Derives modified Einstein and fluid equations for non-minimal matter-Lagrangian-curvature couplings and demonstrates non-equivalence of Schutz and Brown fluid formulations.
Relativistic Fluid Dynamics: Physics for Many Different Scales
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abstract
The relativistic fluid is a highly successful model used to describe the dynamics of many-particle, relativistic systems. It takes as input basic physics from microscopic scales and yields as output predictions of bulk, macroscopic motion. By inverting the process, an understanding of bulk features can lead to insight into physics on the microscopic scale. Relativistic fluids have been used to model systems as ``small'' as heavy ions in collisions, and as large as the universe itself, with ``intermediate'' sized objects like neutron stars being considered along the way. The purpose of this review is to discuss the mathematical and theoretical physics underpinnings of the relativistic (multiple) fluid model. We focus on the variational principle approach championed by Brandon Carter and his collaborators, in which a crucial element is to distinguish the momenta that are conjugate to the particle number density currents. This approach differs from the ``standard'' text-book derivation of the equations of motion from the divergence of the stress-energy tensor, in that one explicitly obtains the relativistic Euler equation as an ``integrability'' condition on the relativistic vorticity. We discuss the conservation laws and the equations of motion in detail, and provide a number of (in our opinion) interesting and relevant applications of the general theory.
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Electromagnetism is reformulated from relativistic fluid dynamics via pull-back of differential forms from matter space, imposing kinematical constraints from the absence of four-forms and identifying a preferred frame where spacetime field strength matches the intrinsic matter-space two-form.
Axial w-mode frequencies in anisotropic neutron stars decrease monotonically with mass, show approximately linear dependence on compactness modified by anisotropy type and strength, and come with empirical fitting expressions for frequency and damping time.
citing papers explorer
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Non-minimal fluid Lagrangian couplings
Derives modified Einstein and fluid equations for non-minimal matter-Lagrangian-curvature couplings and demonstrates non-equivalence of Schutz and Brown fluid formulations.
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Electromagnetism from relativistic fluid dynamics
Electromagnetism is reformulated from relativistic fluid dynamics via pull-back of differential forms from matter space, imposing kinematical constraints from the absence of four-forms and identifying a preferred frame where spacetime field strength matches the intrinsic matter-space two-form.
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Axial $w$-modes of anisotropic neutron stars
Axial w-mode frequencies in anisotropic neutron stars decrease monotonically with mass, show approximately linear dependence on compactness modified by anisotropy type and strength, and come with empirical fitting expressions for frequency and damping time.