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We present a new formulation to construct numerically equilibrium configurations of rotating stars in general relativity. Having in mind the application to their quasi static evolutions, we adopt a Lagrangian formulation of our own…
This paper examines the inhomogeneous Einstein equation for a static spherically symmetric metric with a source term corresponding to a perfect fluid with p=-rho. By a careful treatment of the equation near the origin we find an analytic…
We exhibit a simple and explicit formula for the metric of an arbitrary static spherically symmetric perfect fluid spacetime. This class of metrics depends on one freely specifiable monotone non-increasing generating function. We also…
This paper deals with isothermal Euler-Poisson system which is used to model collapse of self-gravitating Newtonian star. Density dependent viscosity term is added on the right-hand side of momentum equation and it has been proved that…
Here we prove the linear stability of a family of `$n+1$'-dimensional Friedmann Lema\^{i}tre Robertson Walker (FLRW) cosmological models of general relativity. We show that the solutions to the linearized Einstein-Euler field equations…
In this article we obtain a new anisotropic solution for Einstein's field equation of embedding class one metric. The solution is representing the realistic objects such as $Her~X-1$ and $RXJ~1856-37$. We perform detailed investigation of…
Einstein's equations of General Relativity form a highly nonlinear system, so most exact solutions rely on symmetry assumptions. Spherically symmetric spacetimes have been particularly important, providing a tractable yet physically rich…
Spherically symmetric static solutions of the Einstein equations with a positive cosmological constant for the energy-momentum tensor of a barotropic perfect fluid are governed by the Tolman-Oppenheimer-Volkoff-de Sitter equation. Existence…
We investigate the impact of an external pressure on the structure of self-gravitating polytropes for axially symmetric ellipsoids and rings. The confinement of the fluid by photons is accounted for through a boundary condition on the…
Equations for a perfect fluid can be obtained by means of the variational principle both in the Lagrangian description and in the Eulerian one. It is known that we need additional fields somehow to describe a rotational isentropic flow in…
We review the problem of describing the gravitational field of compact stars in general relativity. We focus on the deviations from spherical symmetry which are expected to be due to rotation and to the natural deformations of mass…
When expressed in Lagrangian variables, the equations of motion for compressible (barotropic) fluids have the structure of a classical Hamiltonian system in which the potential energy is given by the internal energy of the fluid. The…
The space of the solutions of the differential equations resulting from considering matter fluids of scalar field type or perfect fluid in Einstein-aether theory is analyzed. The Einstein-aether theory of gravity consists of General…
The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients of order three. We prove that this difference equation can be solved in general. Consequently we can find an exact solution to the…
We provide new exact solutions to the Einstein-Maxwell system of equations for matter configurations with anisotropy and charge. The spacetime is static and spherically symmetric. A quadratic equation of state is utilised for the matter…
We consider solutions to the full (non-isentropic) two-dimensional Euler equations that are constant in time and along rays emanating from the origin. We prove that for a polytropic equation of state, entropy admissible solutions in…
Flash evaporation, a liquid-to-gas phase transition phenomenon in real fluids, is prevalent in aerospace propulsion systems. To elucidate the physical mechanisms of such complex flows and provide theoretical benchmarks for Computational…
The Euler equations governing a relativistic perfect fluid are put into symmetric hyperbolic form with dependent variables the fluid's specific entropy plus a generalized velocity vector equal to the fluid's unit relativistic velocity…
We trace a systematic and consistent method to precisely numerate the magnitude range for various structural and isospin compositional properties of the neutron star. Incompressibility, symmetry energy, slope parameter and curvature of a…
Static spherically symmetric perfect-fluid solutions of Einstein's equations play a central role in relativistic astrophysics and stellar structure theory. While many exact solutions satisfy Einstein's equations mathematically, only a…