Relativistic fluid dynamics and electromagnetic media

Abstract

In this thesis we describe fluid media with electromagnetic properties in the context of general relativity. Using the variational principle we derive the Einstein equations from the Einstein-Hilbert action, the Euler-Lagrange equations for a multicomponent fluid and the Maxwell equations. We provide a covariant description of linear electromagnetic media and we also discuss media with non linear electromagnetic properties. We also provide a formula that generalises the expression for the Lagrangian of linear media, to that of non linear media and we discuss a set of constraints for linear electromagnetic media in terms of the material derivative. We discuss a model for a multifluid with general electromagnetic properties. We also derive the limit for the single fluid ideal magnetohydrodynamics in general relativistic context. In the final part we look into the linear stability of specific systems using the geometric optics method along with the notion of “fast” and “slow” variables. Employing this method we reproduce a number of results in Newtonian context, building gradually to the derivation of the magnetorotational instability. Additionally, we discuss the vanishing magnetic field of this configuration. Subsequently, considering an unperturbed background spacetime we derive the characteristic equations describing the relativistic inertial waves, the relativistic Rayleigh shearing instability and the relativistic magnetorotational instability. Finally, by assuming a low velocity and flat metric limit of the relativistic equations we reproduce the Newtonian characteristic equations.

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Identifiers

ORCID for Nils Andersson: orcid.org/0000-0001-8550-3843

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