以時間相依超平移修正動態黑洞之霍京溫度

Abstract

在眾多嘗試解決黑洞信息遺失悖論的理論當中，軟髮理論是一個相當值得探討的理論，因為此理論無須對廣義相對論或量子場論進行任何修正。軟髮是一種微分同胚的生成源，並被認為可以在漸進區域攜帶非均向性輻射的資訊。然而，這個理論遭遇到了挑戰。在遠離場源的區域，軟髮的效應只是一個阿貝爾群的座標轉換，因此無法攜帶任何資訊。為了並規避這個障礙使軟髮能攜帶資訊，我們考慮在事件視界上的軟髮是藉由吸收一個連續非均向性物質流而產生的情況，並預期黑洞蒸發時，霍京輻射也會與此種軟髮交互作用。上述的理論推廣了考慮震波的情況 。在這個推廣中，我們將軟髮做了兩種不同在時間相依上的延伸。一種對應到連續非均相性類光物質流的反饋，另一種則是一個廣義座標轉換，並且會對霍京光譜造成督卜勒位移。在合併兩種延伸之後，我們發現可以得到在整個流形上精確BMS對稱的生成源(荷)。這使得我們可以在黑洞事件視界上作非微擾的分析，並發現表面重力(霍京溫度)會被修正。這個修正是一個非均向類光物質流的指數平均，並且有著4M的衰減率。這意味著在事件視界上出現了一個新的二維自由度，並有機會擺脫黑洞信息遺失悖論。

One interesting proposal to solve the black hole information loss paradox without modifying either general relativity or quantum field theory, is the soft hair, a diffeomorphism charge that records the anisotropic radiation in the asymptotic region. This proposal, however, has been challenged, given that away from the source the soft hair behaves as a coordinate transformation that forms an Abelian group, thus unable to store any information. To maintain the spirit of the soft hair but circumvent these obstacles, we consider Hawking radiation as a probe sensitive to the entire history of the black hole evaporation, where the soft hairs on the horizon are induced by the absorption of a null anisotropic flow, generalizing the shockwave considered. To do so we introduce two different time-dependent extensions of the diffeomorphism associated with the soft hair, where one is the backreaction of the anisotropic null flow, and the other is a coordinate transformation that produces a Doppler shift to the Hawking spectrum. Together, they form an exact BMS charge generator on the entire manifold that allows the nonperturbative analysis of the black hole horizon, whose surface gravity, i.e. the Hawking temperature, is found to be modified. The modification depends on an exponential average of the anisotropy of the null flow with a decay rate of 4M, suggesting the emergence of a new 2-D degree of freedom on the horizon, which could be a way out of the information loss paradox.