标题： 寻找霍金辐射的经典版本以及视界对库仑场的屏蔽 显示英文标题

标题： Searching for the classical version of Hawking radiation and screening of Coulomb field by the horizon

摘要： 我们研究了黑洞塌缩时空下霍金辐射经典版本的可能性——即由纯 outgoing 波组成的经典场方程解。相应度规的非静态特性导致物质的能量守恒缺失，而这原本可能禁止此类解的存在。我们考虑了一个具体且简单的场景：一个薄壳坍缩形成黑洞，该薄壳不一定具有类似尘埃的性质。在对应的时空内，我们研究了实质量无标量场方程的解，这些解呈现纯 outgoing 波的形式。除了齐次方程外，我们还考察了位于对称中心的场的常点源情况。壳外部的通解用合流 Heun 函数表示，而壳内部的方程及其表面的匹配条件被表述为积分方程。通过对各种解的渐近行为的分析，可以将积分方程简化为矩阵方程，随后通过数值方法求解。 显示英文摘要

摘要： We investigate the possibility of the existence of a classical version of Hawking radiation - solutions to classical field equations that consist solely of outgoing waves, in the spacetime of a collapsing black hole. The non-static nature of the corresponding metric results in the absence of energy conservation for matter, which could otherwise a priori prohibit such solutions. A specific and simple scenario is considered: a black hole formation as a result of the collapse of a thin shell, which is not necessarily dust-like. In the corresponding spacetime, we study solutions of the equations for a real massless scalar field that take the form of purely outgoing waves. In addition to the homogeneous equation, we also examine the case of a constant point source of the field located at the symmetry center. The general solution outside the shell is expressed in terms of the confluent Heun function, while the equations inside the shell and the matching conditions at its surface are formulated as an integral equation. The analysis of various solution asymptotics enables the reduction of the integral equation to a matrix equation, which is subsequently solved numerically.