Shockwaves, black hole interiors and holographic RG flows

We study holographic renormalization group (RG) flows perturbed by a shockwave in any number of dimensions $d\geq 2$. In particular, we consider RG flows that are triggered by deforming the boundary conformal field theory (CFT) 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 shockwave into this deformed background and study the effects on the near-horizon and interior dynamics of the black hole. Using out-of-time-ordered correlators (OTOC), we find that the scrambling time, measured in terms of the horizon radius, decreases as we increase the strength of the boundary deformation, whereas the butterfly velocity displays a non-monotonic behavior. We further examine observables that are more sensitive to the black hole interior, like the thermal $a$-function and the entanglement velocity. The thermal $a$-function jumps discontinuously across the shockwave, signaling an instantaneous loss of degrees of freedom due to the infalling matter. Such a jump is interpreted as a `cosmological time skip' which arises from an infinitely boosted length contraction. The entanglement velocity exhibits a similar dependence to the butterfly velocity as we vary the boundary deformation. Finally, we extend our analyses to a model where the interior develops an infinite sequence of bouncing Kasner epochs.