Hydrodynamical Equations for a Collapsing Object with Spherical Symmetry in Terms of the Scalar-Tensor Theory of Gravity

概要

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Because of a possible relevance of the scalar-tensor theory of gravity to the problem of gravitational collapse, an attempt is made to cast the Brans-Dicke field equations for a gaseous sphere without energy flow into the Lagrangian hydrodynamical equations, in comparison with their general relativistic counterparts due to Misner and Sharp. As regards the exterior solution, the Brans solution of type I (specialized by the author) is adopted because of its resemblance to the Schwarzschild solution in general relativity. The junction conditions at the stellar surface are also set up, which consist of our previous ones and the other two concerning the inertial scalar and its first derivatives. The presence of the inertial scalar makes a simple generalization of Misner-Sharp mass function useless (because its boundary value cannot be constant in time), so that a new mass function is introduced in a heuristic manner. In order to show its appropriateness, the gravitational collapse of a fluid sphere with uniform density, uniform scalar and negligible pressure corresponding to the Oppenheimer-Snyder model in general relativity is dealt with, in spite of the fact that it violates one (concerning the first derivatives of the inertial scalar) of our junction conditions. Several points to be noticed in the numerical analysis of our hydrodynamical equations are also touched upon.
理論物理学刊行会の論文
1972-03-25