Probing inside a charged hairy black hole in massive gravity

Abstract

In this paper, we investigate the internal structure of a charged hairy black hole solution in the non-linear massive gravity. We first consider the impact of various configurations of massive gravity on the condensate operator and then probe the black hole interior dynamics. Like a standard holographic superconductor system, just below the critical temperature, the interior evolves through several distinct epochs, including a collapse of the Einstein-Rosen bridge, Josephson oscillations of the scalar field, and finally a Kasner (or Kasner inversion) cosmology. However, for the large massive gravity parameter, we see distinguishing features for the interior dynamics. In this regime, at a given temperature, the Einstein-Rosen bridge collapse and subsequent Josephson oscillations epochs completely disappear from the interior dynamics and the final Kasner cosmology epoch starts exactly after the would-be inner horizon and the system does not experience the Kasner inversion epoch.

AdS Black Holes with a Bouncing Interior

“…Using the bounce solution (24), this divergence validates two statements that we made above: firstly, that the bounces indeed become progressively narrower, and secondly, that indeed the Kasner velocity changes sign at each bounce.…”

“…4 we verify that the expression (24) gives an excellent description of the bounces found numerically in §3. It may be noted following from a fit to (24). This is a two-parameter fit for ρ n and…”

“…The nth bounce is strongly localized to ρ ≈ ρ n and φ φ n . However, the extended bounces described by (24) are wider and overlap with the Kasner regimes. On the nth…”

“…A recent body of work has demonstrated that a common feature of (minisuperspace) holographic interiors is the emergence of Kasner scaling towards the singularity [11,[13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

What lies beyond the horizon of a holographic p-wave superconductor

“…The interior has subsequently been subjected to further study. This includes the introduction of additional field content and variation of coupling parameters [19][20][21][22][23], use of alternative black hole solutions [24][25][26], analysis of RG flows [27,28], as well as the construction of "no inner-horizon" theorems [29]. Interior solutions for the p-wave model are now also being investigated, with the analogous changes in geometry and matter fields being observed [30].…”