论文标题
LQC中黑洞内部的量子动力学
Quantum dynamics of the black hole interior in LQC
论文作者
论文摘要
已经提出，按照环量子宇宙学的技术进行量化时，均匀的黑洞内部时空的奇异性被黑白的孔过渡所取代。但是，到目前为止，该结果仅使用有效的经典演化方程得出，并取决于对哈密顿约束的所谓聚合方案的细节。在这里，我们建议使用一般相对论的单型构造来研究此迷你苏联空间模型的完整量子动力学。当应用于此类宇宙学模型时，单模型的重力可以通过提供遵循Schrödinger进化方程的真正的哈密顿量来使时间问题变得琐碎。通过选择适合此设置的变量，我们展示了如何编写半古典状态，与后期的Wheeler-Dewitt理论一致，以及如何通过循环量子宇宙学通过可能的奇异性演变，同时保持尖锐的峰值。这为研究这些模型的完整量子动态提供了非常简单的设置，该设置可以希望可以驯服正则化的歧义。
It has been suggested that the homogeneous black hole interior spacetime, when quantized following the techniques of loop quantum cosmology, has a resolved singularity replaced by a black-to-white hole transition. This result has however been derived so far only using effective classical evolution equations, and depends on details of the so-called polymerization scheme for the Hamiltonian constraint. Here we propose to use the unimodular formulation of general relativity to study the full quantum dynamics of this mini-superspace model. When applied to such cosmological models, unimodular gravity has the advantage of trivializing the problem of time by providing a true Hamiltonian which follows a Schrödinger evolution equation. By choosing variables adapted to this setup, we show how to write semi-classical states agreeing with that of the Wheeler-DeWitt theory at late times, and how in loop quantum cosmology they evolve through the would-be singularity while remaining sharply peaked. This provides a very simple setup for the study of the full quantum dynamics of these models, which can hopefully serve to tame regularization ambiguities.
