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Consistency of equations of motion in conformal frames

Four dimensional scalar-tensor theory is considered within two conformal frames, the Jordan frame (JF) and the Einstein frame (EF). The actions for the theory are equivalent and equations of motion can be obtained from each action. It is found that the JF equations of motion, expressed in terms of EF variables, translate directly into and agree with the EF equations of motion obtained from the EF action, provided that certain simple consistency conditions are satisfied, which is always the case. The implication is that a solution set obtained in one conformal frame can be reliably translated into a solution set for the other frame, and therefore the two frames are, at least, mathematically equivalent.