GLOBAL SOLUTIONS TO THE EINSTEIN - SCALAR FIELD EQUATION IN A MAGNETIZED BIANCHI MODEL

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Published: 2015-08-01

Page: 89-100


RAOUL DOMINGO AYISSI *

Department of Mathematics, Faculty of Science, University of Yaounde, POB: 812, Yaounde, Cameroon.

*Author to whom correspondence should be addressed.


Abstract

We prove the global existence of solutions to the coupled Einstein-Scalar field Equation, with the cosmological constant ^ in a Magnetized Bianchi type I space-time. We discuss this global existence using the sign of the derivatives of the initial data of potentials of gravitation a; b and the cosmological constant. To obtain the global existence, we make assumption that the unknown massive scalar field Φ is positive. This is possible because, physically; Φ∼ G -1; G standing for the variable gravitational “constant". We also consider in this work, the case in which the electromagnetic field F derives from a potential vector A = (Aλ) ; imposing to simplify, on A the Lorentz gauge ∇ αAα = 0:Thereafter, we transform the resulting Magnetized Einstein-Scalar field system, which is a second order differential system, into a first order differential system and we apply the standard theory . We then solve the problem of constraints and investigate a time global solution (a; b; Φ; F;A) of the resulting system.

Keywords: Bianchi type, einstein equations, dierential system, potentials of gravitation, scalar massive eld, problem of constraints, global existence


How to Cite

AYISSI, R. D. (2015). GLOBAL SOLUTIONS TO THE EINSTEIN - SCALAR FIELD EQUATION IN A MAGNETIZED BIANCHI MODEL. Journal of Applied Physical Science International, 4(2), 89–100. Retrieved from https://ikprress.org/index.php/JAPSI/article/view/3073

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