Mathematics
Scientific paper
May 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983gregr..15..449v&link_type=abstract
General Relativity and Gravitation (ISSN 0001-7701), vol. 15, May 1983, p. 449-446. Research supported by the Royal Society of L
Mathematics
7
Charged Particles, Relativity, Scalars, Spheres, Tensor Analysis, Unified Field Theory, Conformal Mapping, Einstein Equations, Electrostatics, Gravitation Theory, Maxwell Equation, Reissner-Nordstrom Solution, Riccati Equation, Singularity (Mathematics)
Scientific paper
The charged static and spherically symmetric vacuum field in the general Bergmann-Wagoner-Nordtvedt (BWN) theory of gravity is studied. By a conformal transformation, the field equations are brought into a standard form, which permits a decoupling of the differential equations for the relevant quantities. Using the electrostatic potential as an independent variable results in a particular Ricatti equation, the general solutions of which can be explicitly written down, for positive and for negative scalar energy densities. In distinction with the Reissner-Nordstrom solutions, all nontrivial positive energy BWN theories are shown to possess naked time-like singularities, whereas the negative energy theories admit a peculiar nonsingular solution, which may be interpreted as a field theoretical model of a charged particle. It is argued that the absence of an event horizon in the other solutions is not a consequence of the assumption of spherical symmetry; event horizons are absent in any static geometry which is a nontrivial solution of the (charged or uncharged) BWN equations with positive definite scalar density.
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