量子引力坍缩作为半直线上的Dirac粒子
Quantum gravitational collapse as a Dirac particle on the half-line
摘要：
证明了广义相对论中薄球壳的量子动力学与半直线上的库仑-狄拉克方程是等价的。汉密尔顿算子具有一个单参数自伴扩展族，具有离散能谱$|E| < m$，以及$|E|>m$的连续散射状态，其中$m$是壳的静止质量，$E$是Arnowitt-Deser-Misner质量。对于足够大的$m$，基态能级是负的。这意味着经典的正能量不能在量子化中幸存下来。散射状态提供了奇异性避免的实现。我们推测这些结果的后果黑洞辐射。
英文摘要：
We show that the quantum dynamics of a thin spherical shell in general relativity is equivalent to the Coulomb-Dirac equation on the half line. The Hamiltonian has a one-parameter family of self-adjoint extensions with a discrete energy spectrum $|E| < m$, and a continuum of scattering states for $|E|>m$, where $m$ is the rest mass of the shell and $E$ is the Arnowitt-Deser-Misner mass. For sufficiently large $m$, the ground state energy level is negative. This suggests that classical positivity of energy does not survive quantization. The scattering states provide a realization of singularity avoidance. We speculate on the consequences of these results for black hole radiation.
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