What's inside a hairy black hole in massive gravity?

TL;DR

This paper investigates the internal structure of hairy black holes in massive gravity, revealing how scalar hair influences horizon stability, singularity behavior, and black hole dynamics, with implications for holographic theories and quantum information measures.

Contribution

It demonstrates that scalar hair prevents Cauchy horizon formation, explores the resulting Kasner singularities, and links black hole interior dynamics to entanglement and butterfly velocities.

Findings

Cauchy horizon is absent with scalar hair for many potentials.

Black hole interior ends in a Kasner singularity influenced by scalar kinetic terms.

Kasner exponents relate to entanglement and butterfly velocities.

Abstract

In the context of massive gravity theories, we study holographic flows driven by a relevant scalar operator and interpolating between a UV 3-dimensional CFT and a trans-IR Kasner universe. For a large class of scalar potentials, the Cauchy horizon never forms in presence of a non-trivial scalar hair, although, in absence of it, the black hole solution has an inner horizon due to the finite graviton mass. We show that the instability of the Cauchy horizon triggered by the scalar field is associated to a rapid collapse of the Einstein-Rosen bridge. The corresponding flows run smoothly through the event horizon and at late times end in a spacelike singularity at which the asymptotic geometry takes a general Kasner form dominated by the scalar hair kinetic term. Interestingly, we discover deviations from the simple Kasner universe whenever the potential terms become larger than the kinetic one. Finally, we study the effects of the scalar deformation and the graviton mass on the Kasner singularity exponents and show the relationship between the Kasner exponents and the entanglement and butterfly velocities probing the black hole dynamics. Differently from the holographic superconductor case, we can prove explicitly that Josephson oscillations in the interior of the BH are absent.