CFTs in rotating black hole backgrounds

TL;DR

This paper constructs a holographic dual of a 5D conformal field theory in a rotating black hole background, revealing a negative energy density and analyzing the stress tensor's properties using numerical solutions of Einstein equations.

Contribution

It introduces a novel holographic construction of a 5D CFT in a rotating black hole background with detailed stress tensor analysis and numerical methods.

Findings

Stress tensor is stationary and regular on horizons

Energy density is negative everywhere, indicating vacuum polarization

Numerical solutions of Einstein--DeTurck equations are used for construction

Abstract

We use AdS/CFT to construct the gravitational dual of a 5D CFT in the background of a non-extremal rotating black hole. Our boundary conditions are such that the vacuum state of the dual CFT corresponds to the Unruh state. We extract the expectation value of the stress tensor of the dual CFT using holographic renormalisation and show that it is stationary and regular on both the future and the past event horizons. The energy density of the CFT is found to be negative everywhere in our domain and we argue that this can be understood as a vacuum polarisation effect. We construct the solutions by numerically solving the elliptic Einstein--DeTurck equation for stationary Lorentzian spacetimes with Killing horizons.