The time-dependent problem in the Jordan-Brans-Dicke tensor-scalar theory of gravitation

We state the time-dependent problem in the Jordan-Brans-Dicke tensor-scalar theory of gravitation. We show that in the conformally corresponding space the equations of the problem have the same form as the Einstein equations with an extra source in the form of the components of the energy-momentum tensor of the scalar field. We discuss the question whether Birkhoff's theorem can hold in the Jordan-Brans-Dicke theory. We simultaneously obtain a formula that expresses the mass of an isolated static object as a function of the distribution of pressure of matter. We also discuss the integrability of the vacuum time-dependent equations of the Einstein theory.Translated fromAstrofizika, Vol. 37, No. 3, 1994.The authors are grateful to the participants in the seminar of the Department of Theoretical Physics of Erevan State University for helpful discussions. Two of the authors (VVP and GGA) worked with partial support from grant RY 6000 of the International Science Fund (Soros Foundation).