Regular scalar charged clouds around a Reissner-Nordstrom black hole and no-hair theorems

TL;DR

This paper investigates the existence of charged scalar clouds around Reissner-Nordstrom black holes, proving their non-existence in certain cases and discussing conditions under which they can form, thus contributing to black hole no-hair theorems.

Contribution

The paper provides a theorem proving the non-existence of charged scalar clouds around Reissner-Nordstrom black holes without self-interaction, and discusses how self-interactions enable such clouds.

Findings

No scalar clouds without self-interaction in subextremal and extremal RNBHs.

A theorem proving the absence of such clouds under specified conditions.

Self-interactions can lead to the formation of charged scalar clouds.

Abstract

In this work we reanalyze the possibility of finding bound states (scalar clouds) of a test, charged and complex-valued scalar field with mass and charge q in the background of a Reissner-Nordstrom black hole (RNBH). In order to determine the existence of such scalar clouds we impose suitable regularity conditions for the scalar field at the event horizon. We find numerical evidence for the absence of such clouds in the subextremal and extremal RNBH when the field is massive but not self-interacting. More importantly, we put forward a theorem that proves that such clouds cannot exist. On the other hand, when a suitable self-interacting potential is included, the theorem no longer applies, providing a heuristic justification behind the existence of charged clouds (Q-clouds) that were reported recently.