A pure geometric approach to stellar structure: Mass-radius relation

Abstract

This paper represents the second step towards understanding stellar structure using pure geometric tools. It is an attempt to get a theoretical expression for a mass–radius relation. The stellar model used has been obtained as an analytic solution of the field equations of a pure geometric field theory. The method suggested to get this relation is very simple. It depends mainly on a set of differential equations implying the vanishing of all components of a geometric material-energy tensor on a boundary of stellar configuration. The theoretical relation obtained is a linear one (R=βM)(R=βM) with one free parameter (β).(β). Comparison with observation, using a sample of lower main-sequence stars, members of binary systems, is given. For the primary members (M<2M⊙)(M<2M⊙), we get β=1.16β=1.16. It is worthy of mention that the model obtained is a simple one. Rotation, magnetic field, etc. are not considered in the present treatment. So, the model is far from being complete. It is just a step to show that pure geometric consideration objects can be used to treat problems of stellar structure.