Stability of Higher Dimensional Black Holes in Warped Spacetimes

Abstract

Recent developments in string theory, such as the AdS/CFT correspondence, have increased the interest in higher dimensional curved spaces. The Randall-Sundrum model, a five-dimensional spacetime with strongly warped extra dimension, is a promising model that offers potential solutions to some of the major theoretical physics problems. However, some of the black holes in this model appear to be unstable. We study the mode stability of Randall-Sundrum black holes, focusing on linear perturbations of a specific complex frequency. The instability is a generalization of the Gregory-Laflamme instability, which affects torus shaped black holes in five-dimensional flat space. While previous studies have been numerical, this thesis analytically proves the Gregory-Laflamme instability using spectral theory. We extend this instability to warped spaces to determine the mass range for unstable black holes. We conclude that black holes with a mass below that of the Earth are unstable in the Randall-Sundrum model, suggesting that solar-mass black holes could still exist in this model.