When a black hole first forms, the properties of the emitted radiation as measured by observers near future null infinity are very close to the 1974 prediction of Hawking. However, deviations grow with time and become of order unity after a time $t\sim M_i^{7/3}$, where $M_i$ is the initial mass in Planck units. After an evaporation time, the corrections are large: the angular distribution of the emitted radiation is no longer dominated by low multipoles, with an exponential falloff at high multipoles. Instead, the radiation is redistributed as a power-law spectrum over a broad range of angular scales, all the way down to the scale $\mathrm{\Delta }\theta \sim 1/M_i$, beyond which there is exponential falloff. This effect is a quantum gravitational effect, whose origin is the spreading of the wave function of the black hole’s center-of-mass location caused by the kicks of the individual outgoing quanta, discovered by Page in 1980. The modified angular distribution of the Hawking radiation has an important consequence: the number of soft hair modes that can effectively interact with outgoing Hawking quanta increases from the handful of modes at low multipoles $l$ to a large number of modes, of order $\sim M_i^2$. We argue that this change unlocks the Hawking-Perry-Strominger mechanism for purifying the Hawking radiation.

中文翻译：

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霍金辐射的阶次统一校正

当黑洞第一次形成时，由观测者在未来零点无穷远处测量的发射辐射的特性非常接近于 1974 年霍金的预测。然而，偏差随着时间的推移而增长，并在一段时间后成为秩序统一$吨～{米}_{\mathrm{一世}}^{7/3}$， 在哪里 ${米}_{\mathrm{一世}}$是普朗克单位的初始质量。在蒸发时间之后，修正很大：发射辐射的角分布不再由低多极子主导，在高多极子处呈指数衰减。取而代之的是，辐射在广泛的角尺度范围内以幂律谱的形式重新分布，一直到尺度$\mathrm{\Delta }\theta ～1/{米}_{\mathrm{一世}}$，超过这个值就会出现指数衰减。这种效应是一种量子引力效应，其起源是由佩奇在 1980 年发现的单个出射量子的踢腿引起的黑洞质心位置的波函数的扩展。 霍金角分布的修正辐射有一个重要的后果：可以有效地与传出霍金量子相互作用的软毛模式的数量从低多极点的少数模式中增加$升$ 到大量的模式，有序 $～{米}_{\mathrm{一世}}^2$. 我们认为，这一变化解锁了霍金-佩里-斯特罗明格机制，以净化霍金辐射。