Quantum Singularity in Quasiregular Spacetimes, as Indicated by Klein-Gordon, Maxwell and Dirac Fields

Abstract

Klein-Gordon, Maxwell and Dirac fields are studied in quasiregular spacetimes, those space-times containing a classical quasiregular singularity, the mildest true classical singularity [G. F. R. Ellis and B. G. Schmidt, Gen. Rel. Grav. 8, 915 (1977)]. A class of static quasiregular spacetimes possessing disclinations and dislocations [R. A. Puntigam and H. H. Soleng, Class. Quantum Grav. 14, 1129 (1997)] is shown to have field operators which are not essentially self-adjoint. This class of spacetimes includes an idealized cosmic string, i.e. a four-dimensional spacetime with a conical singularity [L. H. Ford and A. Vilenkin, J. Phys. A: Math. Gen. 14, 2353 (1981)] and a Gal'tsov/Letelier/Tod spacetime featuring a screw dislocation [K. P. Tod, Class. Quantum Grav. 11, 1331 (1994); D. V. Gal'tsov and P. S. Letelier, Phys. Rev. D 47, 4273 (1993)]. The definition of G. T. Horowitz and D. Marolf [Phys. Rev. D52, 5670, (1995)] for a quantum-mechanically singular spacetime is one in which the spatial-derivative operator in the Klein-Gordon equation for a massive scalar field is not essentially self-adjoint. The definition is extended here, in the case of quasiregular spacetimes, to include Maxwell and Dirac fields. It is shown that the class of static quasiregular spacetimes under consideration is quantum-mechanically singular independent of the type of field.