Regular black holes are often geodesically incomplete when their extensions to negative values of the radial coordinate are considered. Here, we propose to use the Simpson–Visser method of regularising a singular spacetime, and apply it to a regular solution that is geodesically incomplete, to construct a geodesically complete regular solution. Our method is generic, and can be used to cure geodesic incompleteness in any spherically symmetric static regular solution, so that the resulting solution is symmetric in the radial coordinate. As an example, we illustrate this procedure using a regular black hole solution with an asymptotic Minkowski core. We study the structure of the resulting metric, and show that it can represent a wormhole or a regular black hole with a single or double horizon per side of the throat. Further, we construct a source Lagrangian for which the geodesically complete spacetime is an exact solution of the Einstein equations, and show that this consists of a phantom scalar field and a nonlinear electromagnetic field. Finally, gravitational lensing properties of the geodesically complete spacetime are briefly studied.

当考虑到径向坐标负值的扩展时，规则黑洞通常在测地线上是不完整的。在这里，我们建议使用正则化奇异时空的 Simpson-Visser 方法，并将其应用于测地线不完全正则解，以构造测地线完全正则解。我们的方法是通用的，可以用来解决任何球对称静态正则解中的测地线不完整性，从而使所得解在径向坐标上是对称的。作为示例，我们使用具有渐近 Minkowski 核的常规黑洞解来说明此过程。我们研究了所得度量的结构，并表明它可以代表虫洞或规则黑洞，喉部每侧具有单视界或双视界。此外，我们构造了一个源拉格朗日量，其中测地完整时空是爱因斯坦方程的精确解，并表明它由幻像标量场和非线性电磁场组成。最后，简要研究了测地完整时空的引力透镜特性。