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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…
In a recent series of papers, new exact analytical solutions to field equations of General Relativity representing interior spacetimes sourced by stationary rigidly rotating cylinders of fluids with various equations of state have been…
The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…
A spherically symmetric charged ideal fluid solution of Einstein field equation is given in the presence of the cosmological constant and two well known example of this type of solution is presented. If the matter is confined in a region,…
A model approach to the description of static stars filled with a charged Pascal perfect fluid within the framework of general relativity is investigated. The metric is written in Bondi's radiation coordinates. The gravitational equations…
Geometric features (including convexity properties) of an exact interior gravitational field due to a self-gravitating axisymmetric body of perfect fluid in stationary, rigid rotation are studied. In spite of the seemingly non-Newtonian…
The purpose of this paper is to demonstrate a new method of generating exact solutions to the Einstein's equations obtained by the Hamiltonian reduction. The key element to the successful Hamiltonian reduction is finding the privileged…
We examine charged slowly rotating perfect fluids in the presence of a cosmological constant. The asymptotic form of the vacuum solutions to the linearised Einstein-Maxwell field equations is found and the possibility of matching this…
Utilizing the ADM equations, we derive a metric and reduced field equations describing a general, spherically symmetric perfect fluid. The metric describes both the interior perfect fluid region and exterior vacuum Schwarzschild spacetime…
In this report the exact rotating charged black hole solution to the Einstein--nonlinear electrodynamics theory with a cosmological constant is presented. This black hole is equipped with mass, rotation parameter, electric and magnetic…
When Einstein's equations for an asymptotically flat, vacuum spacetime are reexpressed in terms of an appropriate conformal metric that is regular at (future) null infinity, they develop apparently singular terms in the associated conformal…
An analytical solution of Einstein-Maxwell equations with a static fluid as a source is presented. The spacetime is represented by the axially symmetric Weyl metric and the energy-momentum tensor describes a coupling of a fluid with an…
A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…
Starting with any stationary axisymmetric vacuum metric, we build anisotropic fluids. With the help of the Ernst method, the basic equations are derived together with the expression for the energy-momentum tensor and with the equation of…
We use Moeller's energy-momentum complex in order to explicitly evaluate the energy and momentum density distributions associated with the three-dimensional magnetic solution to the Einstein-Maxwell equations. The magnetic spacetime under…
We analyze the effect of the quadrupole component in the mass distribution of a rapidly rotating neutron star on energy release in the boundary layer on the surface of the accreting star and in the accretion disk in the cases where the…
We give two classes of spherically symmetric exact solutions of the couple gravitational and electromagnetic fields with charged source in the tetrad theory of gravitation. The first solution depends on an arbitrary function $H({R},t)$. The…
We give an exact solution of the $5D$ Einstein equations which in 4D can be interpreted as a spherically symmetric dissipative distribution of matter, with heat flux, whose effective density and pressure are nonstatic, nonuniform, and…
We present a self-consistent, relativistic model of rapidly rotating neutron stars describing their exterior gravitational field. This is achieved by matching the new solution of Einstein's field equations found by Manko et al. (2000) and…
Einstein's field equations for spatially self-similar locally rotationally symmetric perfect fluid models are investigated. The field equations are rewritten as a first order system of autonomous ordinary differential equations.…