Title: The Blázquez-Salcedo, Knoll, and Radu Wormholes Are Not Solutions to the Einstein-Dirac-Maxwell Equations Show Chinese title

Title: Blázquez-Salcedo、Knoll 和 Radu 虫洞不是爱因斯坦-狄拉克-麦克斯韦方程的解

Abstract: Recently, Bl\'azquez-Salcedo, Knoll, and Radu (BSKR) have given a class of static, spherically symmetric traversable wormhole spacetimes with Dirac and Maxwell fields. The BSKR wormholes are obtained by joining a classical solution to the Einstein-Dirac-Maxwell (EDM) equations on the "up" side of the wormhole ($r \geq 0$) to a corresponding solution on the "down" side of the wormhole ($r \leq 0$). However, it can be seen that the BSKR metric fails to be $C^3$ on the wormhole throat at $r=0$. We prove that if the matching were done in such a way that the resulting spacetime metric, Dirac field, and Maxwell field comprised a solution to the EDM equations in a neighborhood of $r=0$, then all of the fields would be smooth at $r=0$ in a suitable gauge. Thus, the BSKR wormholes cannot be solutions to the EDM equations. The failure of the BSKR wormholes to solve the EDM equations arises both from the failure of the Maxwell field to satisfy the required matching conditions (which implies the presence of an additional shell of charged matter at $r=0$) and, more significantly, from the failure of the Dirac field to satisfy required matching conditions (which implies the presence of a spurious source term for the Dirac field at $r=0$). Show Chinese abstract

Abstract: 最近，Blázquez-Salcedo、Knoll 和 Radu（BSKR）给出了一类具有狄拉克场和麦克斯韦场的静态、球对称的可穿越虫洞时空。 BSKR 虫洞是通过将爱因斯坦-狄拉克-麦克斯韦（EDM）方程的经典解在虫洞的“上”侧（$r \geq 0$）与虫洞的“下”侧（$r \leq 0$）的相应解连接起来得到的。 然而，可以观察到，在虫洞喉部的$r=0$处，BSKR 度规无法满足$C^3$。 我们证明，如果以一种方式完成匹配，使得所得的时空度规、狄拉克场和麦克斯韦场在$r=0$附近构成 EDM 方程的解，那么在适当的规范下，所有场都会在$r=0$处光滑。 因此，BSKR 虫洞不能是 EDM 方程的解。 BSKR虫洞无法解决EDM方程的问题既源于麦克斯韦场未能满足所需的匹配条件（这表明在$r=0$处存在额外的带电物质壳层），也更显著地源于狄拉克场未能满足所需的匹配条件（这表明在$r=0$处存在狄拉克场的虚假源项）。