No-hair theorem for Black Holes in Astrophysical Environments

TL;DR

This paper proves that astrophysical black holes in realistic environments still have no 'hair', meaning their multipole moments and Love numbers vanish, even when distorted by external influences, within the framework of full general relativity.

Contribution

It provides a rigorous proof that black holes in astrophysical settings retain the no-hair property, extending previous approximations to full general relativity.

Findings

Black holes have no induced multipole moments in astrophysical environments.

Second Love numbers of black holes vanish in full general relativity.

Distorted black holes still conform to the no-hair theorem.

Abstract

According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.