The BTZ black hole with a time-dependent boundary

TL;DR

This paper develops a coordinate system for the BTZ black hole that incorporates a time-dependent boundary metric, enabling analysis of dual CFTs in evolving backgrounds and their entanglement properties.

Contribution

It provides explicit coordinate transformations for the BTZ black hole with a dynamic boundary and explores implications for holographic entanglement entropy calculations.

Findings

Derived explicit coordinate transformations for time-dependent boundary metrics.

Analyzed null geodesic expansions in the BTZ background.

Discussed holographic entanglement entropy in evolving backgrounds.

Abstract

The non-rotating BTZ solution is expressed in terms of coordinates that allow for an arbitrary time-dependent scale factor in the boundary metric. We provide explicit expressions for the coordinate transformation that generates this form of the metric, and determine the regions of the complete Penrose diagram that are convered by our parametrization. This construction is utilized in order to compute the stress-energy tensor of the dual CFT on a time-dependent background. We study in detail the expansion of radial null geodesic congruences in the BTZ background for various forms of the scale factor of the boundary metric. We also discuss the relevance of our construction for the holographic calculation of the entanglement entropy of the dual CFT on time-dependent backgrounds.