在可行的洛伦兹违反引力中的旋转黑洞：轻松找到精确解
Rotating Black Holes in a Viable Lorentz-Violating Gravity: Finding Exact Solutions Without Tears
AI总结：
研究在可行的洛伦兹违反引力中找旋转黑洞精确解的方法，通过两步程序找到解，包括奇异区域、视界等情况，还探讨了电磁荷及与观测的一致性，附录给出了线元唯一性、解的类型及方程不可分离性等结论。
摘要：
我们引入了一种两步程序来轻松找到克尔型旋转黑洞解。将霍拉瓦引力的低能部分视为四维中可行的洛伦兹违反引力，其允许不同的引力速度，我们找到了精确的旋转黑洞解（有或没有宇宙学常数）。发现奇异区域从博伊尔 - 林德奎斯特坐标中\(r = 0\)处的环奇点延伸到\(r < 0\)区域。存在两个\(g^{rr}=0\)的 Killing 视界且黑洞热力学定律仍然有效。仅当考虑特定电磁耦合时能找到带电磁荷的旋转黑洞解，此时光速与引力速度相同。这种选择使我们的洛伦兹违反引力与最近观测到的引力波和伽马射线暴信号的时间延迟一致。此外，附录中表明：（a）不变线元\(ds^2\)在 Diff_F 下的唯一性，与洛伦兹违反作用相反；（b）解是具有四个不同主零向量的佩特罗夫 I 型；（c）测地线粒子的哈密顿 - 雅可比方程不可分离。
英文摘要：
We introduce a two-step procedure for finding Kerr-type rotating black hole solutions without tears. Considering the low-energy sector of Horava gravity as a viable Lorentz-violating gravity in four dimensions which admits a different speed of gravity, we find the exact rotating black hole solutions (with or without cosmological constant). We find that the singular region extends to r < 0 region from the ring singularity at r = 0 in Boyer-Lindquist coordinates. There are two Killing horizons where g^rr = 0 and the black hole thermodynamics laws are still valid. We find the rotating black hole solutions with electromagnetic charges only when we consider the noble electromagnetic couplings, in such a way that the speed of light is the same as the speed of gravity. With the noble choice of couplings, our Lorentz-violating gravity can be consistent with the recently-observed time delay of the coincident GW and GRB signals. Furthermore, in Appendices, we show that (a) the uniqueness of the invariant line element ds^2 under Diff_F, contrary to LV action, (b) the solutions are the Petrov type I with four distinct principal null vectors, and (c) the Hamilton-Jacobi equation for the geodesic particles are not separable.
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