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

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