Evolution of Anti-de Sitter black holes in Einstein-Maxwell-dilaton theory

TL;DR

This paper investigates the nonlinear evolution of anti-de Sitter black holes in Einstein-Maxwell-dilaton theory, revealing how scalar fields and black hole properties change over time under perturbations.

Contribution

It provides the first detailed analysis of scalar field evolution and black hole mass dynamics in Einstein-Maxwell-dilaton theory with non-minimal coupling in AdS spacetime.

Findings

Scalar field oscillates with damping and converges to a final value.

Black hole mass increases abruptly then saturates exponentially.

Large charge-to-mass ratio can lead to horizon formation from naked singularities.

Abstract

We study the nonlinear evolution of the spherical symmetric black holes under a small neutral scalar field perturbation in Einstein-Maxwell-dilaton theory with coupling function $f(\phi)=e^{-b\phi}$ in asymptotic anti-de Sitter spacetime. The non-minimal coupling between scalar and Maxwell fields allows the transmission of the energy from the Maxwell field to the scalar field, but also behaves as a repulsive force for the scalar. The scalar field oscillates with damping amplitude and converges to a final value by a power law. The irreducible mass of the black hole increases abruptly at initial times and then saturates to the final value exponentially. The saturating rate is twice the decaying rate of the dominant mode of the scalar. The effects of the black hole charge, the cosmological constant and the coupling parameter on the evolution are studied in detail. When the initial configuration is a naked singularity spacetime with a large charge to mass ratio, a horizon will form soon and hide the singularity.