Shock waves, black hole interiors and holographic RG flows

TL;DR

This paper investigates how shock waves affect the interior dynamics of black holes in holographic RG flows, revealing impacts on scrambling, entanglement, and degrees of freedom, with novel insights into Kasner universe geometries.

Contribution

It introduces shock waves into holographic RG flows with Kasner interiors and analyzes their effects on black hole interior observables and dynamics.

Findings

Scrambling time increases with deformation strength.

The $a$-function jumps discontinuously across shock waves.

Entanglement velocity varies similarly to butterfly velocity.

Abstract

We study holographic renormalization group (RG) flows perturbed by a shock wave in dimensions $d\geq 2$. The flows are obtained by deforming a holographic conformal field theory with a relevant operator, altering the interior geometry from AdS-Schwarzschild to a more general Kasner universe near the spacelike singularity. We introduce null matter in the form of a shock wave into this geometry and scrutinize its impact on the near-horizon and interior dynamics of the black hole. Using out-of-time-order correlators, we find that the scrambling time increases as we increase the strength of the deformation, whereas the butterfly velocity displays a non-monotonic behavior. We examine other observables that are more sensitive to the black hole interior, such as the thermal $a$-function and the entanglement velocity. Notably, the $a$-function experiences a discontinuous jump across the shock wave, signaling an instantaneous loss of degrees of freedom due to the infalling matter. This jump is interpreted as a `cosmological time skip' which arises from an infinitely boosted length contraction. The entanglement velocity exhibits similar dependence to the butterfly velocity as we vary the strength of the deformation. Lastly, we extend our analyses to a model where the interior geometry undergoes an infinite sequence of bouncing Kasner epochs.