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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

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Abstract

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 \(\lambda \), we show that this local solution is global in time.

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Acknowledgements

Calvin Tadmon acknowledges good working conditions at the University of Mainz, Germany, where this paper was finalized during a research stay supported by the Alexander von Humboldt Foundation. The authors express their sincere thankfulness to the anonymous referees for valuable comments and suggestions that helped improve the quality of this article.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Guichard Djiodjo Seugmo & Calvin Tadmon

  2. Institute of Mathematics, Johannes Gutenberg University of Mainz, Staudingerweg 9, 55128, Mainz, Germany

    Calvin Tadmon

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  1. Guichard Djiodjo Seugmo
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Contributions

Guichard Djiodjo Seugmo Writing - Original draft, Writing, literature review, Formal analysis. Calvin Tadmon Conceptualization, Investigation, Methodology, Project administration, Supervision, Review editing, Perusal of the work, Corresponding author.

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Correspondence to Calvin Tadmon.

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Djiodjo Seugmo, G., Tadmon, C. 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. Int J Theor Phys 63, 8 (2024). https://doi.org/10.1007/s10773-023-05525-3

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