[论文解读] Comparing quantum black holes and naked singularities

T. P. Singh|ArXiv.org|Dec 21, 2000

Quantum Electrodynamics and Casimir Effect参考文献 1被引用 4

一句话总结

本文比较了导致裸奇点与黑洞的球面对称引力坍缩的半经典量子辐射。研究发现，裸奇点在其半经典阶段仅辐射约一个普朗克能量——远少于黑洞的霍金辐射——表明其最终演化必须依赖完整的量子引力理论来描述，因此它们是检验量子引力理论的有力候选体系。

ABSTRACT

There are models of gravitational collapse in classical general relativity which admit the formation of naked singularities as well as black holes. These include fluid models as well as models with scalar fields as matter. Even if fluid models were to be regarded as unphysical in their matter content, the remaining class of models (based on scalar fields) generically admit the formation of visible regions of finite but arbitrarily high curvature. Hence it is of interest to ask, from the point of view of astrophysics, as to what a stellar collapse leading to a naked singularity (or to a visible region of very high curvature) will look like, to a far away observer. The emission of energy during such a process may be divided into three phases - (i) the classical phase, during which matter and gravity can both be treated according to the laws of classical physics, (ii) the semiclassical phase, when gravity is treated classically but matter behaves as a quantum field, and (iii) the quantum gravitational phase. In this review, we first give a summary of the status of naked singularities in classical relativity, and then report some recent results comparing the semiclassical phase of black holes with the semiclassical phase of spherical collapse leading to a naked singularity. In particular, we ask how the quantum particle creation during the collapse leading to a naked singularity compares with the Hawking radiation from a star collapsing to form a black hole. It turns out that there is a fundamental difference between the two cases. A spherical naked star emits only about one Planck energy during its semiclassical phase, and the further evolution can only be determined by the laws of quantum gravity. This contrasts with the semiclassical evaporation of a black hole.

研究动机与目标

• 研究导致裸奇点与黑洞的引力坍缩过程中半经典量子粒子产生现象。
• 评估裸奇点是否可作为量子引力效应的可观测测试平台。
• 比较裸奇点与黑洞在其半经典阶段的能量辐射特征。
• 评估裸奇点极低能量辐射对宇宙监督猜想与量子引力有效性的影响。
• 探讨非球面对称坍缩是否会导致与球面对称坍缩截然不同的粒子产生。

提出的方法

• 利用标量场和流体物质模型分析球面对称坍缩模型，以生成裸奇点与黑洞。
• 应用半经典引力技术计算坍缩过程中的粒子产生，将引力视为经典场，而物质则视为量子场。
• 比较裸奇点与黑洞在半经典阶段的能量流与粒子发射速率。
• 结合广义相对论与弯曲时空中的量子场论的数值与解析方法，模拟辐射过程。
• 基于尘埃与标量场坍缩模型的结果，推断在违反宇宙监督的坍缩情景下的一般行为。
• 通过分析曲率可见性与粒子产生潜力的定性差异，将结论扩展至非球面对称坍缩。

实验结果

研究问题

• RQ1 在球面对称坍缩形成的裸奇点中，其半经典粒子辐射与黑洞的霍金辐射相比如何？
• RQ2 裸奇点坍缩的半经典阶段总共辐射了多少能量？
• RQ3 裸奇点的最终演化能否用半经典引力描述，还是必须依赖完整的量子引力？
• RQ4 非球面对称裸奇点在粒子产生与能量辐射方面与球面对称裸奇点有何不同？
• RQ5 在天体物理坍缩中，哪些观测特征可能用于区分裸奇点与黑洞？

主要发现

• 球面对称裸奇点的半经典阶段仅辐射约一个普朗克能量，表明粒子产生可忽略不计。
• 相比之下，黑洞会经历长时间的半经典蒸发，持续释放显著能量，直至残留一个普朗克质量的残余物。
• 裸奇点极低的能量辐射表明其最终演化无法用半经典引力描述，必须依赖完整的量子引力理论。
• 结果表明，球面对称坍缩形成的裸奇点并非通过量子辐射可观测的天体物理候选体，而黑洞则相反。
• 该行为在不同物质模型（尘埃、标量场）下均成立，表明其为球面对称裸奇点形成的普遍特征。
• 非球面对称裸奇点可能表现出截然不同的粒子产生，甚至可能引发爆炸性辐射，但目前仍理解不足。