Holographic flows with scalar self-interaction toward the Kasner universe

Abstract

Considering a thermal state of the dual CFT with a uniform deformation by a scalar operator, we study a holographic renormalization group flow at nonzero temperature in the bulk described by the Einstein-scalar field theory with the self-interaction term λφ 4 in asymptotic anti-de Sitter spacetime. We show that the holographic flow with the self-interaction term could run smoothly through the event horizon of a black hole and deform the Schwarzschild singularity to a Kasner universe at late times. Furthermore, we also study the effect of the scalar self-interaction on the deformed near-singularity Kasner exponents and the relationship between entanglement velocity and Kasner singularity exponents at late times.

Trans-IR Flows to Black Hole Singularities

“…A natural extension of our work is to consider more types of flows, such as those sourced by combinations of interacting scalars, higher-rank fields, and axions [36][37][38][39][40]72]. One may also consider higher-curvature gravity [52], but note that we would expect corrections to the a T -function by analogy to the a-function of [9,10].…”

“…It is reasonable to ask how to generalize from free Kasner flows. One way is to construct Kasner flows sourced by more complicated matter sectors [36][37][38][39][40], via numerical methods, and plot a T -a concrete but ad hoc approach. Another is to assume a Belinskii-Khalatnikov-Lifshitz (BKL) singularity [41][42][43]-reviewed by [44]-as the trans-IR endpoint and analyze the near-singularity geometry.…”

“…One may ask about Kasner flows sourced by more complicated matter sectors, such as the self-interacting φ 4scalar theory of [36] or φ coupled to Maxwellian and/or axionic fields [37][38][39]. One could even consider dimensional reductions of supergravity theories [40] or modify the gravitational theory to include higher-curvature terms [52] (upon appropriate changes to a T (7) [9,10]).…”

Black hole singularities across phase transitions

“…One difference is that here the double trace deformation parameter is relevant. 9 One example where the Kasner exponents oscillate is for holographic superconductor system [7,8]. More generally, if we consider the spatial dependence of background fields, usually the Kasner exponents show chaotic behavior [4].…”

“…Other work on the Kasner singularities in gravitational systems can be found in e.g [6,7,8,9,10,11,12]…”