Hairless Black Hole by Superradiance

TL;DR

This paper studies how scalarization and superradiance interact around charged black holes, finding that superradiance prevents scalar hair formation and leads to efficient energy extraction from the black hole.

Contribution

It introduces the concept of tachyonic superradiance, combining scalarization and superradiance effects, and provides formulas for energy fluxes in dynamical black hole spacetimes.

Findings

Superradiance depletes scalar condensate via accretion and radiation.

Scalarization is suppressed in the presence of superradiance.

Derived energy flux formulas applicable to numerical relativity.

Abstract

We investigate the interplaying effects of black hole scalarization and superradiance in the context of the Einstein-Maxwell-scalar model, with the scalar field possessing electric charge. Restricted to spherical symmetry, our linear analysis about a Reissner-Nordstr\"om background confirms the persistence of tachyonic scalar modes upon inclusion of electric charge. However, fully nonlinear numerical simulations reveal that the system no longer evolves into a scalarized, hairy black hole state. Instead, we find that the superradiance phenomenon (specifically the electromagnetic version of the effect) causes the scalar condensate to become fully depleted through accretion into the black hole and radiation to spatial infinity. The combination of the two effects, which we refer to as "tachyonic superradiance", may thus be seen as a particularly efficient mechanism for the extraction of energy from a black hole, exploiting both the tachyonic growth and superradiant emission. We accurately compute the amounts of energy transfer in different channels by deriving formulae for the energy fluxes of matter fields in the presence of a dynamical horizon, which are amenable for evaluation in numerical relativity calculations.