Related papers: Generating anisotropic fluids from vacuum Ernst eq…
The staid subject of exact static spherically symmetric perfect fluid solutions of Einstein's equations has been reinvigorated in the last decade. We now have several solution generating techniques which give rise to new exact solutions.…
While it is known that any spherical fluid distribution may only source the spherically symmetric Schwarzschild space-time, the inverse is not true. Thus, in this manuscript, we find exact axially symmetric and static fluid (interior)…
For static fluid spheres, the condition of hydrostatic equilibrium is given by the generalized Tolman--Oppenheimer--Volkoff (TOV) equation, a Riccati equation in the radial pressure. For a perfect fluid source, it is known that finding a…
The fluid models mentioned in the title are classified. All characteristics of the fluid are expressed through a master potential, satisfying an ordinary second order differential equation. Different constraints are imposed on this core of…
We study spherically symmetric geometries made of anisotropic perfect fluid based on general relativity. The purpose of the work is to find and classify black hole solutions in closed spacetime. In a general setting, we find that a static…
Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on…
Considering the isentropic Euler equations of compressible fluid dynamics with geometric effects included, we establish the existence of entropy solutions for a large class of initial data. We cover fluid flows in a nozzle or in spherical…
We present a simple technique for generating new solutions of Einstein's equations using such function transformations that leave the field equations in the Ernst form. In this context we recover all the known covariant transformations of…
A new class of solutions to Einstein's classical field equations of general relativity is presented. The solutions describe a non-rotating, spherically symmetric, compact self gravitating object, residing in a static electro-vacuum space…
The condition for the vanishing of the Weyl tensor is integrated in the spherically symmetric case. Then, the resulting expression is used to find new, conformally flat, interior solutions to Einstein equations for locally anisotropic…
Locally rotationally symmetric perfect fluid solutions of Einstein's gravitational equations are matched along the hypersurface of vanishing pressure with the NUT metric. These rigidly rotating fluids are interpreted as sources for the…
The fluid models mentioned in the title are studied in a modified approach, based on two formulas for the mass function. All characteristics of the fluid are expressed through a master potential, satisfying an ordinary second order…
We study stationary configurations of compressible barotropic fluids lying inside an incompressible fluid and acted upon by a constant gravitational field. Without gravity, it is a simple matter to construct solutions consisting of…
In this work, we present a class of relativistic and well-behaved solution to Einstein's field equations for anisotropic matter distribution. We perform our analysis by using the Buchdahl ansatz for the metric function grr. Three different…
We investigate how a spherically symmetric fluid modifies the Schwarzschild vacuum solution when there is no exchange of energy-momentum between the fluid and the central source of the Schwarzschild metric. This system is described by means…
We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach…
The existence of stationary solutions to the Einstein-Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat…
We study Born-Infeld gravity coupled to an anisotropic fluid in a static, spherically symmetric background. The free function characterizing the fluid is selected on the following grounds: i) recovery of the Reissner-Nordstr\"om solution of…
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…
Relativistic, spherically symmetric configurations consisting of a gravitating magnetized anisotropic fluid are studied. For such configurations, we obtain static equilibrium solutions with an axisymmetric, poloidal magnetic field produced…