Stellar explosion in the weak field approximation of the Brans-Dicke theory

Abstract

We treat a very crude model of an exploding star, in the weak field approximation of the Brans-Dicke theory, in a scenario that resembles some characteristics data of a Type Ia Supernova. The most noticeable feature, in the electromagnetic component, is the relationship between the absolute magnitude at maximum brightness of the star and the decline rate in one magnitude from that maximum. This characteristic has become one of the most accurate method to measure luminosity distances to objects at cosmological distances. An interesting result is that the active mass associated with the scalar field is totally radiated to infinity, representing a mass loss in the ratio of the "tensor" component to the scalar component of 1 to $(2 \omega + 3)$ ($\omega$ is the Brans-Dicke parameter), in agreement with a general result of Hawking. Then, this model shows explicitly, in a dynamical case, the mechanism of radiation of scalar field, which is necessary to understand the Hawking result.