Speaker: Masashi Kimura (CENTRA)

Title: A simple test for the stability of a black hole

Abstract: We propose a simple method to show the linear mode stability of a black hole when the perturbed field equation takes the form of the Schrodinger equation. In this system, all information of the spacetime is included in the potential term V in the Schrodinger equation. In this talk, we show that the existence of a regular solution of the differential equation dS/dr_* - S^{^2} + V = 0 implies the linear mode stability of the black hole, and there always exists a regular solution if the spacetime is stable. Applying this method to some examples, we easily show the stability of black hole spacetimes numerically. Also, we extend this method to coupled systems, i.e., when two or more physical degrees of freedom exist and they are coupled.