsive (anti-gravitating) behavior at large distances. At intermediate distances the gravitational potential of a modified black hole may mimics the presence of dark matter. Modified black hole solutions are also found numerically in more realistic massive gravity models which are attractors of the cosmological evolution.

Nonperturbative unitarity of the gravitational Higgs mechanism

“…6 We argue that this is indeed the case 7 by studying full nonlinear Hamiltonian for the relevant conformal and helicity-0 longitudinal modes with no spatial dependence, 4 For earlier and subsequent related works, see, e.g., [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38], and references therein. 5 For instance, in the de Sitter case, this becomes evident from the fact that in the full nonlinear theory no enhanced local gauge symmetry (or ghost) is present for any value of the Hubble parameter, while its appearance in the perturbative framework already at the quadratic order appears to be a mere artifact of linearization [12].…”

Holographic Van der Waals phase transition of the higher-dimensional electrically charged hairy black hole

“…(18), (19) and (20). Obviously, for these small values, these critical quantities are modified from the RN AdS values.…”

“…Since there exist hair parameters, hairy black hole solutions become far richer than in General Relativity [19,20]. The model for higher-dimensional hairy black holes was first introduced by Oliva and Ray in 2011.…”

Holographic research on phase transitions for a five dimensional AdS black hole with conformally coupled scalar hair

“…However, by introducing a cosmological constant and a conformal coupling, no-hair theorems can be circumvented. By virtue of the existence of "hair", the solutions of hairy black holes become richer than ordinary ones in general relativity [31][32][33]. In particular, G. Giribet et al [34,35] in 2014 proved the analytic solutions to higher dimensional hairy black holes do exist and the scalar configuration is regular every where outside and on the horizon.…”