Related papers: Interior solution for the Kerr metric
The time independent spherically symmetric solutions of General Relativity (GR) coupled to a dynamical unit timelike vector are studied. We find there is a three-parameter family of solutions with this symmetry. Imposing asymptotic flatness…
We present a family of exact rotating anisotropic fluid solutions, which satisfy all energy conditions for certain values of their parameters. The components of the Ricci tensor $R_{\mu\nu}$ the eigenvalues of the tensor $R_\mu^\nu$ and the…
In this paper we consider spherically symmetric interior spacetimes filled by anisotropic fluids in the context of Ho\v{r}ava gravity and Einstein-aether theory. We assume a specific non-static configuration of the aether vector field and…
In this work, we have obtained exact solutions of Einstein equations for static and axially symmetric magnetized matter, specifically in plane-symmetric and almost-plane symmetric cases. Although these solutions impose constraints on the…
The line element of a class of solutions which match to the solution of Kerr on an oblate spheroid if the two functions $ F(r)$ and $H(r)$ on which it depends satisfy certain matching conditions is presented. The non vanishing components of…
Complete sequences of new analytic solutions of Einstein's equations which describe thin super massive disks are constructed. These solutions are derived geometrically. The identification of points across two symmetrical cuts through a…
We study exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres consist of an anisotropic fluid with a charge distribution that gives rise…
Charged axially symmetric solution of the coupled gravitational and electromagnetic fields in the tetrad theory of gravitation is derived. The metric associated with this solution is an axially symmetric metric which is characterized by…
The Einstein field equations have no known and acceptable interior solution that can be matched to an exterior Kerr field. In particular, there are no interior solutions that could represent objects like the Earth or other rigidly rotating…
Via a straightforward integration of the Einstein equations with cosmological constant, all static circularly symmetric perfect fluid 2+1 solutions are derived. The structural functions of the metric depend on the energy density, which…
An exact charged axially symmetric solution of the coupled gravitational and electromagnetic fields in the teleparallel equivalent of Einstein theory is derived. It is characterized by three parameters ``$ $the gravitational mass $M$, the…
We obtain well behaved interior solutions describing hydrostatic equilibrium of anisotropic relativistic stars in scale-dependent gravity, where Newton's constant is allowed to vary with the radial coordinate throughout the star. Assuming…
The asymptotic properties of conformally static metrics in Einstein-aether theory with a perfect fluid source and a scalar field are analyzed. In case of perfect fluid, some relativistic solutions are recovered such as: Minkowski spacetime,…
We consider the equations for the coefficients of stationary rotating axisymmetric metrics governed by the Einstein-Euler equations, that is, the Einstein equations together with the energy-momentum tensor of a barotropic perfect fluid.…
We introduce a new type of generating theorems in General Relativity for anisotropic, static, spherically symmetric solutions of the Einstein field equations. The results are used to derive a class of solutions that can serve as new models…
We present a new exact perfect fluid interior solution for a particular scalar-tensor theory. The solution is regular everywhere and has a well defined boundary where the fluid pressure vanishes. The metric and the dilaton field match…
Two distinct non-singular interior models that describe anisotropic spherical configurations are presented in this work. We develop the Einstein field equations and the associated mass function in accordance with a static spherical…
Expansion of a locally equilibrated fluid is considered in an anisotropic space-time given by Bianchi type I metric. Starting from isotropic equilibrium phase-space distribution function in the local rest frame, we obtain expressions for…
One of the effects of noncommutative coordinate operators is that the delta-function connected to the quantum mechanical amplitude between states sharp to the position operator gets smeared by a Gaussian distribution. Although this is not…
We ask the following question: Of the exact solutions to Einstein's equations extant in the literature, how many could represent the field associated with an isolated static spherically symmetric perfect fluid source? The candidate…