We introduce the relativistic version of the well-known Henon’s isochrone spherical models: static spherically symmetrical spacetimes in which all bounded trajectories are isochrone in Henon’s sense, i.e., their radial periods do not depend on their angular momenta. Analogously to the Newtonian case, these “isochrone spacetimes” have as particular cases the so-called Bertrand spacetimes, in which all bounded trajectories are periodic. We propose a procedure to generate isochrone spacetimes by means of an algebraic equation, present explicitly several families of these spacetimes, and discuss briefly their main properties. We identify, in particular, the family whose Newtonian limit corresponds to the Henon’s isochrone potentials and that could be considered as the relativistic extension of the original Henon’s proposal for the study of globular clusters. Nevertheless, isochrone spacetimes generically violate the weak energy condition and may exhibit naked singularities, challenging their physical interpretation in the context of General Relativity.

我们介绍了著名的 Henon 等时球面模型的相对论版本：静态球对称时空，其中所有有界轨迹在 Henon 意义上都是等时的，即，它们的径向周期不取决于它们的角动量。类似于牛顿的情况，这些“等时时空”具有所谓的伯特兰时空作为特殊情况，其中所有有界轨迹都是周期性的。我们提出了一个通过代数方程生成等时时空的程序，明确地展示了这些时空的几个族，并简要讨论了它们的主要性质。我们特别确定了牛顿极限对应于 Henon 等时势的族，并且可以将其视为原始 Henon 球状星团研究建议的相对论扩展。然而，等时时空通常违反弱能量条件，并可能表现出裸奇点，挑战它们在广义相对论背景下的物理解释。