arXiv 2002.103312020-02hep-thastro-ph.HEgr-qchep-ph

作为量子场组态的黑洞

Black Hole as a Quantum Field Configuration

Hikaru Kawai, Yuki Yokokura

备注：: ver4: We added a new paragraph to Sec.2.1. and made Appendix B
发表信息：: Universe 2020, 6(6), 77
DOI：: 10.3390/universe6060077

摘要：

通过求解半经典爱因斯坦方程$G_{μν}=8πG \langle ψ|T_{μν}|ψ\rangle$和量子物质场，将四维蒸发黑洞描述为量子场的组态。作为物质场，我们考虑$N$无质量自由标量场（$N$是大的）。我们找到了度量$g_{μν}$和状态$|ψ\rangle$的球对称自洽解。在这里，$g_{μν}$是局部的$AdS_2\times S^2$几何，$|ψ\rangle$提供了$\langle ψ|T_{μν}|ψ\rangle=\langle0|T_{μν}|0 \rangle+T_{μν}^{(ψ)}$，其中$|0\rangle$是度规中物质场的基态，而$T_{μν}^{(ψ)}$由描述坍缩物质的s波的激发和霍金辐射以及进入的负能量流组成。由于具有大角动量的束缚模的真空涨落，该物体由大的切向压力$\langle0|T^θ_θ|0 \rangle$支持。当考虑蒸发的反反应时，这描述了黑洞的内部。黑洞是一个紧凑的物体，它的表面（而不是视界）从外部看起来像传统的黑洞，最终蒸发而不会出现奇点。如果我们计算自洽组态$\{|ψ\rangle\}$的数目，我们再现了熵的面积定律。这说明信息是由黑洞内部的s波携带的。$|ψ\rangle$还描述了霍金辐射产生的负能流叠加在坍缩物质上，使总能量降低而总能量密度保持为正的过程。作为一种特殊情况，我们考虑共形物质场，并表明内部度规是由理论的物质含量决定的，这导致了对物质含量的新约束。

英文摘要：

We describe 4D evaporating black holes as quantum field configurations by solving the semi-classical Einstein equation $G_{μν}=8πG \langle ψ|T_{μν}|ψ\rangle$ and quantum matter fields in a self-consistent manner. As the matter fields we consider $N$ massless free scalar fields ($N$ is large). We find a spherically symmetric self-consistent solution of the metric $g_{μν}$ and state $|ψ\rangle$. Here, $g_{μν}$ is locally $AdS_2\times S^2$ geometry, and $|ψ\rangle$ provides $\langle ψ|T_{μν}|ψ\rangle=\langle0|T_{μν}|0 \rangle+T_{μν}^{(ψ)}$, where $|0\rangle$ is the ground state of the matter fields in the metric and $T_{μν}^{(ψ)}$ consists of the excitation of s-waves that describe the collapsing matter and Hawking radiation with the ingoing negative energy flow. This object is supported by a large tangential pressure $\langle0|T^θ_θ|0 \rangle$ due to the vacuum fluctuation of the bound modes with large angular momenta. This describes the interior of the black hole when the back reaction of the evaporation is considered. The black hole is a compact object with a surface (instead of horizon) that looks like a conventional black hole from the outside and eventually evaporates without a singularity. If we count the number of self-consistent configurations $\{|ψ\rangle\}$, we reproduce the area law of the entropy. This tells that the information is carried by the s-waves inside the black hole. $|ψ\rangle$ also describes the process that the negative ingoing energy flow created with Hawking radiation is superposed on the collapsing matter to decrease the total energy while the total energy density remains positive. As a special case, we consider conformal matter fields and show that the interior metric is determined by the matter content of the theory, which leads to a new constraint to the matter content.

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。

摘要：

英文摘要：

相关论文