Related papers: Minimal Geometric Deformation: the inverse problem
We revisit the static spherically symmetric solutions of Einstein's General Relativity with a conformally coupled scalar field in arbitrary dimensions. Using a four rank tensor introduced earlier we recast the field equations in a…
In the present paper, we discuss the role of gravitational decoupling to isotropize the anisotropic solution of Einstein's field equations in the context of the complete geometric deformation (CGD) approach and its influence on the…
In this article, new wormhole solutions in the framework of General Relativity are presented. Taking advantage of gravitational decoupling by means of minimal geometric deformation approach and, the so-called noncommutative geometry…
We apply the Simpson-Visser phenomenological regularization method to a cylindrically symmetric solution of the Einstein-Maxwell equations known as an inverted black hole. In addition to analyzing some properties of thus regularized…
In this work, we apply the anholonomic deformation method for constructing new classes of anisotropic cosmological solutions in Einstein gravity and/or generalizations with nonholonomic variables. There are analyzed four types of, in…
Einstein gravity minimally coupled to a self-interacting scalar field is investigated in the static and isotropic situation. We explicitly construct in partially closed form a new black-hole solution with exponentially decaying scalar hair.…
In this paper, we consider a non-static spherical geometry and formulate its extension for the case of anisotropic matter configuration through minimal gravitational decoupling in $f(\mathbb{R},\mathbb{T})$ theory. We apply a particular…
This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been…
This work presents a novel methodology for deriving stationary and axially symmetric solutions to Einstein field equations using the 1+3 tetrad formalism. This approach reformulates the Einstein equations into first order scalar equations,…
We study the possible existence of static traversable wormholes without invoking exotic matter in the framework of the Einstein--Cartan theory. A family of exact static, spherically symmetric wormhole solutions with an arbitrary throat…
This Note presents the resolution of a differential system on the plane that translates a geometrical problem about isotropic deformations of area and length. The system stems from a probability study on deformed random fields [J.Fournier…
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…
Many problems in Euclidean geometry, arising in computational design and fabrication, amount to a system of constraints, which is challenging to solve. We suggest a new general approach to the solution, which is to start with analogous…
We argue that a spherically symmetric traversable wormhole solution of the Einstein field equations can be supported by minimally coupled self-interacting scalar field which allows a spontaneous symmetry breaking of the field around the…
We summarize some our recent results on encoding exact solutions of field equations in Einstein and modified gravity theories into solitonic hierarchies derived for nonholonomic curve flows with associated bi-Hamilton structure. We argue…
There are explored off-diagonal deformations of "prime" metrics in Einstein gravity (for instance, for wormhole configurations) into "target" exact solutions in f(R,T)-modified and massive/ bi-metric gravity theories. The new classes of…
We investigate how a spherically symmetric fluid modifies the Schwarzschild vacuum solution when there is no exchange of energy-momentum between the fluid and the central source of the Schwarzschild metric. This system is described by means…
The aims of this work are 1) to sketch a proof that there are such parameterizations of the local frame and canonical connection structures when the gravitational field equations in f(R,T)-modified gravity, MG, can be integrated in generic…
Exact solutions to the Einstein field equations may be generated from already existing ones (seed solutions), that admit at least one Killing vector. In this framework, a space of potentials is introduced. By the use of symmetries in this…
We find a reconstruction algorithm able to generate all the static spherically symmetric interior solutions in the framework of Ho\v{r}ava gravity and Einstein-\ae ther theory in presence of anisotropic fluids. We focus for simplicity on…