Ringing of the regular black-hole/wormhole transition

TL;DR

This paper investigates the transition between regular black holes and traversable wormholes using quasinormal modes, revealing echoes during the transition and remnants in the perturbation profiles, supported by analytical and numerical methods.

Contribution

It provides a detailed analysis of quasinormal modes across black hole and wormhole states, introducing an analytical formula in the eikonal regime and demonstrating the transition characteristics.

Findings

Echoes characterize the black-hole/wormhole transition.

Remnants of black hole states appear in wormhole perturbations.

WKB and time-domain methods agree well in mode calculations.

Abstract

A simple one-parameter generalization of the Schwarzschild spacetime was recently suggested by A. Simpson and M. Visser [JCAP 1902, 042 (2019)] as a toy model describing the regular black hole and traversable wormhole states separated by the border (one-way wormhole) state. We study quasinormal modes of all the three states and show that the black-hole/wormhole transition is characterized by echoes, while the remnant of the black hole state is kept in the time-domain profile of the wormhole perturbation at the initial stage of the exponential fall off. Calculations of quasinormal modes using the WKB method with Pad\'{e} expansion and the time-domain integration are in good agreement. An analytical formula governing quasinormal modes in the eikonal regime is given.