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arXiv 1503.03240gr-qcastro-ph.HE
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天体物理环境中黑洞的无毛定理

No-hair theorem for Black Holes in Astrophysical Environments

Norman Gürlebeck

摘要:

根据无毛定理,静态黑洞可以用史瓦西时空来描述,前提是没有其他的引力场源。然而,这一要求在天体物理现实场景中经常被违反,例如,如果黑洞是一个双星系统的一部分,或者如果它被一个吸积盘包围。在这些情况下,黑洞由于潮汐力而扭曲。尽管如此,无毛定理的后续表述仍然成立:扭曲黑洞对描述接近无穷大的引力场的多极矩的贡献,因此,所有的源都是史瓦西黑洞的贡献。它仍然没有头发。这意味着在黑洞中不存在诱导的多极矩,并且它的第二个勒夫数(用来测量扭曲的某些方面)消失了,就像在广义相对论的近似中已经显示的那样。但在这里,我们证明了这一性质的天体物理相关的黑洞在充分的广义相对论。

英文摘要:

According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.

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