Abstract
Soft hair of black hole has been proposed recently to play an important role in the resolution of the black hole information paradox. Recent work has emphasized that the soft modes cannot affect the black hole S-matrix due to Weinberg soft theorems. However as soft hair is generated by supertranslation of geometry which involves an angular dependent shift of time, it must have non-trivial quantum effects. We consider supertranslation of the Vaidya black hole and construct a non-spherical symmetric dynamical spacetime with soft hair. We show that this spacetime admits a trapping horizon and is a dynamical black hole. We find that Hawking radiation is emitted from the trapping horizon of the dynamical black hole. The Hawking radiation has a spectrum which depends on the soft hair of the black hole and this is consistent with the factorization property of the black hole S-matrix.
Highlights
Spacetime, this means that supertranslated black hole carries an infinite amount of soft hair characterized by the BMS charges
We end this section by noting that while in this paper we focus on BMS supertranslations as asymptotic symmetries defined at null infinity and its effect on the physics at the black hole horizon, there is a different sort of supertranslations as asymptotic symmetries defined at black hole horizons, known as horizon supertranslations, which has been studied for example in [14, 33,34,35,36,37,38,39,40]
We show that soft hairs have non-trivial effects on the quantum physics of black hole
Summary
Let us start with a brief review on supertranslation for an asymptotically flat metric in four dimensions. At the infinity, depending on the physical situation one wants to describe, one may impose different falloff conditions on the metric. In general one wants to choose the falloff conditions such that interesting solutions such as gravitational radiations are included, but unphysical solutions (e.g. those with infinite energy) are ruled out. The choice of falloff conditions of Bondi, van der Burg, Metzner and Sachs (BMS) [17, 18, 44, 45] considers metric with the asymptotic expansion near the past null infinity I− [15], ds2 = −dv2 + 2dvdr + r2γABdΘAdΘB
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