New exact solutions to the Eddington-inspired-Born-Infeld equations for a relativistic perfect fluid in a Bianchi type I spacetime |
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| Authors: | Calvin Tadmon Guichard Djiodjo-Seugmo |
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| Affiliation: | 1.Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, PO Box 67, Dschang, Cameroon;2.The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, I-34151 Trieste, Italy |
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| Abstract: | We consider a Bianchi type I physical metric g, an auxiliary metric q and a density matter ρ in Eddington-inspired-Born-Infeld theory. We first derive a system of second order nonlinear ordinary differential equations. Then, by a suitable change of variables, we arrive at a system of first order nonlinear ordinary differential equations. Using both the solution-tube concept for the first order nonlinear ordinary differential equations and the nonlinear analysis tools such as the Arzelá–Ascoli theorem, we prove an existence result for the nonlinear system obtained. The resolution of this last system allows us to obtain new exact solutions for the model considered. Finally, by studying the asymptotic behaviour of the exact solutions obtained, we conclude that this solution is the counterpart of the Friedman–Lemaître–Robertson–Walker spacetime in Eddington-inspired-Born-Infeld theory. |
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| Keywords: | Eddington-inspired-Born-Infeld theory Bianchi type I spacetime solution-tube Friedmann–Lemaître–Robertson–Walker spacetime density matter ordinary differential equations |
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