Soft hairs on isolated horizon implanted by electromagnetic fields

TL;DR

This paper demonstrates that isolated horizons in Einstein-Maxwell theory can carry soft electric hairs, which are related to asymptotic symmetries and electric multipole moments, extending the concept of soft hair on black holes.

Contribution

It explicitly characterizes the soft electric hairs on isolated horizons and links them to asymptotic $U(1)$ charges and electric multipole moments.

Findings

Isolated horizons carry infinite soft electric hairs.

Soft hairs are equivalent to electric multipole moments.

Supertranslations relate to foliation ambiguity and horizon memory effects.

Abstract

Inspired by the recent proposal of soft hair on black holes in Phys. Rev. Lett. 116, 231301 (2016), we have shown that an isolated horizon carries soft hairs implanted by electromagnetic fields. The solution space and the asymptotic symmetries of Einstein-Maxwell theory have been worked out explicitly near isolated horizon. The conserved current has been computed and an infinite number of near horizon charges have been introduced from the electromagnetic fields associated to the asymptotic $U(1)$ symmetry near the horizon, which indicates the fact that isolated horizon carries a large amount of soft electric hairs. The soft electric hairs, i.e. asymptotic $U(1)$ charges, are shown to be equivalent to the electric multipole moments of isolated horizons. It is further argued that the isolated horizon supertranslation is from the ambiguity of its foliation and an analogue of memory effect on horizon can be expected.