Force-free electrodynamics and foliations in an arbitrary spacetime. (19th November 2020)

• Record Type: Journal Article
• Authors: Menon, Govind
• Is Part Of: Classical and quantum gravity. Volume 37:Number 24(2020:Dec.)
• Publication Date: 2020-11-19
• Subjects: force-free electrodynamics -- general relativity -- foliations; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/1361-6382/abbf30
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: In this paper, we formulate the relationship between force-free electrodynamics and foliations. The background metric is considered predetermined and electrically neutral, but otherwise arbitrary. As it turns out, solutions to force-free electrodynamics are intimately connected to the existence of foliations of spacetime with prescribed properties. We prove a local existence and uniqueness theorem concerning foliations when the field is non-null. In the null case, we show that there will always be a class of solutions with exactly two degrees of freedom for every admissible foliation. We are also able to also prove a singularity theorem for when non-null solutions approach the null limit. All new results are clarified with examples. For a variety in the discussion, we conclude with a solution to Maxwell's equations in FRW cosmology.