标题： 一种雷斯纳-诺德斯特罗姆黑洞的量子力学模型 显示英文标题

标题： A Quantum Mechanical Model of the Reissner-Nordstrom Black Hole

摘要： 我们考虑球对称、渐近平坦的电真空时空的哈密顿量子理论。 这类时空的物理相空间由雷斯纳-诺德斯特伦黑洞的质量和电荷参数$M$和$Q$以及相应的共轭动量所张成。 在这个四维相空间中，我们进行一个正则变换，使得所得的配置变量以自然的方式描述雷斯纳-诺德斯特伦黑洞的动力学性质。 用这些变量及其共轭动量表示的经典哈密顿量被替换为相应的自伴哈密顿算符，并从远处静止观察者的角度来看，得到了黑洞ADM质量的本征值方程。 我们的本征值方程表明，黑洞的ADM质量和电荷谱是离散的，且质量谱有下限。 此外，当选择适当的自伴扩张时，量$M^2-Q^2$的谱严格为正。 WKB分析得出结果，量$\sqrt{M^2-Q^2}$的大本征值形式为$\sqrt{2n}$，其中$n$是一个整数。 结果发现，这一结果与贝肯斯坦关于黑洞视界面积谱离散性的提议密切相关。 显示英文摘要

摘要： We consider a Hamiltonian quantum theory of spherically symmetric, asymptotically flat electrovacuum spacetimes. The physical phase space of such spacetimes is spanned by the mass and the charge parameters $M$ and $Q$ of the Reissner-Nordstr\"{o}m black hole, together with the corresponding canonical momenta. In this four-dimensional phase space, we perform a canonical transformation such that the resulting configuration variables describe the dynamical properties of Reissner-Nordstr\"{o}m black holes in a natural manner. The classical Hamiltonian written in terms of these variables and their conjugate momenta is replaced by the corresponding self-adjoint Hamiltonian operator, and an eigenvalue equation for the ADM mass of the hole, from the point of view of a distant observer at rest, is obtained. Our eigenvalue equation implies that the ADM mass and the electric charge spectra of the hole are discrete, and the mass spectrum is bounded below. Moreover, the spectrum of the quantity $M^2-Q^2$ is strictly positive when an appropriate self-adjoint extension is chosen. The WKB analysis yields the result that the large eigenvalues of the quantity $\sqrt{M^2-Q^2}$ are of the form $\sqrt{2n}$, where $n$ is an integer. It turns out that this result is closely related to Bekenstein's proposal on the discrete horizon area spectrum of black holes.