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Global Dynamics for a Relativistic Charged and Colliding Plasma in Presence of a Massive Scalar Field in Friedmann-Lemaître-Robertson-Walker Spacetimes in Eddington-inspired-Born-Infeld Gravity

International Journal of Theoretical Physics, ISSN: 1572-9575, Vol: 63, Issue: 1
2024
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Article Description

We consider a Friedmann-Lemaître-Robertson-Walker physical metric g, an auxiliary metric q with a relativistic charged and colliding plasma in presence of a massive scalar field in Eddington-inspired-Born-Infeld theory of gravity. We first derive a governing system of second order nonlinear partial differential equations. By a judicious change of variables, we manage to build a system of partial differential equations of the first order equivalent to the system of the second order previously found. Then, by the method of characteristics applied to the Boltzmann equation which is a first order hyperbolic equation having as unknown the distribution function f, we construct an iterated sequence and prove the existence and uniqueness of a local solution on a positive time interval [0, T). Then, by the continuation criterion and under certain assumptions of smallness on the initial data, the Eddington parameter k and the dimensionless parameter λ , we show that this local solution is global in time.

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