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arXiv 1611.04044gr-qchep-th
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用初始数据饱和引力坍缩的Bekenstein-Hawking熵界

Saturating The Bekenstein-Hawking Entropy Bound With Initial Data Sets For Gravitational Collapse

Sina Bahrami

发表信息：
Phys. Rev. D 95, 026006 (2017)
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摘要：

我们有可能找到引力坍缩的初始状态，它的熵近似饱和了最后一个黑洞的贝肯斯坦-霍金熵。这种状态的典型例子是由Zurek和Thorne以及Susskind设想的：对于一个质量为$\sim M$的黑洞，在$\sim M^3$量级的时间尺度上吸积了许多能量为$1/M$量级的$\sim M^2$量子，这是霍金蒸发的近似时间反演。有一种说法认为，所有使贝肯斯坦-霍金熵饱和的初始态都必须包含这个数量级的形成时标$M^3$，而不是更短的动力学时标$M$。索尔金、瓦尔德和张，以及许和里布，都以半经典初始数据集的形式找到了这一理论的反例。然而，与这些反例相对应的时空在过去拥有白洞，在未来也有黑洞，这让人怀疑它们的物理相关性。我们修改的反例，以消除白洞，产生形成时间尺度的顺序$M^2$，并认为，传说是没有根据的。

英文摘要：

It is possible to find initial states for gravitational collapse whose entropy approximately saturates the Bekenstein-Hawking entropy of the final black hole. The prototypical example of such a state is that envisaged by Zurek and Thorne, and also by Susskind: for a black hole of mass $\sim M$ , a number $\sim M^2$ of quanta with energies of order $1/M$ are accreted on a timescale of order $\sim M^3$, an approximate time-reverse of Hawking evaporation. There is lore that all initial states which saturate the Bekenstein-Hawking entropy must involve a formation timescale of this order, $M^3$ , and not the much shorter dynamical timescale $M$ . Counterexamples to this lore have been found by Sorkin, Wald and Zhang, and also by Hsu and Reeb, in the form of semiclassical initial data sets. However the spacetimes that correspond to these counterexamples possess white holes in the past, as well as black holes in the future, which casts doubt on their physical relevance. We modify the counterexamples to eliminate the white holes, yielding formation timescales of order $M^2$ , and argue that the lore is unfounded.

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