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We investigate static spherically symmetric spacetimes within the framework of symmetric teleparallel $f(Q)$ gravity in order to describe relativistic stars. We adopt a specific ansatz for the background geometry corresponding to a…
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…
In this talk we show a stiff fluid solution of the Einstein equations for a cylindrically symmetric spacetime. The main features of this metric are that it is non-separable in comoving coordinates for the congruence of the worldlineS of the…
In this work a class of interior solution for Einstein field equations corresponding to a spherically symmetric anisotropic fluid sphere has been obtained under the assumption that the cosmological constant is spatially variable. The…
Cataldo has found all rigidly rotating self-gravitating perfect fluid solutions in 2+1 dimensions with a negative cosmological constant $\Lambda$, for a density that is specified a priori as a function of a certain radial coordinate. We…
We examine static perfect fluid spheres in the presence of a cosmological constant. New exact matter solutions are discussed which require the Nariai metric in the vacuum region. We generalize the Einstein static universe such that neither…
Static and spherically symmetric perfect fluid solutions of Einstein's field equations with cosmological constant are analysed. After showing existence and uniqueness of a regular solution at the centre the extension of this solution is…
Aims: In the present work we search for a new model of compact star within embedding class one spacetime i.e., four dimensional spacetime embedded in five dimensional Pseudo Euclidean space. Methods: In particular we propose a new mass…
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 investigate perfect fluid stars in $(2+1)$ dimension in pseudo spheroidal spacetime with the help of Vaidya-Tikekar metric where the physical $3$-space ($t=$ constant) is described by pseudo-spheroidal geometry. Here the spheroidicity…
We investigate non-linear, spherically symmetric solutions to the coupled system of a quintessence field and Einstein gravity. In the presence of a scalar potential, we find regular solutions that to an outside observer very closely…
According to Birkhoff's theorem the only spherically symmetric solution of the vacuum Einstein field equations is the Schwarzschild solution. Inspite of imposing asymptotically flatness and staticness as initial conditions we obtain that…
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…
In this work we investigate analytic static and spherically symmetric solutions of a generalized theory of gravity in the Einstein-Cartan formalism. The main goal consists in analyzing the behavior of the solutions under the influence of a…
We consider a configuration consisting of a wormhole filled by a perfect fluid. Such a model can be applied to describe stars as well as neutron stars with a nontrivial topology. The presence of a tunnel allows for motion of the fluid,…
We study spherically symmetric static spacetimes generally filled with an anisotropic fluid in the nonrelativistic general covariant theory of gravity. In particular, we find that the vacuum solutions are not unique, and can be expressed in…
In this article, we provide a discussion on a composite class of exact static spherically symmetric vacuum solutions of Einstein's equations. We construct the composite solution of Einstein field equation by match the interior vacuum metric…
A numerical solution of Einstein field equations for a spherical symmetric and stationary system of identical and auto-gravitating particles in phase transition is presented. The fluid possess a perfect fluid energy momentum tensor, and the…
In this article, we present a class of relativistic solutions describing spherically symmetric and static anisotropic stars in hydrostatic equilibrium. For this purpose, we consider a particularized matric potential, namely, Buchdahl ansatz…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…