Related papers: On the relativistic compressibility conditions
We show that a relativistic gas may be at ``global'' equilibrium in the expanding universe for any equation of state $0 < p \leq \rho /3$, provided that the gas particles move under the influence of a self-interacting, effective…
Slow flows of an ideal compressible fluid (gas) in the gravity field in the presence of two isentropic layers are considered, with a small difference of specific entropy between them. Assuming irrotational flows in each layer [that is ${\bf…
In this paper we address the problem of the quantization of the perfect relativistic fluids formulated in terms of the K\"{a}hler parametrization. This fluid model describes a large set of interesting systems such as the power law energy…
It has been established in the literature that the matter Lagrangian of an ideal fluid can be expressed either as its total energy density or as its pressure. In this work, we demonstrate that identifying the matter Lagrangian with the…
Looking for the underlying hydrodynamic mechanisms determining the elliptic flow we show that for an expanding relativistic perfect fluid the transverse flow may derive from a solvable hydrodynamic potential, if the entropy is transversally…
Skew-symmetric massless fields, their potentials being $r$-forms, are close analogues of Maxwell's field (though the non-linear cases also should be considered). We observe that only two of them ($r=$2 and 3) automatically yield…
We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the…
A generally relativistic theory of thermodynamics is developed, based on four main physical principles: heat is a local form of energy, therefore described by a thermal energy tensor; conservation of mass, equivalent to conservation of…
Foundations of the analysis of scaling in randomly stirred compressible fluid with the aid of stochastic differential equations are discussed in the example of perfect gas. The structure of the stress tensor with nonnegative shear and bulk…
When solving the equations of General Relativity in a symmetric sector, it is natural to consider the same symmetry for the geometry and stress-energy. This implies that for static and isotropic spacetimes, the most general natural…
For the physical vacuum free boundary problem with the sound speed being $C^{{1}/{2}}$-H$\ddot{\rm o}$lder continuous near vacuum boundaries of the three-dimensional compressible Euler equations with damping, the global existence of…
A new class of accelerating, exact, explicit and simple solutions of relativistic hydrodynamics is presented. Since these new solutions yield a finite rapidity distribution, they lead to an advanced estimate of the initial energy density…
This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein--Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density…
We ask the following question: Of the exact solutions to Einstein's equations extant in the literature, how many could represent the field associated with an isolated static spherically symmetric perfect fluid source? The candidate…
The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 {\it Relativistic Fluids and Magneto-Fluids} (Cambridge: Cambridge University Press)). In this report, we…
Smooth solutions of the forced incompressible Euler equations satisfy an energy balance, where the rate-of-change in time of the kinetic energy equals the work done by the force per unit time. Interesting phenomena such as turbulence are…
In this work we investigate the thermodynamic properties satisfied by an expanding universe filled with a monoatomic ideal gas. We show that the equations for the energy density, entropy density and chemical potential remain the same of an…
A thermodynamic argument is proposed in order to discuss the most appropriate form of the local energy balance equation within the Oberbeck-Boussinesq approximation. The study is devoted to establish the correct thermodynamic property to be…
The relativistic transformation rule for temperature is a subject under debate for more than 110 years. Several incompatible proposals exist in the literature, but a final resolution is still missing. In this work, we reconsider the problem…
In the context of general relativity, both energy and linear momentum constraints lead to the same equation for the evolution of the speed of free localized particles with fixed proper mass and structure in a homogeneous and isotropic…