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arXiv 1606.06178hep-thgr-qc
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经典引力和量子引力中史瓦西奇点的求解

Resolving the Schwarzschild singularity in both classic and quantum gravity

Ding-fang Zeng

摘要:

Schwarzschild奇点的解对于解开黑洞的视界熵的起源以及黑洞蒸发过程中的信息缺失之谜具有重要的价值。在这项工作中,我们提供了一般的动态内度规的崩溃与地平线和非平凡的径向质量分布的恒星。我们发现静态中心奇点不是系统的最终状态。相反,系统的最终状态是一个周期性的零交叉呼吸球。通过3+1分解的广义相对论及其量子表述,建立了控制该呼吸球微观态的泛函薛定谔方程,并证明了所有物质都集中在中心点的系统组态不是唯一的本征能量密度解.利用类似Bohr-Sommerfield的“轨道”量子化假设,我们证明了对于视界半径为$r_h$的黑洞,存在大约$e^{r_h^2/\ell^2_\mathrm{pl}}$允许的本征能量密度分布.这就引出了对视界熵微观起源的解释,以及对霍金辐射中信息缺失之谜的解答。

英文摘要:

The Schwarzschild singularity's resolution has key values in cracking the key mysteries related with black holes, the origin of their horizon entropy and the information missing puzzle involved in their evaporations. We provide in this work the general dynamic inner metric of collapsing stars with horizons and with non-trivial radial mass distributions. We find that static central singularities are not the final state of the system. Instead, the final state of the system is a periodically zero-cross breathing ball. Through 3+1 decomposed general relativity and its quantum formulation, we establish a functional Schrödinger equation controlling the micro-state of this breathing ball and show that, the system configuration with all the matter concentrating on the central point is not the unique eigen-energy-density solution. Using a Bohr-Sommerfield like "orbital" quantisation assumption, we show that for each black hole of horizon radius $r_h$, there are about $e^{r_h^2/\ell^2_\mathrm{pl}}$ allowable eigen-energy-density profile. This naturally leads to physic interpretations for the micro-origin of horizon entropy, as well as solutions to the information missing puzzle involved in Hawking radiations.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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