Soft hairs on isolated horizon implanted by electromagnetic fields

Inspired by the recent proposal of soft hair on black holes in Hawking et al (2016 Phys. Rev. Lett . 116 231301 ), 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 the isolated horizon. The conserved current has been computed and an infinite number of near horizon charges have been introduced from the electromagnetic fields associated with the asymptotic U (1) symmetry near the horizon, which indicates the fact that the 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.