Ringdown in Vaidya spacetimes: time-dependent frequencies, Penrose limit and time-domain analyses

Abstract

We examine the possible characterization of ringdown waves in a dynamical Vaidya spacetime using the Penrose limit geometry around the dynamical photon sphere. In the case of a static spherically symmetric black hole spacetime, it is known that the quasinormal frequency in the eikonal limit can be characterized by the angular velocity and the Lyapunov exponent for the null geodesic congruence on the orbit of the unstable circular null geodesic. This correspondence can be further backed up by the analysis of the Penrose limit geometry around the unstable circular null geodesic orbit. We try to extend this analysis to a Vaidya spacetime, focusing on the dynamical photon sphere in it. Then we discuss to what extent the Penrose limit geometry can be relevant to the ringdown waves in the Vaidya spacetime, comparing the results with the numerically calculated waveform in the Vaidya spacetime.