Asymptotically AdS spacetimes with a timelike Kasner singularity

TL;DR

This paper presents exact Einstein solutions with a timelike Kasner singularity in holographic models, describing a flow from asymptotic AdS to a timelike singularity, and explores their physical properties and implications.

Contribution

It introduces new exact solutions with a timelike Kasner singularity in holographic Einstein models, expanding understanding of IR geometries and their boundary duals.

Findings

IR geometry features a timelike Kasner singularity

Solutions interpolate between AdS black hole and AdS soliton

Causality constraints are satisfied in these models

Abstract

Exact solutions to Einstein's equations for holographic models are presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz) singularity, and the UV is asymptotically AdS. This solution describes a holographic RG flow between them. The solution's appearance is an interpolation between the planar AdS black hole and the AdS soliton. The causality constraint is always satisfied. The entanglement entropy and Wilson loops are discussed. The boundary condition for the current-current correlation function and the Laplacian in the IR is examined. There is no infalling wave in the IR, but instead, there is a normalizable solution in the IR. In a special case, a hyperscaling-violating geometry is obtained after a dimensional reduction.