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

Takashi Nakamura,Hiroyuki Nakano

doi:10.1093/ptep/ptw026

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.

Highlights

Coalescing binary black holes (BHs) form a BH in numerical relativity simulations [1,2,3]
The BH radiates characteristic gravitational waves (GWs) with quasinormal mode (QNM) frequencies that dominate in the final phase of the merger of two BHs
QNM will be detected by the second-generation GW detectors such as Advanced LIGO [4], Advanced

Summary

Introduction

Coalescing binary black holes (BHs) form a BH in numerical relativity simulations [1,2,3]. After adopting the new potential VNNT , what we will do is to ask which part of the Kerr metric determines the QNMs for given a 0.8 < q < 1. As for the accuracy of the fundamental n = 0 QNM frequency with = 2, the errors of the real (ωr = Re(ω)) and the imaginary (ωi = Im(ω)) parts are 7% and 0.7%, respectively, To distinguish the original VSN from the new SN equation, we use VNNT on. Compared with the numerical results of Chandrasekhar and Detweiler [22] This suggests that, for the fundamental QNM of the a = 0 case, the space-time of a Schwarzschild BH around r ≈ 3.28M is confirmed through the detection of the QNM GWs. The word “around” has two meanings, that the GW cannot be localized due to the equivalence principle and that the imaginary part of the QNMs is determined by the curvature of the potential, which reflects the space-time structure of the Schwarzschild BH around r ≈ 3.28M. 0.9999, respectively, which shows that the results do not depend significantly on the choice of g

Result

Discussion