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

M. I. Wanas

Astronomy Department, Faculty of Science, Cairo University, Giza, Egypt

E-mail Address: miwanas@sci.cu.edu.eg

E-mail Address: wanas@scu.eg

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Samah A. Ammar

Mathematics Department, Faculty of Girls, Ain Shams University, Cairo, Egypt

E-mail Address: samah.ammar@women.asu.edu.eg

E-mail Address: samahammar@eun.eg

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, and

Mona M. Foda

Astronomy Department, Faculty of Science, Cairo University, Giza, Egypt

E-mail Address: mfoda@sci.cu.edu.eg

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https://doi.org/10.1142/S0219887818501347Cited by:2 (Source: Crossref)

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 $(R = β M)$ with one free parameter $(β) .$ Comparison with observation, using a sample of lower main-sequence stars, members of binary systems, is given. For the primary members $(M < 2 M_{⊙})$ , we get $β = 1.16$ . 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.

All the authors of this article are members of the Egyptian Relativity Group (ERG).

Keywords:

AMSC: 51P05, 83D05, 85A15

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