Stellar Structure in Scalar-Tensor Gravity

Abstract

Stellar structure is investigated within the framework of scalar-tensor gravity. Novel perturbative analytical results are obtained for constant-density stars and for Newtonian polytropes in the quadratic model with coupling function A(Φ) = exp(αΦ+1/2βΦ^2). They are compared to full numerical calculations, and possible applications to main-sequence stars, white dwarfs, and the Chandrasekhar mass are indicated. It is found that Buchdahl's theorem is violated in Brans-Dicke theory for stars with exponentially-decaying density profiles. However, the mass-to-radius ratio M/R tends to the constant-density value in a certain limit. It is observed that for β < 0, there exists a maximum value of η = P0/ρo for constant-density stars, where P0 and ρ0 are the central pressure and density, respectively. It is conjectured that if such a maximum value also exists for other equations of state, and is less than the constant-density maximum value, then knowledge of P/ρ in the centre of a star can be used to constrain β.