Solutions of a scalar–tensor theory from Einstein’s theory

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Abstract
The vacuum field equations of a scalar–tensor theory proposed by Sen and Dunn are investigated. The metric coefficients are assumed to be functions of three variables only. It is then shown that if one assumes a functional relationship between some one of the metric coefficients and the scalar function, one can find a solution of the vacuum field equations of Sen and Dunn’s scalar–tensor theory in terms of a solution of the vacuum field equations of Einstein’s theory. This result is applied to some well‐known solutions, viz., Schwarzschild solution, the static plane symmetric solution of Taub, the conformastat solution of Das, and the static axially symmetric solutions of Levi‐Civita and Curzon; and the corresponding solutions of the scalar–tensor theory are obtained.

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