标题： 一个正则度量并不保证时空的正则性 显示英文标题

标题： A regular metric does not ensure the regularity of spacetime

摘要： 在本文中，我们试图阐明一个正则度规可以生成奇异时空。 我们的工作集中在静态且球对称的时空上，在这种情况下，当黎曼张量的所有分量都是有限的时候，正则性存在。 文献中有一些工作假设度规的正则性是保证其正则性的充分条件。 我们研究了三个正则度规，并表明它们具有奇异时空。 我们还表明，这些度规可以解释为黑洞的解，其物质源由非线性电动力学描述。 我们分析了测地线方程和Kretschmann标量以验证曲率奇点的存在。 此外，我们使用了线元的变换$r \rightarrow \sqrt{r^2+a^2}$，这是文献中已知的时空正则化过程。 然后我们重新计算测地线方程和Kretschmann标量，并表明所有度规现在都具有正则时空。 这个过程将它们转化为黑洞反弹解，其中两个是新的。 我们讨论了所有模型的事件视界性质和能量条件。 显示英文摘要

摘要： In this paper we try to clarify that a regular metric can generate a singular spacetime. Our work focuses on a static and spherically symmetric spacetime in which regularity exists when all components of the Riemann tensor are finite. There is work in the literature that assumes that the regularity of the metric is a sufficient condition to guarantee it. We study three regular metrics and show that they have singular spacetime. We also show that these metrics can be interpreted as solutions for black holes whose matter source is described by nonlinear electrodynamics. We analyze the geodesic equations and the Kretschmann scalar to verify the existence of the curvature singularity. Moreover, we use a change of the line element $r \rightarrow \sqrt{r^2+a^2}$, which is a process of regularization of spacetime already known in the literature. We then recompute the geodesic equations and the Kretschmann scalar and show that all metrics now have regular spacetime. This process transforms them into black-bounce solutions, two of which are new. We have discussed the properties of the event horizon and the energy conditions for all models.