Gravitational collapse of charged scalar fields

TL;DR

This study models the gravitational collapse of charged scalar fields in spherical symmetry, showing that such collapse can form Reissner-Nordström black holes and supporting cosmic censorship.

Contribution

It develops a numerical framework using BSSN formalism for charged scalar fields and explores collapse outcomes with different initial charges.

Findings

Charged scalar fields can collapse into sub-extremal Reissner-Nordström black holes.

Increasing scalar field charge results in more neutral final black holes.

Collapse behavior supports the cosmic censorship conjecture for charged matter.

Abstract

In order to study the gravitational collapse of charged matter we analyze the simple model of an self-gravitating massless scalar field coupled to the electromagnetic field in spherical symmetry. The evolution equations for the Maxwell-Klein-Gordon sector are derived in the 3+1 formalism, and coupled to gravity by means of the stress-energy tensor of these fields. To solve consistently the full system we employ a generalized Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of General Relativity that is adapted to spherical symmetry. We consider two sets of initial data that represent a time symmetric spherical thick shell of charged scalar field, and differ by the fact that one set has zero global electrical charge while the other has non-zero global charge. For compact enough initial shells we find that the configuration doesn't disperse and approaches a final state corresponding to a sub-extremal Reissner-N\"ordstrom black hole with $|Q|<M$. By increasing the fundamental charge of the scalar field $q$ we find that the final black hole tends to become more and more neutral. Our results support the cosmic censorship conjecture for the case of charged matter.