Critical Phenomena in Gravitational Collapse and the Black Hole Evaporation

黑洞物理学在研究强引力的有趣性质方面引起了人们的广泛关注。然而，该研究领域的主要发展仅限于静止黑洞。本课题旨在对无质量标量场球对称引力坍缩中的动态黑洞进行详细的研究，以期在经典和量子水平上，特别是在临界现象和量子蒸发方面，发现新的方面。1. 对于标量场坍缩，由于自引力和波色散的相互作用，黑洞形成过程中出现了一些临界现象。利用临界坍缩的自相似模型，在正则形式下量子化了场变量的动态演化，并显式导出了蒸发黑洞的波函数。这是第一个成功证明量子引力在黑洞动力学中的作用的例子。2. 对标量场坍缩的经典动力学进行了更广泛的研究，发现近临界黑洞的质量尺度规律是由于标量场的振荡模式的产生干扰了自相似的坍缩。质量标度定律的临界指数由振荡周期决定。中心奇点附近的动力学行为对黑洞质量也有重要影响。3. 提出了动力学黑洞表面引力的新定义，给出了量子蒸发过程中的热温度。然后，将自相似模型中显示的量子蒸发称为非热过程。在未来的工作中，将研究更广泛的量子临界坍缩模型，以建立蒸发黑洞的这种非热（动力学）性质。

Black holes physics has attracted much attention to investigate interesting properties of strong gravity. However, the main depvelopments of the research area have been limited to stationary black holes. This research project is to study in detail dynamical black holes in spherically symmetric gravitational collapse of a massless scalar field, with the purpose of finding new aspects in classical and quantum levels especially in terms of the critical phenomena and the quantum evaporation. 1. For scalar field collapse some critical phenomena in black hole formation occur as a result of the interaction between self-gravity and wave dispersion. By using the self-similar model of the critical collapse, the dynamical evolution of field variables is quantized under the canonical formalism, and the wave function of evaporating black hole is explicitly derived. This is the first successful example to show the effect of quantum gravity in black hole dynamics. 2. The classical dynamics of scalar field collapse is more extensively studied, and the mass-scaling law of near-critical black holes is found to be due to the generation of an oscillatory mode of scalar fielddisturbing the self-similar collapse. The critical exponent of the mass-scaling law is shown to be determined by the period of the oscillation. The dynamical behavior near the central singularity is also pointed out to be crucial to the black hole mass. 3. A new definition of the surface gravity for dynamical black holes, which gives thermal temperature in quantum evaporation, is proposed. Then, the quantum evaporation shown in the self-similar model is claimed to be a non-thermal process. The more extensive models of quantum critical collapse will be investigated in future works to establish such a non-thermal (dynamical) property of evaporating black holes.