Global dynamics for a collisionless charged plasma in Bianchi spacetimes in Eddington-inspired-Born–Infeld gravity

Abstract

Abstract We consider a Bianchi type I–IX physical metric g, an auxiliary metric q with a collisionless charged relativistic plasma in Eddington-inspired-Born–Infeld theory. We first derive a governing system of second order nonlinear partial differential equations. Then, by the characteristics method applied to the Vlasov equation whose solution is the distribution function f, we manage to construct an iterated sequence. This leads to the existence and uniqueness of a local solution on an interval [ 0 , T ) , with T < ∞ . Then under certain assumptions of smallness on the mean curvatures in both directions, the Eddington parameter k and the dimensionless parameter λ, we show that this solution is global in time.