Einstein black holes, free scalars and AdS/CFT correspondence

TL;DR

This paper explores the AdS/CFT correspondence for Einstein black holes in higher dimensions, using free scalar fields to analyze boundary correlators and stress-energy, revealing thermal properties and proposing a new mass definition.

Contribution

It provides new insights into the boundary stress-energy and mass definitions for higher-dimensional Einstein black holes within the AdS/CFT framework.

Findings

Boundary states are thermal and reflect bulk geometry properties.

Proposes a novel definition for black hole mass in AdS/CFT.

Identifies limitations in including compactified horizon corrections for d=5.

Abstract

We investigate AdS/CFT correspondence for two families of Einstein black holes in d > 3 dimensions, modelling the boundary CFT by a free conformal scalar field and evaluating the boundary two-point function in the bulk geodesic approximation. For the d > 3 counterpart of the nonrotating BTZ hole and for its Z_2 quotient, the boundary state is thermal in the expected sense, and its stress-energy reflects the properties of the bulk geometry and suggests a novel definition for the mass of the hole. For the generalised Schwarzschild-AdS hole with a flat horizon of topology R^{d-2}, the boundary stress-energy has a thermal form with energy density proportional to the hole ADM mass, but stress-energy corrections from compactified horizon dimensions cannot be consistently included at least for d=5.