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Relativistic fluid dynamics and electromagnetic media

Relativistic fluid dynamics and electromagnetic media
Relativistic fluid dynamics and electromagnetic media
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.
University of Southampton
Palapanidis, Konstantinos
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Palapanidis, Konstantinos
41d7207c-c208-43df-a3c6-e7695bfbb5f8
Andersson, Nils
2dd6d1ee-cefd-478a-b1ac-e6feedafe304

Palapanidis, Konstantinos (2018) Relativistic fluid dynamics and electromagnetic media. University of Southampton, Doctoral Thesis, 165pp.

Record type: Thesis (Doctoral)

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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Konstantinos Palapanidis PhD Thesis - Version of Record
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Published date: October 2018

Identifiers

Local EPrints ID: 427364
URI: https://eprints.soton.ac.uk/id/eprint/427364
PURE UUID: c3078678-004b-41a5-a3b0-9efff904bbe2

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Date deposited: 14 Jan 2019 17:30
Last modified: 13 Mar 2019 17:44

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