纺锤形变形克尔黑洞的测地线与阴影
Geodesics and shadows of the spindle-deformed Kerr black hole
AI总结：
研究四维广义相对论中含参数\(B\)的纺锤形变形克尔黑洞时空，利用微扰分离方程研究其测地线运动与黑洞阴影，确定相关区域和轨道并与光线追踪比较，验证微扰处理并量化与克尔的偏差。
AI中文摘要：
最近，在四维广义相对论中构建了一个新的精确里奇平坦旋转黑洞解，其中一个额外参数\(B\)表征克尔几何的纺锤形变形。我们研究此时空的测地线运动和黑洞阴影。对于类时或类光测地线，哈密顿 - 雅可比方程并非完全可分离。然而，值得注意的是，在领先的非平凡阶\({\cal O}(B^2)\)，类光而非类时测地线变得可分离。在类时部分，纺锤形变形移动了最内稳定圆轨道并能产生一个最外稳定圆轨道。在类光部分，利用微扰分离方程，我们解析地确定了光子区域、赤道光子轨道和黑洞阴影，并将结果预测与精确时空中的直接光线追踪进行比较。数值结果验证了微扰处理并量化了与克尔的偏差。
英文摘要：
Recently, a new exact Ricci-flat rotating black-hole solution was constructed in four-dimensional general relativity, in which an additional parameter $B$ characterizes a spindle deformation of the Kerr geometry. We study geodesic motion and black-hole shadows in this spacetime. The Hamilton-Jacobi equation is not exactly separable for either timelike or null geodesics. Remarkably, however, at the leading nontrivial order, ${\cal O}(B^2)$, null but not timelike geodesics become separable. In the timelike sector, the spindle deformation shifts the innermost stable circular orbit and can give rise to an outermost stable circular orbit. In the null sector, exploiting the perturbatively separated equations, we analytically determine the photon region, equatorial photon orbits, and black-hole shadow, and compare the resulting predictions with direct ray tracing in the exact spacetime. The numerical results validate the perturbative treatment and quantify the deviations from Kerr.
