Global existence of solutions to the Einstein–Maxwell–Massive scalar field system in 3 + 1 formulation on Bianchi spacetimes

Abstract

Global existence to the coupled Einstein–Maxwell–Massive Scalar Field system which rules the dynamics of a kind of charged pure matter in the presence of a massive scalar field is proved, in Bianchi I–VIII spacetimes. The result is established in the case of a cosmological constant bounded from below by a strictly negative constant depending only on the potential of the massive scalar field, for strictly negative initial data of the mean curvature.

Keywords:

• global existence
• local existence
• massive scalar field
• differential system
• charged particles
• constraints

AMS Subject Classification:

• 83C22

Acknowledgments

We acknowledge with thanks the support of Perimeter Institute for Theoretical Physics, Toronto(Waterloo), Canada, where this paper was initiated.