Hawking Flux from a Black Hole with Nonlinear Supertranslation Hair

Abstract

We study the Hawking flux from a black hole with soft hair by the anomaly cancellation method proposed by Robinson and Wilczek. Unlike the earlier studies considering the black hole with linear supertranslation hair, our study takes into account the supertranslation hair to the quadratic order, which then yields the angular dependent horizon. As a result, highly nontrivial kinetic-mixings appear among the spherical Kaluza-Klein modes of the (1+1)d near-horizon reduced theory, which obscures the traditional derivation of the Hawking flux. However, after a series of field re-definitions, we can disentangle the mode-mixings into canonical normal modes, but the reduced metrics for these normal modes are mode-dependent. Despite of this, the resultant Hawking flux turns out to be mode-independent and remains the same as the Schwarzschild's one. Thus, one cannot tell the black holes with nonlinear supertranslation hairs from the Schwarzschild's one by examining the Hawking flux, so that the nonlinear soft hairs can be thought as the microstates.

arXiv comment9 pages ; v2: references added and minor modification, v3: accepted version, v4: [28] is added and typos in (22) and (36) are corrected

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• Hawking flux of 4D Schwarzschild black hole with supertransition correction to second-order
• Dressed Tunneling in Soft Hair
• Entanglement at the Soft-Hair Horizon
• Conic Sections on the Sky: Shadows of Linearly Superrotated Black Holes
• Shock wave quantum memory in shocked detector
• Hawking radiation of Dirac particles from soft-hairy black holes