Rotating Black Holes

Abstract

For this last lecture, we will focus on particular properties of astrophysically realistic 4d black holes, which are rotating and uncharged. We will concentrate on the stationary Kerr black hole solution which is the final state of collapse of matter. After reviewing its main features, we will study the maximally spinning limit of the Kerr solution, the extremal Kerr black hole. It is a very interesting solution because it admits near horizon limits with enhanced conformal symmetry. The limiting near-horizon geometries share features with anti-de Sitter spacetimes where holography and therefore quantum gravity is most understood. The attempts (with successes and failures) to describe the extremal Kerr black hole with holographic techniques is called the Kerr/CFT correspondence and will be briefly reviewed here.

The final part of these lectures will be devoted to the analysis of gravitational perturbations around Kerr geometries. The Kerr black hole is currently under experimental tests by the LIGO/Virgo gravitational wave detectors. The final stages of black hole mergers consist in a quasi-normal mode ringing of the resulting black hole which is well-described by perturbation theory around the Kerr black hole. Since the Kerr black hole only depends upon two parameters, namely the mass and angular momentum, the resonance frequencies of the black hole are characteristic signatures of Einstein gravity. The emerging experimental science of black hole spectroscopy will soon test the limits of Einstein gravity and look for possible deviations.