Semiclassical Einstein equations from holography and boundary dynamics

TL;DR

This paper develops a holographic approach to semiclassical Einstein equations, incorporating boundary dynamics and quantum stress-energy contributions, revealing stability conditions for boundary black holes in AdS/CFT.

Contribution

It formulates semiclassical Einstein equations within holography using boundary effective actions and identifies a universal parameter governing boundary dynamics.

Findings

Derived semiclassical Einstein equations from holography.

Identified a universal parameter controlling boundary CFT effects.

Found boundary BTZ black hole instability due to quantum backreaction.

Abstract

In this paper, we consider how to formulate semiclassical problems in the context of the AdS/CFT correspondence, based on the proposal of Compere and Marolf. Our prescription involves the effective action with self-action term for boundary dynamical fields, which can be viewed as imposing mixed boundary conditions for the gravity dual. We derive the semiclassical Einstein equations sourced by boundary CFT stress-energy tensor. Analyzing perturbations of the holographic semiclassical Einstein equations, we find a universal parameter $\gamma_d$ which controls the contribution from boundary CFTs and specifies dynamics on the AdS boundary. As a simple example, we examine the semiclassical Einstein equations in $3$-dimensions with $4$-dimensional AdS gravity dual, and show that the boundary BTZ black hole with vanishing expectation value of the stress-energy tensor becomes unstable due to the backreaction from quantum stress-energy tensor when the parameter $\gamma_d$ exceeds a certain critical value.