Black hole spectroscopy and nonlinear echoes in Einstein-Maxwell-scalar theory

TL;DR

This paper investigates black hole perturbations and nonlinear dynamics in Einstein-Maxwell-scalar theory, revealing long-lived modes and echoes in the gravitational response, including in nonlinear regimes, which is a novel finding in such theories.

Contribution

It demonstrates for the first time that echoes can occur in a fully nonlinear setting within Einstein-Maxwell-scalar theory, extending previous linear analyses.

Findings

Presence of long-lived quasinormal modes in the potential cavity.

Detection of echoes in the nonlinear regime through simulations.

Black holes with stable photon spheres exhibit these features.

Abstract

In the context of Einstein-Maxwell-scalar theory with a nonminimal coupling between the electromagnetic and scalar field, we study linear (non)radial perturbations and nonlinear radial dynamics of spherically symmetric black holes. In a certain region of the parameter space, this theory admits hairy black holes with a stable photon sphere. This has a counterpart in the effective potential of linear perturbations, featuring multiple maxima and minima. The corresponding quasinormal mode spectrum contains long-lived modes trapped in the potential cavity and the time-domain linear response displays echoes, as previously observed for horizonless compact objects. Interestingly, the black-hole dynamics in this theory can be studied at the nonlinear level. By performing fully-fledged 1+1 simulations, we show that echoes are present even when the nonlinearities are significant. To our knowledge, this is the first example of echoes appearing in a consistent theory beyond a linearized analysis. In a follow-up work we will study whether this feature is also present in the post-merger signal from black hole collisions in this theory.