How close can we approach the event horizon of the Kerr black hole from the detection of the gravitational quasinormal modes?

Abstract

Using the WKB method, we show that the peak location ($r_{\mathrm{peak}}$) of the potential, which determines the quasinormal mode frequency of the Kerr black hole, obeys an accurate empirical relation as a function of the specific angular momentum $a$ and the gravitational mass $M$. If the quasinormal mode with $a/M\sim 1$ is observed by gravitational wave detectors, we can confirm the black-hole space-time around the event horizon, $r_{\mathrm{peak}}=r_{+}+O(\sqrt{1-q})$ where $r_{+}$ is the event horizon radius. While if the quasinormal mode is different from that of general relativity, we are forced to seek the true theory of gravity and/or face to the existence of the naked singularity.

8 pages, 4 figures

References in corpus (5)

• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Double Compact Objects III: Gravitational Wave Detection Rates
• Matched-filtering and parameter estimation of ringdown waveforms
• Slow relaxation of rapidly rotating black holes
• The detection of Quasinormal Mode of Pop III Binary Black Hole merger with final $M\sim 60M_{\odot }$ and $a/M\sim 0.7$ would confirm the strong gravity space-time around $\sim 2M$ which is only $\sim 1.17$ times the event horizon radius

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• Fundamental Tone and Overtones of Quasinormal Modes in Ringdown Gravitational Waves: A Detailed Study in Black Hole Perturbation
• Estimate of the radius responsible for quasinormal modes in the extreme Kerr limit and asymptotic behavior of the Sasaki-Nakamura transformation