A differential-forms-based action principle for perfect fluids is extended to null flows, where the equations force ρ + P = 0 and the stress-energy tensor splits into a variable-pressure vacuum term plus null dust.
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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Derives modified Einstein and fluid equations for non-minimal matter-Lagrangian-curvature couplings and demonstrates non-equivalence of Schutz and Brown fluid formulations.
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.
Spacetime-symmetry-breaking Goldstone EFTs systematically describe bulk and localized excitations of solids, fluids, and superfluids, with new thermodynamic identifications and corrected scattering rates.
Axial w-mode frequencies of anisotropic neutron stars decrease monotonically with mass, depend approximately linearly on compactness with anisotropy modifying slope and intercept, damping times increase with mass, and empirical expressions are given for both as functions of compactness and anisotrop
citing papers explorer
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Perfect fluids revisited: an action principle approach
A differential-forms-based action principle for perfect fluids is extended to null flows, where the equations force ρ + P = 0 and the stress-energy tensor splits into a variable-pressure vacuum term plus null dust.
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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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Effective Field Theories for Material Media
Spacetime-symmetry-breaking Goldstone EFTs systematically describe bulk and localized excitations of solids, fluids, and superfluids, with new thermodynamic identifications and corrected scattering rates.
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Axial $w$-modes of anisotropic neutron stars
Axial w-mode frequencies of anisotropic neutron stars decrease monotonically with mass, depend approximately linearly on compactness with anisotropy modifying slope and intercept, damping times increase with mass, and empirical expressions are given for both as functions of compactness and anisotrop