标题： 蒸发黑洞的波函数 显示英文标题

标题： Wave Function of Evaporating Black Holes

摘要： 我们研究了动态黑洞的一些量子力学方面，其中使用Vaidya度规作为代表蒸发黑洞的模型。结果表明，在考虑入射（或出射）Vaidya度规并选择合适的坐标框架时，该模型中的Wheeler-DeWitt方程在整个时空区域内是可解的。这个波函数具有奇特的特性，即在曲率奇点附近由于大的量子效应而剧烈振荡，而在其他区域则表现出相当温和且完全规则的行为。通过纯粹的量子力学方法推导出了关于黑洞辐射的一般公式，当选择$r = 2M$时，该公式会简化为Hawking的半经典结果。目前的表述基本上可以应用于任何具有球对称黑洞的任意时空维度的系统。 显示英文摘要

摘要： We study some quantum mechanical aspects of dynamical black holes where the Vaidya metric is used as a model representing evaporating black holes. It is shown that in this model the Wheeler-DeWitt equation is solvable in whole region of spacetime, provided that one considers the ingoing (or outgoing) Vaidya metric and selects a suitable coordinate frame. This wave function has curious features in that near the curvature singularity it oscillates violently owing to large quantum effects while in the other regions the wave function exhibits a rather benign and completely regular behavior. The general formula concerning the black hole radiation, which reduces to the Hawking's semiclassical result when $r = 2M$ is chosen, is derived by means of purely quantum mechanical approach. The present formulation can be applied essentially to any system with a spherically symmetric black hole in an arbitrary spacetime dimension.