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Static spherically symmetric solutions of the Einstein's field equations in isotropic coordinates representing perfect fluid matter distributions from Newtonian potential-density pairs are investigated. The approach is illustrated with…
The ideal incompressible fluid in two dimensions (Euler fluid) evolves at relaxation from turbulent states to highly coherent states of flow. For the case of double spatial periodicity and zero total vorticity it is known that the…
The ultra--relativistic Euler equations describe gases in the relativistic case when the thermal energy dominates. These equations for an ideal gas are given in terms of the pressure, the spatial part of the dimensionless four-velocity, and…
We analyze the thermodynamics of spherically symmetric thin-shell solutions to Einstein's equations, including solutions with negative interior mass. We show the inclusion of such solutions is essential for the thermodynamic consistency of…
We investigate some new similarity inhomogeneous solutions of anisotropic dark energy and perfect fluid in Bianchi type-I space-time. Three different equation of state parameters along the spatial directions are introduced to quantify the…
We obtain a mass function solving the Tolman-Oppenheimer-Volkoff (TOV) equation for isotropic and spherically symmetric system via homotopy perturbation method (HPM). Using the mass function we construct a stellar model which can be…
In this paper, we consider an isothermal Euler-Poisson system with self-gravitational force, modeling a compact star such as strange quark star. We prove that there exists a global entropy solution with spherically symmetry outside a ball,…
We derive the equilibrium hydrostatic equation of a spherical star for any gravitational Lagrangian density of the form $L=\sqrt{-g}f(R)$. The Palatini variational principle for the Helmholtz Lagrangian in the Einstein gauge is used to…
A Lagrangian formulation of perfect fluid due to a noncanonical three-form field is investigated. The thermodynamic quantities such as energy density, pressure and the four velocity are obtained and then analyzed by comparing with the…
We reformulate the relativistic perfect fluid system on curved space-time. Using standard variables, the velocity field $u$,energy density $\rho$ and pressure $p$, the covariant Euler-Lagrange equation is obtained from variational…
A new class of solutions of Einstein's equations is derived providing a physically plausible hydrodynamic description of cosmological matter in the radiation era of the Universe expansion. The solutions are characterized by the LTB metric…
We show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finite and infinite-dimensional maximum entropy problems concerning probability distributions, spectral densities and covariance…
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…
We present the Ernst potential and the line element of an exact solution of Einstein's vacuum field equations that contains as arbitrary parameters the total mass, the angular momentum, and the quadrupole moment of a rotating mass…
We derive the spin Euler equation for ideal flows by applying the spherical Clebsch mapping. This equation is based on the spin vector rather than the velocity. It enables a feasible Lagrangian study of fluid dynamics, as the isosurface of…
We present a general solution of the Einstein gravitational field equations for the static spherically symmetric gravitational interior spacetime of an isotropic fluid sphere. The solution is obtained by transforming the pressure isotropy…
Electro-energy-reaction-diffusion systems are thermodynamically consistent continuum models for reaction-diffusion processes that account for temperature and electrostatic effects in a way that total charge and energy are conserved. The…
We investigate the interior Einstein's equations in the case of a static, axially symmetric, perfect fluid source. We present a particular line element that is specially suitable for the investigation of this type of interior gravitational…
Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The…
An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect fluid solutions of Einstein's equations. For physically relevant…