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Exact Solutions to General Relativistic Force-Free Electrodynamics
Adhikari, Rakshak
Adhikari, Rakshak
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Abstract
Force-free electrodynamics (FFE) is a theoretical framework used to describe electromagnetic fields in regions where plasma inertia is negligible compared to the electromagnetic field strength and the field can evolve without contributions from the plasma degrees of freedom. Force-free fields are extensively studied around accreting black holes as these fields are believed to extract rotational energy from the black hole in the form of relativistic jets. However, the equations of FFE are coupled non-linear partial differential equations, and finding exact solutions has historically been difficult. Similarly, many studies of cosmological magnetic fields assume force-free fields, but despite that, there have never been systematic studies on what type of force-free fields are allowed in an expanding universe described by the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric. In this dissertation, we successfully employ the geometric approach to force-free fields pioneered by Menon that involves the study of foliations of a spacetime manifold into submanifolds that allow for the existence of force-free fields. As a result, we are able to find several non-null solutions to FFE equations in Kerr spacetime. Similarly, we present several null and non-null solutions in the FLRW spacetime, and we also present, to our knowledge, the first ever exact force-free field that transitions smoothly from magnetically dominated to null and then to an electrically dominated regime.
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2024-08-31
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University of Kansas
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Physics, Cosmology, General Relativity, Relativistic Astrophysics