arXiv 1108.46862011-08-23gr-qchep-th

黑洞附近谱维数的下界

Lower bound on the spectral dimension near a black hole

S. Carlip, D. Grumiller

备注：: 6 pp, 2 eps figs
发表信息：: Phys.Rev. D84 (2011) 084029
DOI：: 10.1103/PhysRevD.84.084029

摘要：

我们考虑一个蒸发的史瓦西黑洞，在这个框架中，时空的光谱维数从大距离处的4连续变化到小距离处的小于3的数，正如量子引力的各种方法所建议的那样。我们证明，蒸发停止时，视界半径达到一个尺度，在这个尺度上，时空成为有效的三维，并认为，观察者留在视界之外不能探测性能的黑洞在较小的尺度。这个结果是普遍的意义上说，它不依赖于作为扩散时间的函数的有效尺寸的细节。落入黑洞的观测者可以分辨更小的尺度，外部观测者在存在宇宙学常数的情况下也可以。然而，即使在这些情况下，我们也得到了有效维数的绝对界D>2，这在任何试图测量黑洞性质的尝试中都可以看到。

英文摘要：

We consider an evaporating Schwarzschild black hole in a framework in which the spectral dimension of spacetime varies continuously from four at large distances to a number smaller than three at small distances, as suggested by various approaches to quantum gravity. We demonstrate that the evaporation stops when the horizon radius reaches a scale at which spacetime becomes effectively 3-dimensional, and argue that an observer remaining outside the horizon cannot probe the properties of the black hole at smaller scales. This result is universal in the sense that it does not depend on the details of the effective dimension as a function of the diffusion time. Observers falling into the black hole can resolve smaller scales, as can external observers in the presence of a cosmological constant. Even in these cases, though, we obtain an absolute bound D>2 on the effective dimension that can be seen in any such attempt to measure the properties of the black hole.

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