标题： 非圆Kerr测地线解的轨道形状的完整表征，其具有圆轨道运动常数 显示英文标题

标题： A complete characterisation of the orbital shapes of the non-circular Kerr geodesic solutions with circular orbit constants of motion

摘要： 我们提供了描述克尔时空中方向向内和向外螺旋轨道族的解析解。 这些解是精确的，并且因其简洁性而引人注目。 这些轨道都具有在半径$r_c$处圆轨道的角动量和能量，但不受限于保持在该圆轨道上，这一特性在牛顿引力中是不可能的。 我们证明存在五种不同的轨道解最终终止于黑洞奇点，以及三种解要么逃逸到无限远，要么保持束缚。 不同的轨道解完全由黑洞自旋$a$和$r_c$的位置来表征。 光子轨道在进入或离开其（不稳定的）圆轨道半径时也被分析。 这些轨道具有与本文讨论的类双曲线质量粒子轨道相似的性质。 显示英文摘要

摘要： We present analytical solutions describing a family of both inwardly and outwardly spiralling orbits in the Kerr spacetime. The solutions are exact, and remarkable for their simplicity. These orbits all have the angular momentum and energy of a circular orbit at some radius $r_c$, but are not restricted to remaining on that circular orbit, a property not possible in Newtonian gravity. We demonstrate that there are five distinct orbital solutions which terminate at the black hole singularity, and three solutions which either escape to infinity or remain bound. The different orbital solutions are characterised entirely by the black hole spin $a$ and the location of $r_c$. Photon orbits spiralling into or out of their (unstable) circular orbit radii are also analysed. These have properties similar to the hyperbolic class of massive particle orbits discussed herein.