Related papers: Algorithms for Generating All Static Spherically S…
We construct a black hole initial data for the Einstein equations with prescribed scalar curvature, or more precisely a piece of initial data contained inside the black hole. The constraints translate into a parabolic equation, with radius…
We analyze the isothermal property in static fluid spheres within the framework of the modified $f(R, T)$ theory of gravitation. The equation of pressure isotropy of the standard Einstein theory is preserved however, the energy density and…
Recent works by the second author and Maxwell et al. have shown that the Einstein-scalar field conformal constraint equations are highly complex and generally intractable, even in the vacuum case. In this article, to gain a clearer…
This article is the second in a series devoted to the study of spacetimes sourced by a stationary cylinder of fluid rigidly rotating around its symmetry axis and exhibiting an anisotropic pressure by using new exact interior solutions of…
We investigate the global dynamics of the field equations of (pure) quadratic theories of gravity which generalise Einstein's theory in spatially flat homogeneous and isotropic cosmological models with a perfect fluid. We introduce global…
Following a solution generating technique introduced recently by one of us, we transform the Einstein static Universe into a two - fold infinity class of physically acceptable exact perfect fluid solutions of Einstein's equations. Whereas…
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 review analytical solutions of the Einstein equations which are expressed in terms of elementary functions and describe Friedmann-Lema\^itre-Robertson-Walker universes sourced by multiple (real or effective) perfect fluids with constant…
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.…
The trace-free Einstein equations contain one equation less than the complete field equations. In a static and spherically symmetric spacetime, the number of field equations is thus reduced to two. The equation of pressure isotropy of…
We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is…
An exact rotating anisotropic fluid solution and a family of exact rotating anisotropic fluid solutions are presented which satisfy all energy conditions for certain values of their parameters. The components of the Ricci tensor the…
Starting from the solution of the Einstein field equations in a static and spherically symmetric spacetime which contains an isotropic fluid, we construct a model to represent the interior of compact objects with compactness rate…
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 spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which…
This paper synthesizes anytime algorithms, in the form of continuous-time dynamical systems, to solve monotone variational inequalities. We introduce three algorithms that solve this problem: the projected monotone flow, the safe monotone…
Einstein field equations for anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities.…
We construct spherically symmetric solutions to the Einstein-Euler equations, which contains a positive cosmological constant, say, the Einstein-Euler-de Sitter equations. We assume a realistic barotropic equation of state. Equilibria of…
We analyse the gravitational behaviour of a relativistic heat conducting fluid in a shear-free spherically symmetric spacetime. We show that the isotropy of pressure is a consistency condition which realises a second order nonlinear…
In this paper, we present a formalism to generate a family of interior solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner-Nordstr\"om…