T-Witts from the horizon

Abstract

Expanding around null hypersurfaces, such as generic Kerr black hole horizons, using co-rotating Kruskal-Israel-like coordinates we study the associated surface charges, their symmetries and the corresponding phase space within Einstein gravity. Our surface charges are not integrable in general. Their integrable part generates an algebra including superrotations and a BMS 3 -type algebra that we dub "T-Witt algebra". The non-integrable part accounts for the flux passing through the null hypersurface. We put our results in the context of earlier constructions of near horizon symmetries, soft hair and of the program to semi-classically identify Kerr black hole microstates.

Symmetries at null boundaries: two and three dimensional gravity cases

“…One can use these trivial diffeomorphisms to set sub-leading terms in gvr component of metric, or equivalently η, and then we are left with only r independent η. This point, in a very similar 4d setup, was discussed in some detail in [29]. Since the analysis is essentially the same we do not repeat them here.…”

“…In this work, we studied "asymptotic symmetries" near a null boundary in two and threedimensional gravity theories. This work is motivated by questions regarding black holes and is a continuation of similar analysis in four-dimensional vacuum Einstein theory [29]. We analysed the problem in full generality and in particular, we did not impose any specific boundary conditions.…”

“…Moreover, one can model what is inside a black hole horizon by replacing the inside region with a membrane, placed at the stretched horizon, as is done in the membrane paradigm [14,15]. Furthermore, near horizon degrees of freedom and symmetries, are the essentials of the formulation of the soft hair proposal [16] and have been explored in several different publications [17][18][19][20][21][22][23][24][25][26][27][28][29]. Nonetheless, neither realize the maximal set of b.d.o.f.…”

“…analysed. One method to deal with the non-intergable charges is to use the Barnich-Troessaert modified bracket [11,39] (see also [29] for more discussions) to extract out the integrable part of the non-integrable charges. That is, to write / δQ ξ = δQ I ξ + F where Q I is the integrbale charge and F is a non-zero "flux".…”

The Λ-BMS4 charge algebra

“…A similar situation where the 2-cocycle can be absorbed in the redefinition of the Hamiltonian was recently discussed in[95] in the context of asymptotic symmetries in the vicinity of black holes horizons.…”