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arXiv 0711.3145gr-qchep-th
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黑洞准正规模谱的物理解释

The physical interpretation of the spectrum of black hole quasinormal modes

Michele Maggiore

摘要:

当经典黑洞受到微扰时,它的弛豫由一组复频率为ω= ω_R+iω_I的拟正规模控制.我们证明了这种行为与实频率为(ω_R^2+ω_I^2)^{1/2}而不是简单的ω_R的阻尼谐振子的行为相同。由于对于高激发模,ω_I >> ω_R,这一观测结果极大地改变了对黑洞光谱的物理理解,并迫使人们重新审视文献中的各种结果。特别地,通过修改Hod的推导,我们发现史瓦西黑洞的视界面积以单位ΔA=8π \lpl^2量化,其中\lpl是普朗克长度(与原始结果ΔA=4 \log(3)\lpl^2相反)。由此产生的面积量子化并没有遭受许多困难的原始建议;特别是,它是一个内在的属性的黑洞,独立的自旋的扰动。

英文摘要:

When a classical black hole is perturbed, its relaxation is governed by a set of quasinormal modes with complex frequencies ω= ω_R+iω_I. We show that this behavior is the same as that of a collection of damped harmonic oscillators whose real frequencies are (ω_R^2+ω_I^2)^{1/2}, rather than simply ω_R. Since, for highly excited modes, ω_I >> ω_R, this observation changes drastically the physical understanding of the black hole spectrum, and forces a reexamination of various results in the literature. In particular, adapting a derivation by Hod, we find that the area of the horizon of a Schwarzschild black hole is quantized in units ΔA=8π\lpl^2, where \lpl is the Planck length (in contrast with the original result ΔA=4\log(3) \lpl^2). The resulting area quantization does not suffer from a number of difficulties of the original proposal; in particular, it is an intrinsic property of the black hole, independent of the spin of the perturbation.

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