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

TL;DR

This paper derives an empirical relation for the peak location of the potential in Kerr black holes using the WKB method, enabling proximity estimation to the event horizon through gravitational wave observations of quasinormal modes.

Contribution

It provides a new empirical relation for the potential peak location in Kerr black holes, linking quasinormal mode observations to the near-horizon geometry.

Findings

Peak location $r_{\rm peak}$ relates to the event horizon $r_+$ with $O(\sqrt{1-q})$ accuracy.

Observation of $a/M \sim 1$ modes confirms the black-hole spacetime near the horizon.

Deviations from general relativity's quasinormal modes suggest alternative gravity theories or naked singularities.

Abstract

Using the WKB method, we show that the peak location ($r_{\rm peak}$) 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, $r_{\rm peak}=r_+ +O(\sqrt{1-q})$ 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.