Hair mass bound in the black hole with nonzero cosmological constants

TL;DR

This paper investigates mass bounds of Maxwell fields and the distribution of hair in Einstein-Born-Infeld black holes with various cosmological constants, revealing how boundary conditions influence hair condensation.

Contribution

It extends the understanding of black hole hair bounds to Einstein-Born-Infeld black holes with different cosmological constants, highlighting the role of boundary conditions.

Findings

Hod's lower bound holds in asymptotically flat and dS spaces.

Hod's lower bound can be violated in asymptotically AdS spaces.

AdS boundary facilitates Born-Infeld hair condensation.

Abstract

We study mass bounds of Maxwell fields in RN black holes and genuine hair in Einstein-Born-Infeld black holes with various cosmological constants. It shows that the Maxwell field serves as a good probe to disclose the hair distribution described with the event horizon and the photonsphere. And we find that the Hod's lower bound obtained in asymptotically flat space also holds in the asymptotically dS Einstein-Born-Infeld hairy black holes. In contrast, the Hod's lower bound can be invaded in the asymptotically AdS Einstein-Born-Infeld hairy black holes. It implies that the AdS boundary could make the Born-Infeld hair easier to condense in the near horizon area.