arXiv 0801.08892008-01gr-qcastro-phhep-th

黑洞可以有卷曲的毛发

Black holes can have curly hair

K. A. Bronnikov, O. B. Zaslavskii

备注：: 5 pages, no figures. Some discussion added, misprints corrected
发表信息：: Phys.Rev.D78:021501,2008
DOI：: 10.1103/PhysRevD.78.021501

摘要：

本文研究了静态球对称黑洞与经典物质在径向压力密度比p_r/ρ= w（u）下的平衡条件，其中u为径向坐标。它表明，这样的平衡是可能的，在两种情况下：（i）众所周知的情况w \to -1作为$u \to u_h（地平线），即，“真空”物质，其中ρ（u_h）可以不为零;（ii）w \to-1/（1+2k）和ρ \sim（u-u_h）^k作为u \to u_h，其中k>0是正整数（在一般情况下k=1，w=-1/3）。这两种物质的非相互作用混合物也可以存在。整个推理是局部的，因此结果不依赖于任何全局或渐近条件。特别是，它们意味着静态的黑洞不能生活在非负压和非密度的恒星内部。作为一个例子，一个各向同性流体的精确解w = -1/3（即，无序宇宙弦的流体），有或没有真空物质，提出。

英文摘要：

We study equilibrium conditions between a static, spherically symmetric black hole and classical matter in terms of the radial pressure to density ratio p_r/ρ= w(u), where u is the radial coordinate. It is shown that such an equilibrium is possible in two cases: (i) the well-known case w\to -1 as $u\to u_h (the horizon), i.e., "vacuum" matter, for which ρ(u_h) can be nonzero; (ii) w \to -1/(1+2k) and ρ\sim (u-u_h)^k as u\to u_h, where k>0 is a positive integer (w=-1/3 in the generic case k=1). A non-interacting mixture of these two kinds of matter can also exist. The whole reasoning is local, hence the results do not depend on any global or asymptotic conditions. They mean, in particular, that a static black hole cannot live inside a star with nonnegative pressure and density. As an example, an exact solution for an isotropic fluid with w = -1/3 (that is, a fluid of disordered cosmic strings), with or without vacuum matter, is presented.

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