On a WKB formula for echoes

TL;DR

This paper develops a unified analytical approach to study gravitational echoes from horizonless compact objects like wormholes, providing formulas for their quasinormal modes and showing static wormholes do not radiate quantum mechanically.

Contribution

It introduces an analytical method to analyze gravitational echoes and quasinormal modes of horizonless objects, extending understanding beyond black holes.

Findings

Characteristic echoes can distinguish horizonless objects from black holes.

An approximate formula for quasinormal mode frequencies is derived.

Static wormholes do not emit radiation at the quantum level.

Abstract

We present an unified approach for the study of idealized gravitational compact objects like wormholes and horizonless stars, here simulated by the presence of boundary conditions at a deeply inner wall. At classical level, namely neglecting quantum effects, the presence of the wall leads to characteristic echoes following the usual ringdown phase, such that it can discriminate black holes from other horizonless, and probably exotic, compact objects. With regard to this issue, an analytical though approximated expression for the complex frequencies of the quasinormal echoes is found and discussed. At quantum level, we show that static wormholes do not radiate.