The BTZ black hole with a time-dependent boundary

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.

14 pages, 13 figures, title changed in journal, conformal diagrams added, references added, final version to appear in Classical and Quantum Gravity

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Cited by in corpus (7)

• Entanglement from Dissipation and Holographic Interpretation
• Entanglement entropy in FRW backgrounds
• Expanding plasmas from Anti de Sitter black holes
• Non-Vacuum AdS Cosmologies and the Approach to Equilibrium of Entanglement Entropy
• Quantum (in)stability of maximally symmetric space-times
• Entanglement entropy in a four-dimensional cosmological background
• Holographic Horizons