arXiv 2209.148732022-09gr-qchep-thmath-phmath.MP

五维静止黑洞周围的光环与裸奇点

Light Rings around Five Dimensional Stationary Black Holes and Naked Singularities

Aydin Tavlayan, Bayram Tekin

备注：: 11 pages, 7 figures, v2 matches the published version
发表信息：: Phys. Rev. D 107, 024016 (2023)
DOI：: 10.1103/PhysRevD.107.024016

摘要：

时空中光环的存在与黑洞视界的存在和可观测量（如环缩和阴影）密切相关。黑洞与非真空超压缩物体相比，有着相当独特的环境。为此，最近[P. V. P. Cunha和C.A.R. Herdeiro，Phys. Rev. Lett. \textbf{124}，181101（2020）]的拓扑参数，独立于基本的引力理论，被用来证明{ \it 4}维渐近平坦、静止、轴对称、非极值黑洞的Killing视界外存在不稳定的光环.在这里，我们将这些论点推广到五维静止黑洞。一般在五维空间中，有两种可能的守恒角动量，因此四维空间的讨论没有逐字扩展到五维空间;然而，我们证明了对于一个静止的黑洞，每个旋转方向都有一个光环。我们给出了静态和Myers-Perry旋转黑洞的例子。我们还表明，当黑洞的视界消失，奇点变得赤裸裸的，只有一个光环幸存下来，类似的现象也发生在四维空间，这可能允许测试宇宙审查假说。

英文摘要：

The existence of light rings in a spacetime is closely related to the existence of black hole horizons and observables such as the ringdown and the shadow. Black holes, compared to nonvacuum ultracompact objects, have rather unique environments. To this aim, recently [P.V.P. Cunha and C.A.R. Herdeiro, Phys. Rev. Lett. \textbf{124}, 181101 (2020)] topological arguments, independent of the underlying gravity theory, were developed to prove the existence of unstable light rings outside the Killing horizon of {\it four} dimensional asymptotically flat, stationary, axisymmetric, nonextremal black holes. Here we extend these arguments to five-dimensional stationary black holes. Generically in five dimensions, there are two possible conserved angular momenta, hence the four-dimensional discussion does not extend verbatim to five dimensions; nevertheless, we prove that there is a light ring for each rotation sense for a stationary black hole. We give the static and the Myers-Perry rotating black holes as examples. We also show that when the horizon of the black hole disappears and the singularity becomes naked, only one of the light rings survives; a similar phenomenon also occurs in four dimensions which might allow testing the cosmic censorship hypothesis.

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英文摘要：

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