Kavli Affiliate: Robert M. Wald
| First 5 Authors: Daine L. Danielson, Gautam Satishchandran, Robert M. Wald, Robert J. Weinbaum,
| Summary:
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 composed 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 $r=0$.
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