Instability of a membrane intersecting a black hole

TL;DR

This paper investigates the stability of a membrane intersecting a charged black hole in a de Sitter spacetime, revealing that such membranes are generally unstable and that a positive cosmological constant enhances this instability.

Contribution

The study applies covariant perturbation formalism and numerical solutions to demonstrate the instability of membranes intersecting charged black holes, including extremal cases, in de Sitter spacetime.

Findings

Membranes intersecting charged black holes are unstable.

Positive cosmological constant increases membrane instability.

Numerical solutions confirm the instability across various charge states.

Abstract

The stability of a Nambu-Goto membrane at the equatorial plane of the Reissner-Nordstr{\o}m-de Sitter spacetime is studied. The covariant perturbation formalism is applied to study the behavior of the perturbation of the membrane. The perturbation equation is solved numerically. It is shown that a membrane intersecting a charged black hole, including extremely charged one, is unstable and that the positive cosmological constant strengthens the instability.