Static conformally flat solutions in a general scalar-tensor theory of gravitation
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Explicit field equations in the general scalar-tensor theory of gravitation proposed by Nordtvedt are obtained with the aid of a static spherically symmetric conformally flat metric. Exact static solutions of Nordtvedt-Barker field equations both in vacuum and in the presence of a source-free electromagnetic field are presented and studied. It is shown that there are no spherically symmetric static conformally flat solutions of Nordtvedt-Barker field equations representing perfect fluid distribution with disordered radiation obeying the equation of stateρ=3p, except for the trivial empty flat space-time of Einstein's theory.
KeywordsRadiation Electromagnetic Field Static Solution Field Equation Differential Geometry
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