Slow relaxation of rapidly rotating black holes

2008/10/27 by Shahar Hod · 3 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #astro-ph #gr-qc #hep-th #quant-ph

paper · pdf · doi:10.1103/physrevd.78.084035

published as Phys.Rev.D78:084035,2008 · 5 pages

openalex publication_date 2008/10/27 · arxiv created 2008/11/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study analytically the relaxation phase of perturbed, rapidly rotating black holes. In particular, we derive a simple formula for the fundamental quasinormal resonances of near-extremal Kerr black holes. The formula is expressed in terms of the black hole physical parameters: \ensuremathω=m\ensuremathΩ\ensuremath-i2\ensuremathπT_BH(n+(1)/(2)), where T_BH and \ensuremathΩ are the temperature and angular velocity of the black hole, and m is the azimuthal harmonic index of a corotating equatorial mode. This formula implies that the relaxation period \ensuremathτ\ensuremath∼1/\ensuremath\mathfrakI\ensuremathω of the black hole becomes extremely long as the extremal limit T_BH\ensuremath→0 is approached. The analytically derived formula is shown to agree with direct numerical computations of the black hole resonances. We use our results to demonstrate analytically the fact that near-extremal Kerr black holes saturate the recently proposed universal relaxation bound.

Citations

• Introducing the black hole
• Black holes in general relativity
• Perturbations of a rotating black hole. III - Interaction of the hole with gravitational and electromagnetic radiation
• Quasinormal modes: the characteristic `sound' of black holes and neutron stars

Cited by

• Classes of exact solutions to the Teukolsky master equation
• Quasinormal modes of black holes and black branes
• Resonance spectrum of near-extremal Kerr black holes in the eikonal limit