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.

中文翻译：

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来自具有非线性超平移头发的黑洞的霍金通量

我们用Robinson和Wilczek提出的异常消除方法研究了具有柔软毛发的黑洞的Hawking通量。与早期的考虑黑洞和线性超平移头发的研究不同，我们的研究将超平移头发考虑到二次方，然后得出角度相关的视界。结果，高度平凡的动力学混合出现在（1 + 1）d近视面简化理论的球形Kaluza-Klein模态之间，这掩盖了Hawking通量的传统推导。但是，在重新定义了一系列字段之后，我们可以将模式混合分​​解为规范的普通模式，但是这些普通模式的简化度量取决于模式。尽管如此，最终产生的霍金通量与模式无关，并且与Schwarzschild的相同。从而，