Rotating Topological Black Branes in Various Dimensions and AdS/CFT Correspondence

TL;DR

This paper studies rotating topological black branes in various dimensions within AdS spacetime, introduces new solutions with multiple rotational parameters, and refines counterterm methods to remove divergences, revealing non-zero mass densities in certain cases.

Contribution

It presents new higher-dimensional rotating topological black brane solutions with multiple rotational parameters and improves counterterm techniques for divergence removal in AdS spacetimes.

Findings

Counterterms need modification beyond five dimensions.

Divergences in action, mass, and angular momentum are removable with new counterterms.

Mass density remains non-zero in odd dimensions when mass parameter is zero.

Abstract

We consider rotating topological black branes with one rotational parameter in various dimensions. Also a general five-dimensional higher genus solution of the Einstein equation with a negative cosmological constant which represents a topological black brane with two rotational parameters is introduced. We find out that the counterterms inspired by conformal field theory introduced by Kraus, Larsen and Sieblink cannot remove the divergences in $r$ of the action in more than five dimensions. We modify the counterterms by adding a curvature invariant term to it. Using the modified counterterms we show that the $r$ divergences of the action, the mass, and the angular momentum densities of these spacetimes are removed. We also find out in the limit of $m=0$ the mass density of these spacetimes in odd dimensions is not zero.