Black holes in full quantum gravity
Black holes in full quantum gravity
复制标题
全量子引力下的黑洞
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
C. Rovelli
中科院分区：
文献类型：
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作者：
K. Krasnov;C. Rovelli
量子黑洞已经在量子引力和弦理论中使用各种半经典或背景相关的方法进行了广泛的研究。我们探索在完整的非微扰量子理论中研究黑洞的可能性，而不需要重复半经典的考虑，并且在圈量子引力的背景下。我们提出了量子黑洞的定义：不影响无穷远可观测量的量子自由度的集合。根据这个定义，对于无穷远处的观察者来说，黑洞是由 SU(2) 交织算子描述的。这种交织体的希尔伯特空间的维数随着视界面积呈指数增长。这些考虑因素揭示了对黑洞熵有贡献的微观状态的物理性质。特别是，可以看出，计算熵的微观状态具有描述不同视界形状的解释。这里描述的黑洞微观状态空间与最近由 Engle 等人 (2009, arXiv:0905.3168) 和不久前由 Smolin (1995, J. Math. Phys. 36 6417) 得出的空间相关，但在这里直接在完整的量子理论中获得。
Quantum black holes have been studied extensively in quantum gravity and string theory, using various semiclassical or background-dependent approaches. We explore the possibility of studying black holes in the full non-perturbative quantum theory, without recurring to semiclassical considerations, and in the context of loop quantum gravity. We propose a definition of a quantum black hole as the collection of the quantum degrees of freedom that do not influence observables at infinity. From this definition, it follows that for an observer at infinity a black hole is described by an SU(2) intertwining operator. The dimension of the Hilbert space of such intertwiners grows exponentially with the horizon area. These considerations shed some light on the physical nature of the microstates contributing to the black hole entropy. In particular, it can be seen that the microstates being counted for the entropy have the interpretation of describing different horizon shapes. The space of black hole microstates described here is related to the one arrived at recently by Engle et al (2009, arXiv:0905.3168) and sometime ago by Smolin (1995, J. Math. Phys. 36 6417), but obtained here directly within the full quantum theory.