How do spherical black holes grow monopole hair?
How do spherical black holes grow monopole hair?
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DOI：
10.1103/physrevd.105.064041
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发表时间：
2022-01
影响因子：
5
通讯作者：
Abhishek Hegade K. R.-Abhishek-Hegade-K. R.-2133943042;E. Most;J. Noronha;Helvi Witek;N. Yunes
中科院分区：
文献类型：
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作者：
Abhishek Hegade K. R.-Abhishek-Hegade-K. R.-2133943042;E. Most;J. Noronha;Helvi Witek;N. Yunes
在某些修正的艾德引力理论中，黑洞包含一个耦合到曲率不变量的标量场，已知黑洞具有（标量）标量毛发，而非黑洞时空（如中子星）则没有。因此，当中子星星坍缩成黑洞时，标量头发必须生长，直到它沉降到具有（微）头发的静止黑洞解。在本文中，我们详细研究了这一过程，并表明标量头发的生长与事件视界的出现和生长（在表观视界形成之前）有关，这迫使标量模式否则（在未来）会变得发散。我们首先对一大类修正的艾德理论严格地证明了这一结果，然后通过研究两种背景下标量Gauss-Bonnet引力中标量场的时间演化来证明这一结果：（i）坍缩的Oppenheimer-Snyder背景，（ii）坍缩的中子星星背景。在情况（i）中，我们通过解析找到了一个精确的标量场解，而在情况（ii）中，我们通过数值求解了标量场的时间演化，这两种情况都支持上面给出的结论。我们的结果表明，在一大类改进的艾德引力理论中，标量场辐射爆发的发射是黑洞形成的必要条件。
Black holes in certain modified gravity theories that contain a scalar field coupled to curvature invariants are known to possess (monopole) scalar hair while non-black-hole spacetimes (like neutron stars) do not. Therefore, as a neutron star collapses to a black hole, scalar hair must grow until it settles to the stationary black hole solution with (monopole) hair. In this paper, we study this process in detail and show that the growth of scalar hair is tied to the appearance and growth of the event horizon (before an apparent horizon forms), which forces scalar modes that would otherwise (in the future) become divergent to be radiated away. We prove this result rigorously in general first for a large class of modified theories, and then we exemplify the results by studying the temporal evolution of the scalar field in scalar Gauss-Bonnet gravity in two backgrounds: (i) a collapsing Oppenheimer-Snyder background, and (ii) a collapsing neutron star background. In case (i), we find an exact scalar field solution analytically, while in case (ii) we solve for the temporal evolution of the scalar field numerically, with both cases supporting the conclusion presented above. Our results suggest that the emission of a burst of scalar field radiation is a necessary condition for black hole formation in a large class of modified theories of gravity.