Ergoregion instability of exotic compact objects: electromagnetic and gravitational perturbations and the role of absorption

TL;DR

This paper analyzes the ergoregion instability in ultracompact, horizonless spinning objects, deriving analytical instability criteria for electromagnetic and gravitational perturbations, and highlights the role of absorption in stabilizing these exotic objects.

Contribution

It extends previous scalar analyses to electromagnetic and gravitational perturbations, providing analytical formulas for instability timescales and stability conditions based on absorption.

Findings

Electromagnetic and gravitational instabilities are stronger than scalar ones.

Larger absorption coefficients are needed to stabilize high-spin objects.

A minimum absorption of 60% can quench the instability regardless of spin.

Abstract

Spinning horizonless compact objects may be unstable against an 'ergoregion instability'. We investigate this mechanism for electromagnetic perturbations of ultracompact Kerr-like objects with a reflecting surface, extending previous (numerical and analytical) work limited to the scalar case. We derive an analytical result for the frequency and the instability time scale of unstable modes which is valid at small frequencies. We argue that our analysis can be directly extended to gravitational perturbations of exotic compact objects in the black-hole limit. The instability for electromagnetic and gravitational perturbations is generically stronger than in the scalar case and it requires larger absorption to be quenched. We argue that exotic compact objects with spin $\chi\lesssim 0.7$ ($\chi\lesssim 0.9$) should have an absorption coefficient of at least $0.3\%$ ($6\%$) to remain linearly stable, and that an absorption coefficient of at least $\approx60\%$ would quench the instability for any spin. We also show that - in the static limit - the scalar, electromagnetic, and gravitatonal perturbations of the Kerr metric are related to one another through Darboux transformations.