Instability of nonlinear scalar field on strongly charged asymptotically AdS black hole background

TL;DR

This paper investigates how the stability of a conformal scalar field on charged AdS black holes varies with black hole parameters, revealing a critical charge where stability transitions occur, with implications for rotating black holes.

Contribution

It demonstrates the dependence of scalar field stability on black hole charge, size, and boundary conditions, identifying a critical charge value for stability transition in Reissner-Nordström-AdS backgrounds.

Findings

Stability of scalar field depends on black hole charge and size.

A critical charge value marks the transition in stability.

Similar effects may occur in rotating black holes.

Abstract

The conformally invariant scalar equation permits the Robin boundary condition at infinity of asymptotically-AdS spacetimes. We show how the dynamics of conformal cubic scalar field on the Reissner-Nordstr\"{o}m-anti-de Sitter background depend on the black hole size, charge, and choice of the boundary condition. We study the whole range of admissible charges, including the extremal case. In particular, we observe the transition in stability of the field for large black holes at the specific critical value of the charge. Similarities between Reissner-Nordstr\"{o}m and Kerr black hole let us suspect that a similar effect may also occur in rotating black holes.