On generic parametrizations of spinning black-hole geometries
On generic parametrizations of spinning black-hole geometries
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DOI：
10.1103/physrevd.89.064007
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发表时间：
2014-01
影响因子：
5
通讯作者：
V. Cardoso;P. Pani;João Rico
中科院分区：
文献类型：
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作者：
V. Cardoso;P. Pani;João Rico
构造一个自旋几何的通用参数化，使其能连续地与Kerr度规相匹配，是广义相对论中一个重要的公开问题。它的分辨率不仅仅是学术兴趣，因为它允许参数化和量化与无毛定理的可能偏差。人们提出了各种解决这个问题的方法，但都有各自的（严重的）局限性。本文讨论了Johannsen和Psaltis最近提出的度规，指出：（1）原来的度规只描述了保持非自旋几何的视界面积-质量关系的修正;（2）通过引入一个新的参数，可以放松这种不必要的限制，这个新的参数实际上在后牛顿和强场区域都起主导作用;（iii）在这个框架内，我们构建了最通用的旋转黑洞几何，其中包含两倍的（无限）参数的原始度规;（iv）在强场制度，所有参数大致同等重要。这一事实在高速旋转的黑洞中引入了严重的简并问题。最后，我们证明，即使是我们的推广未能描述少数已知的旋转黑洞度量在修改后的重力。
The construction of a generic parametrization of spinning geometries which can be matched continuously to the Kerr metric is an important open problem in General Relativity. Its resolution is more than of academic interest, as it allows to parametrize and quantify possible deviations from the no-hair theorem. Various approaches to the problem have been proposed, all with their own (severe) limitations. Here we discuss the metric recently proposed by Johannsen and Psaltis, showing that (i) the original metric describes only corrections that preserve the horizon area-mass relation of nonspinning geometries; (ii) this unnecessary restriction can be relaxed by introducing a new parameter that in fact dominates in both the post-Newtonian and strong-field regimes; (iii) within this framework, we construct the most generic spinning black-hole geometry which contains twice as many the (infinite) parameters of the original metric; (iv) in the strong-field regime, all parameters are roughly equally important. This fact introduces a severe degeneracy problem in the case of highly-spinning black holes. Finally, we prove that even our generalization fails to describe the few known spinning black-hole metrics in modified gravity.