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An algorithm recently presented by Lake to obtain all static spherically symmetric perfect fluid solutions, is extended to the case of locally anisotropic fluids (principal stresses unequal). As expected, the new formalism requires the…
Modified gravity theories can be used for the description of homogeneous and isotropic cosmological models through the corresponding field equations. These can be cast into systems of autonomous differential equations because of their sole…
The main objective of this work, is to show two inequivalent methods to obtain new spherical symmetric solutions of Einstein's Equations with anisotropy in the pressures in isotropic coordinates. This was done inspired by the MGD method,…
In this paper Einstein's field equations, for static spherically symmetric perfect fluid models with a linear barotropic equation of state, are recast into a 3-dimensional regular system of ordinary differential equations on a compact state…
It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "open" model $H^ 3$ for this…
In the macroscopic gravity approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We present exact cosmological solutions to the…
We demonstrate a technique to generate new class of exact solutions to the Einstein-Maxwell system describing a static spherically symmetric relativistic star with anisotropic matter distribution. An interesting feature of the new class of…
We study the possible singularities of isotropic cosmological models that have a varying speed of light as well as a varying gravitational constant. The field equations typically reduce to two dimensional systems which are then analyzed…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
We apply the topological quantization method to some gravitational fields which can be represented as generalized harmonic maps. This representation extends the well-known concept of harmonic maps and allows us to describe some solutions to…
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…
Einstein-Dirac equations for two spinor fields are considered. It is shown that in this case one can obtain self-consistent equations set for these gravitating spinors. The key idea to obtain Einstein-Dirac equations is to use special…
The full set of equations governing the structure and the evolution of self--gravitating spherically symmetric dissipative fluids with anisotropic stresses, is written down in terms of five scalar quantities obtained from the orthogonal…
Solutions of Einstein vacuum equations, for a static pseudospherically symmetric system, are presented. They describe a naked singularity and a singular solution with many resemblances to the Schwartzschild solution but with two major…
In this paper we study the dynamics of {\it orthogonal spatially homogeneous} Bianchi cosmologies in $R^n$-gravity. We construct a compact state space by dividing the state space into different sectors. We perform a detailed analysis of the…
By viewing Einstein's field equations -- reduced to two dimensions -- as an integrable system, one can simultaneously obtain exact solutions to both the equations themselves and their associated Lax pair via a canonical Wiener-Hopf…
We explore the new physics phenomena of gravidynamics governed by the inhomogeneous spin gauge symmetry based on the gravitational quantum field theory. Such a gravidynamics enables us to derive the generalized Einstein equation and an…
In this work we develop a simple protocol to construct interior solutions through Gravitational Decoupling by the Minimal Geometric Deformation extended satisfying the vanishing complexity condition. The method is illustrated by using…
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…
We study the solution of the system of equations describing the dynamical evolution of spontaneous ruptures generated in a prestressed elastic-gravitational deforming body and governed by rate and state friction laws. We propose an…