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

摘要

Using the Wentzel–Kramers–Brillouin method, we show that the peak location ($r_{ m peak}$) 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, $r_{ m peak}=r_+ +O!left (sqrt {1-q} ight )$, where $r_+$ is the event horizon radius. However, if the quasinormal mode is different from that of general relativity, we are forced to seek the true theory of gravity and/or face the existence of the naked singularity.