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We investigate the physical properties of equilibrium sequences of non-self-gravitating surfaces that characterize thick disks around a rotating deformed compact object described by a stationary generalization of the static q-metric. The…
We present an anisotropic cosmological model based on a new exact solution of Einstein equations. The matter content consists of an anisotropic scalar field minimally coupled to gravity and of two isotropic perfect fluids that represent…
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…
A coordinate-free approach to limits of spacetimes is developed. The limits of the Schwarzschild metric as the mass parameter tends to 0 or $\infty$ are studied, extending previous results. Besides the known Petrov type D and 0 limits,…
The exact axisymmetric and static solution of the Einstein equations coupled to axisymmetric and static gravitating scalar (or phantom) field is presented. The spacetimes modified by the scalar field are explicitly given for the so called…
We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…
We provide all basic equations and concepts required to carry out a general study on axially symmetric static sources. The Einstein equations and the conservation equations are written down for a general anisotropic static fluid endowed…
The complete solution of Einstein's gravitational equations with a vacuum-vacuum Kerr-Schild pencil of metrics $g_{ab}+V l_al_b$ is obtained. Our result generalizes the solution of the Kerr-Schild problem with a flat metric $g_{ab}$…
We consider diagonal cylindrically symmetric metrics, with an interior representing a general non-rotating fluid with anisotropic pressures. An exterior vacuum Einstein-Rosen spacetime is matched to this using Darmois matching conditions.…
The paper deals with a special kind of problems that appear in solutions of Einstein's field equations for extended bodies: many structure-dependent terms appear in intermediate calculations that cancel exactly in virtue of the local…
The Schwarzschild metric, its Reissner-Nordstrom-de Sitter generalizations to higher dimensions, and some further generalizations all share the feature that g_{tt} g_{rr}=-1 in Schwarzschild-like coordinates. In this pedagogical note we…
This study explores singularity-free solutions to the static, spherical symmetric Einstein equations with the standard Schwarzschild solution as a boundary condition. Imposing the absence of curvature singularities and requiring…
Recent work in the literature has studied a version of non-commutative Schwarzschild black holes where the effects of non-commutativity are described by a mass function depending on both the radial variable r and a non-commutativity…
In this paper we derive some new invariant solutions of Einstein-Maxwell's field equations for string fluid as source of matter in cylindrically symmetric space-time with Variable Magnetic Permeability. We also discuss the physical and…
We consider vacuum metrics admitting conformal compactification which is smooth up to the scri $\mathscr{I^+}$. We write metric in the Bondi-Sachs form and expand it into power series in the inverse affine distance $1/r$. Like in the case…
We study static cylindrically symmetric vacuum solutions in Weyl coordinates in the context of the metric f(R) theories of gravity. The set of the modified Einstein equations is reduced to a single equation and it is shown how one can…
A class of solutions of Einstein field equations satisfying Karmarkar embedding condition is presented which could describe static, spherical fluid configurations, and could serve as models for compact stars. The fluid under consideration…
The exact static spherically symmetric solutions for pure-aether theory and Einstein-aether theory are presented. It is shown that both theories can deliver the Schwarzschild metric, but only the Einstein-aether theory contains solutions…
It is shown in this article that if the Einstein Equivalence Principle is valid on a particular metric theory of gravitation in a spherically symmetric space-time, then the time metric component is not equal to the negative of the inverse…
The Schwarzschild-Melvin spacetime is an exact solution of the Einstein electrovacuum equations describing a black hole immersed in a magnetic field which is asymptotically aligned with the z-axis. It plays an important role in our…