Soft hairs on isolated horizon implanted by electromagnetic fields

TL;DR

The paper addresses whether an isolated horizon supports soft hair generated by electromagnetic fields. It builds an explicit near-horizon solution space for Einstein-Maxwell theory and derives a closed algebra of asymptotic symmetries comprising supertranslations, superrotations, and a $U(1)$ gauge symmetry, along with the corresponding conserved currents. A key result is the existence of an infinite set of soft electric charges on the horizon, identified with the horizon's electric multipole moments, while the supertranslation sector remains electromagnetically blind, indicating soft photons on the horizon. The work further shows a foliation-ambiguity under horizon supertranslations that parallels the memory effect at null infinity, and discusses prospects for extending near-horizon symmetries into the bulk and for horizon state counting and quantum memory applications.

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.