Geometry and stability of spinning branes in AdS gravity

TL;DR

This paper investigates the geometry, stability, and singularities of spinning branes in Anti-de Sitter space across various dimensions, revealing conditions for their stability and the nature of their singularities.

Contribution

It introduces a detailed analysis of spinning branes in AdS, including non-extremal solutions, singularity characterization, and stability conditions within Chern-Simons supergravity.

Findings

Spinning branes can be constructed via isometries with fixed points.

Singularities are characterized as Dirac delta distributions in curvature.

Stable BPS branes are identified, with extremal in 3D and non-extremal in higher dimensions.

Abstract

The geometry of spinning codimension-two branes in AdS spacetime is analyzed in three and higher dimensions. The construction of non-extremal solutions is based on identifications in the covering of AdS space by isometries that have fixed points. The discussion focuses on the cases where the parameters of spinning states can be related to the velocity of a boosted static codimension-two brane. The resulting configuration describes a single spinning brane, or a set of intersecting branes, each one produced by an independent identification. The nature of the singularity is also examined, establishing that the AdS curvature acquires one in the form of a Dirac delta distribution. The stability of the branes is studied in the framework of Chern-Simons AdS supergravity. A class of branes, characterized by one free parameter, are shown to be stable when the BPS conditions are satisfied. In 3D, these stable branes are extremal, while in higher dimensions, the BPS branes are not the extremal ones.