Infrared effects in the late stages of black hole evaporation
Infrared effects in the late stages of black hole evaporation
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DOI：
10.1007/jhep07(2021)137
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发表时间：
2021-02
影响因子：
5.4
通讯作者：
E. Flanagan
中科院分区：
文献类型：
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作者：
E. Flanagan
当黑洞蒸发时，每个传出的霍金量子都会带走一些与扩展邦迪-梅茨纳-萨克斯群相关的黑洞渐近电荷。这些包括庞加莱能量电荷，线性动量，固有角动量，轨道角动量或质心电荷，以及与超平移和超洛伦兹变换相关的这些量的扩展，即超动量，超自旋和超质心电荷（也称为软毛）。由于每个发射的量子都有单位阶的涨落，因此黑洞电荷的涨落在蒸发过程中会增加。我们用一个简单的模型来估计这些波动的规模。结果是，在普朗克单位中：(i)黑洞的位置在后期具有不确定性，其中mi是初始质量（先前由Page发现）。（ii）在达到普朗克尺度之前，黑洞质量M在M ~时期的不确定性与质量M本身的不确定性相当。相应的，蒸发结束的时间也有顺序上的不确定性。（iii）超动量和超自旋电荷不是相互独立的，而是由庞加莱荷和超质心电荷决定的。（iv）表征超质心电荷的超平移具有在普朗克单位中具有有序单位的多极1阶的波动。在大l处，有一个波动的幂律谱，延伸到l ~，超过l ~后，波动呈指数下降，对应的总均方根剪切张量波动~ M i M−3/2。
As a black hole evaporates, each outgoing Hawking quantum carries away some of the black holes asymptotic charges associated with the extended Bondi-Metzner-Sachs group. These include the Poincaré charges of energy, linear momentum, intrinsic angular momentum, and orbital angular momentum or center-of-mass charge, as well as extensions of these quantities associated with supertranslations and super-Lorentz transformations, namely supermomentum, superspin and super center-of-mass charges (also known as soft hair). Since each emitted quantum has fluctuations that are of order unity, fluctuations in the black hole’s charges grow over the course of the evaporation. We estimate the scale of these fluctuations using a simple model. The results are, in Planck units:(i) The black hole position has a uncertainty ofat late times, where M i is the initial mass (previously found by Page).(ii) The black hole mass M has an uncertainty of order the mass M itself at the epoch when M∼, well before the Planck scale is reached. Correspondingly, the time at which the evaporation ends has an uncertainty of order.(iii) The supermomentum and superspin charges are not independent but are determined from the Poincaré charges and the super center-of-mass charges.(iv) The supertranslation that characterizes the super center-of-mass charges has fluctuations at multipole orders l of order unity that are of order unity in Planck units. At large l, there is a power law spectrum of fluctuations that extends up to l∼, beyond which the fluctuations fall off exponentially, with corresponding total rms shear tensor fluctuations∼ M i M− 3/2.