Effect of Gravitational Scalar Field on High-Density Star Structure

The theory of gravitation allowing variation of the gravitational constant $G$ by means of a scalar field introduced by Brans and Dicke is applied in the case of a fluid sphere in gravitational equilibrium. The departure of the mass-radius relation in this theory from the Einstein theory is investigated for different values of the constant $\omega$ and for high central-energy densities in completely degenerate stars (neutron stars).