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Einstein's spherically symmetric interior gravitational equations are investigated. Following Synge's procedure, the most general solution of the equations is furnished in case $T^{1}_{1}$ and $T^{4}_{4}$ are prescribed. The existence of a…
We investigate accretion of dark matter onto a moving Schwarzschild black hole. The dark matter is modeled by the collisionless Vlasov gas, assumed to be in thermal equilibrium at infinity. We derive an exact stationary solution and provide…
The main objective of this work is the construction of regular black hole solutions in the context of the Einstein-Maxwell theory. The strategy is to match an interior regular solution to an exterior electrovacuum solution. With this…
We present exact solutions in Einstein-aether theory in a static spherically symmetric background space with a spacelike aether field, as a difference with the usual selection of timelike aether field. We assume a coupling between the…
We present, in an explicit form, the metric for all spherically symmetric Schwarzschild-Bach black holes in Einstein-Weyl theory. In addition to the black hole mass, this complete family of spacetimes involves a parameter that encodes the…
We review explicit solutions to the stationary axisymmetric Einstein-Maxwell equations which can be interpreted as disks of charged dust. The disks of finite or infinite extension are infinitesimally thin and constitute a surface layer at…
The static vacuum spherically symmetric solutions in massive gravity are obtained both analytically and numerically. The solutions depend on two parameters (integration constants): the mass M (or, equivalently, the Schwarzschild radius),…
Schwarzschild's solution to the Einstein Field Equations was one of the first and most important solutions that lead to the understanding and important experimental tests of Einstein's theory of General Relativity. However, Schwarzschild's…
It is formulated a new 'anholonomic frame' method of constructing exact solutions of Einstein equations with off--diagonal metrics in 4D and 5D gravity. The previous approaches and results are summarized and generalized as three theorems…
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate…
Massive gravity is a good theoretical laboratory to study modifications of General Relativity. The theory offers a concrete set-up to study models of dark energy, since it admits cosmological self-accelerating solutions in the vacuum, in…
We obtain electrically charged black hole solutions of the Einstein equations in arbitrary dimensions with a nonlinear electrodynamics source. The matter source is deriving from a Lagrangian given by an arbitrary power of the Maxwell…
We look for "static" spherically symmetric solutions of Einstein's Equations for perfect fluid source with equation of state $p=w\rho$. In order to include the possibilities of recently popularized dark energy and phantom energy possibly…
In the realm of astrophysics, black holes exist within nonvacuum cosmological backgrounds, making it crucial to investigate how these backgrounds influence the properties of black holes. In this work, we first introduce a novel static…
The black hole solutions in higher-dimensional spacetimes with the presence of the power-Maxwell field, surrounded by quintessence, are investigated for Einstein as well as Rastall gravity. The obtained solutions accommodate for spherical,…
We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two…
An exact solution of the Einstein equations for a Bianchi -I universe in the presence of dust, stiff matter and cosmological constant, generalising the well-known Heckmann-Schucking solution is presented. PACS: 04.20-q; 04.20.Dw Keywords:…
After the original discovery of the Kerr metric, Newman and Janis showed that this solution could be ``derived'' by making an elementary complex transformation to the Schwarzschild solution. The same method was then used to obtain a new…
An infinite family of new exact solutions of the Einstein vacuum equations for static and axially symmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply…
We present numerical evidences for the validity of the inequality between the total mass and the total angular momentum for multiple axially symmetric (non-stationary) black holes. We use a parabolic heat flow to solve numerically the…