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arXiv 1202.6682hep-thgr-qc
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无幽灵双引力理论中的多毛黑洞

Hairy black holes in the ghost-free bigravity theory

Mikhail S. Volkov

摘要:

我们在最近提出的无鬼理论中研究了两个引力子的黑洞,其中一个引力子有质量,另一个引力子无质量。这些黑洞拥有一个规则的事件视界,这是共同的两个度量,并具有相同的值的表面重力和霍金温度相对于每个度量。由两个度量测量的事件视界半径的比率是标记解的自由参数。我们提出了一个数字的证据,他们的存在,并发现,他们包括几个类。每一类中的黑洞在无穷远处接近相同的AdS型渐近,但在短程大质量模式所在的事件视界附近彼此不同。此外,还有一些解在离视界有限的适当距离处显示出曲率奇异性。对于某些特殊的解,引力子的质量可能变成有效的虚数,导致在无穷远处围绕平坦度规的振荡。我们发现的唯一一个渐近平坦的黑洞--通过识别两个度规得到的史瓦西解--似乎是例外的,因为即使稍微改变它的视界边界条件,也会完全改变无穷远处的渐近行为。我们还构建了全球正规的解决方案,描述“块的纯重力”,可以被视为黑洞残余物的限制,事件视界收缩。最后,通过引入一个物质源,我们得到了全局正则且渐近平坦的解,在有限区域内表现出广义相对论恢复的Vainstein机制。

英文摘要:

We study black holes in the recently proposed ghost-free theory with two gravitons, one of which is massive and another is massless. These black holes possess a regular event horizon which is common for both metrics and has the same values of the surface gravity and Hawking temperature with respect to each metric. The ratio of the event horizon radii measured by the two metrics is a free parameter that labels the solutions. We present a numerical evidence for their existence and find that they comprise several classes. Black holes within each class approach the same AdS-type asymptotic at infinity but differ from each other in the event horizon vicinity where the short-range massive modes reside. In addition, there are solutions showing a curvature singularity at a finite proper distance from the horizon. For some special solutions the graviton mass may become effectively imaginary, causing oscillations around the flat metric at infinity. The only asymptotically flat black hole we find -- the Schwarzschild solution obtained by identifying the two metrics -- seems to be exceptional, since changing even slightly its horizon boundary conditions completely changes the asymptotic behavior at infinity. We also construct globally regular solutions describing `lumps of pure gravity' which can be viewed as black hole remnants in the limit where the event horizon shrinks. Finally, adding a matter source we obtain globally regular and asymptotically flat solutions exhibiting the Vainstein mechanism of recovery of General Relativity in a finite region.

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