Holographic Stress Tensors for Kerr-AdS Black Holes

TL;DR

This paper calculates holographic stress tensors for Kerr-AdS black holes in various dimensions, confirming their relation to dual conformal field theories and exploring properties like trace and energy, with implications for AdS/CFT correspondence.

Contribution

It provides explicit calculations of stress tensors for Kerr-AdS black holes in multiple dimensions and verifies their correspondence with dual CFT energies, including new insights into trace properties.

Findings

Total energy matches Casimir energy in dual CFTs.

Zero mass stress tensor aligns with holographic predictions.

Different regularizations yield traceless stress tensors.

Abstract

We use the counterterm subtraction method to calculate the action and stress-energy-momentum tensor for the (Kerr) rotating black holes in AdS_{n+1}, for n=2, 3 and 4. We demonstrate that the expressions for the total energy for the Kerr-AdS_3 and Kerr-AdS_5 spacetimes, in the limit of vanishing black hole mass, are equal to the Casimir energies of the holographically dual n-dimensional conformal field theories. In particular, for Kerr-AdS_5, dual to the case of four dimensional N=4 supersymmetric Yang-Mills theory on the rotating Einstein universe, we explicitly verify the equality of the zero mass stress tensor from the two sides of the correspondence, and present the result for general mass as a prediction from gravity. Amusingly, it is observed in four dimensions that while the trace of the stress tensor defined using the standard counterterms does not vanish, its integral does, thereby keeping the action free of ultraviolet divergences. Using a different regularisation scheme another stress tensor can be defined, which is traceless.