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Conditions for smooth cosmological models are set out and applied to inhomogeneous spherically symmetric models constructed by matching together different Lemaitre-Tolman-Bondi solutions to the Einstein field equations. As an illustration…
The static black hole solutions to the Einstein-Maxwell equations are all spherically symmetric, as are many of the recently discovered black hole solutions in theories of gravity coupled to other forms of matter. However, counterexamples…
We construct spherically symmetric solutions to the Einstein-Euler equations, which give models of gaseous stars in the framework of the general theory of relativity. We assume a realistic barotropic equation of state. Equilibria of the…
Known examples in plane symmetry or Gowdy symmetry show that given a $1$-parameter family of solutions to the vacuum Einstein equations, it may have a weak limit which does not satisfy the vacuum equations, but instead has a non-trivial…
We consider dynamical spherically symmetric spacetimes, which are conformal to the static spherically symmetric metrics, and find new solutions of Einstein equations by symmetry considerations. Our study help us classify various conformal…
The dynamics of the Einstein-Vlasov equations for a class of cosmological models with four Killing vectors is discussed in the case of massive particles. It is shown that in all models analysed the solutions with massive particles are…
Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are…
We derive the analog of the Tolman - Oppenheimer - Volkoff equation in conformal Killing gravity in a static spherically symmetric spacetime, sourced by anisotropic fluid matter. It differs from the original equation by new dark terms…
We identify an anisotropic divergence-free conformal Killing tensor $K_{jl}$ for static spherically symmetric spacetimes, and write the conformal Killing gravity equations as Einstein equations augmented by this tensor. The field equations…
We investigate the relation between the standard Newtonian equations for a pressureless fluid (dust) and the Einstein equations in a double expansion in small scales and small metric perturbations. We find that parts of the Einstein…
We obtain an exact simple solution of the Einstein equation describing a spherically symmetric cosmological model without the big-bang or any other kind of singularity. The matter content of the model is shear free isotropic fluid with…
By using of the Euler-Lagrange equations, we find a static spherically symmetric solution in the Einstein-aether theory with the coupling constants restricted. The solution is similar to the Reissner-Nordstrom solution in that it has an…
Interior solutions of Einstein's equations with a non-zero cosmological constant are given for static and spherically symmetric configurations of uniform density. The metric tensor and pressure are determined for both positive and negative…
We prove a theorem that characterizes a large family of non-static solutions to Einstein equations, representing, in general, spherically symmetric Type II fluid. It is shown that the best known dynamical black hole solutions to Einstein…
During gravitational collapse of dust in spherical symmetry, matter particles may collide forming shell crossing surfaces (SCS) on which the Einstein equations become indeterministic. We show that there is a unique evolution beyond SCS such…
Beginning with a special form of the Einstein-Rosen metric, we find new cosmological solutions of the Einstein equations, having two hypersurface-orthogonal Killing vectors , with ideal fluid. The equation of state is in the most cases of…
We attempt to solve the Einstein equations for string dust and null flowing radiation for the general axially symmetric metric, which we believe is being done for the first time. We obtain the string-dust and radiating generalizations of…
A new class of solutions to the coupled, spherically symmetric Einstein-Maxwell equations for a compact material source is constructed. Some of these solutions can be made to satisfy a number of requirements for being physically relevant,…
We classify all spherically symmetric spacetimes admitting a kinematic self-similar vector of the second, zeroth or infinite kind. We assume that the perfect fluid obeys either a polytropic equation of state or an equation of state of the…
We derive an equation for the acceleration of a fluid element in the spherical gravitational collapse of a bounded compact object made up of an imperfect fluid. We show that non-singular as well as singular solutions arise in the collapse…