论文标题
“时间” -CovariantSchrödinger方程和Reissner-Nordström黑洞的规范量化
"Time"-covariant Schrödinger equation and the canonical quantization of the Reissner-Nordström black hole
论文作者
论文摘要
定义了Reissner-Nordström（RN）Black Hole的MinisuperSpace模型定义的“时间” - 交流Schrödinger方程，作为“内在时间”Schrödinger和Wheeler-Dewitt（WDW）方程之间的“混合”。为此，构建了一个减少，规则和“时间（R）” - 依赖的哈密顿密度，而不会“破坏”重新参数协方差$ r \ rightarrow f（\ tilde {r}）$。结果，可以根据参数$ r $的演变和对产生的量子描述的概率解释，而不同规格选择的量子方案是按构造等效的。这些解决方案是针对狄拉克的三角洲和高斯初始状态的。通过BOHM分析提出了对波函数的几何解释。旁边还提出了一个标准，以裁定，在两个奇异的空间之间是“更多”或“更少”的单数。比较了鉴定奇点存在的两种方法（比较了经典奇异性和半古典时空奇点的概率密度消失）。最后，还揭示了还原方程与3D电磁PP波段时期的等效性。
A "time"-covariant Schrödinger equation is defined for the minisuperspace model of the Reissner-Nordström (RN) black hole, as a "hybrid" between the "intrinsic time" Schrödinger and Wheeler-DeWitt(WDW) equations. To do so, a reduced, regular and "time(r)"-dependent Hamiltonian density was constructed, without "breaking" the re-parametrization covariance $r\rightarrow f(\tilde{r})$. As a result, evolution of states with respect to the parameter $r$ and probabilistic interpretation of the resulting quantum description is possible, while quantum schemes for different gauge choices are equivalent by construction. The solutions are found for a Dirac's delta and a Gaussian initial states. A geometrical interpretation of the wavefunctions is presented via Bohm analysis. Alongside, a criterion is presented to adjudicate which, between two singular spacetimes is "more" or "less" singular. Two ways to adjudicate about the existence of singularities are compared (vanishing of the probability density at the classical singularity and semi-classical spacetime singularity). Finally, an equivalence of the reduced equations with these of a 3D electromagnetic pp-wave spacetime is revealed.
