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Static solutions of the combined Dirac-electromagnetic-gravitational field equations O'Hanlon, John David

Abstract

It is assumed that charged, spin-½, matter distributions can be described in terms of a Dirac spinor field interacting with the electromagnetic field and a scalar gravitational field. The field equations and the energy-momentum tensor are found from an action principle. The fields are not quantized. The field equations are examined and various limiting forms discussed. This thesis deals particularly with the time-independent spherically-symmetric case. Solutions are found for the exterior region of a charged gravitating sphere. The behaviour of these solutions depend on the value of the charge-mass ratio. When this ratio has the value (4πG)½, where G is the gravitational constant, the entire system can be solved analytically. The ensuing solution, called the Weyl-Majumdar solution, is obtained and discussed. When the charge-mass ratio is smaller than (4πG)½, normalised solutions are found which yield electrostatic and gravitational potentials singular at the origin. The matter density is well-behaved everywhere. Normalised solutions were not found for larger charge-mass ratios. The significance of the solutions, and the accuracy of the numerical technique are discussed. Alternative Lagrangian densities are considered which may yield non-singular solutions.

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