Related papers: Exact analytical vacuum solutions of $ R^n $-gravi…
It is shown that the Fermi-Walker gauge allows the general solution of determining the metric given the sources, in terms of simple quadratures. We treat the general stationary problem providing explicit solving formulas for the metric and…
It is known that B\"acklund transformations can be used to generate stationary axisymmetric solutions of Einstein's vacuum field equations with any number of constants. We will use this class of exact solutions to describe the exterior…
An exact solution for the bulk 5-dimensional geometry is derived for F(R) gravity with non-flat de-Sitter 3-branes located at the $M_4 \times Z_2$ orbifold boundaries. The corresponding form of F(R) that leads to such an exact solution of…
The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. In this context, we study the exact vacuum solutions of Bianchi type I, III and Kantowski-Sachs spacetimes in the metric…
A method is presented to construct a particular, non-minimally coupled scalar-tensor theory such that a given metric is an exact vacuum solution in that theory. In contrast to the standard approach in studies of gravitational dynamics,…
The equations of motion of four-dimensional conformal gravity, whose Lagrangian is the square of the Weyl tensor, require that the Bach tensor $E_{\mu\nu}= (\nabla^\rho\nabla^\sigma + \ft12 R^{\rho\sigma})C_{\mu\rho\nu\sigma}$ vanishes.…
We study the three-dimensional gravity with torsion given by the Mielke-Baekler (MB) model coupled to gravitational Chern-Simons term, and that possess electric charge described by Maxwell-Chern-Simons electrodynamics. We find and discuss…
The field equations of a special class of teleparallel theory of gravitation and electromagnetic fields have been applied to tetrad space having cylindrical symmetry with four unknown functions of radial coordinate $r$ and azimuth angle…
We investigate spontaneous symmetry breaking in a conformally invariant gravitational model. In particular, we use a conformally invariant scalar tensor theory as the vacuum sector of a gravitational model to examine the idea that…
We investigate diffusion equations which have concentration dependent diffusion coefficients with physically two relevant Ans\"atze, the self-similar and the traveling wave Ansatz. We found that for power-law concentration dependence some…
The metric-affine gauge theory of gravity provides a broad framework in which gauge theories of gravity can be formulated. In this article we fit metric-affine gravity into the covariant BRST--antifield formalism in order to obtain gauge…
In this paper we report some results obtained by applying the radial gauge to 2+1 dimensional gravity. The general features of this gauge are reviewed and it is shown how they allow the general solution of the problem in terms of simple…
We study a type of geometric theory with a non-dynamical one-form field. Its dynamical variables are an $su(2)$ gauge field and a triad of $su(2)$ valued one-forms. Hamiltonian decomposition reveals that the theory has a true Hamiltonian,…
Using the Navarro-Frenk-White (NFW) dark matter density profile we reconstruct an effective field theory model for gravity at large distances from a central object by demanding that the vacuum solution has the same gravitational properties…
We consider $f\left(R\right) $-gravity in a Friedmann-Lema\^itre-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of $f\left(R\right) $ and…
In the cosmological scenario in $f\left( T\right) $ gravity, we find analytical solutions for an isotropic and homogeneous universe containing a dust fluid and radiation and for an empty anisotropic Bianchi I universe. The method that we…
We continue to study the spherically symmetric vacuum solutions of the tensor-four-scalars theory which is a modification of general relativity. Our aim is to construct vacuum solutions with asymptotically constant circular velocity curves…
We present a gauge formulation of the special affine algebra extended to include an antisymmetric tensorial generator belonging to the tensor representation of the special linear group. We then obtain a Maxwell modified metric affine…
We extend the results of antecedent literature on quadratic Metric-Affine Gravity by studying a new quadratic gravity action in vacuum which, besides the usual (non-Riemannian) Einstein-Hilbert contribution, involves all the parity even…
The implications from the existence of a proper Homothetic Vector Field (HVF) on the dynamics of vacuum anisotropic models in $F(R)$ gravitational theory are studied. The fact that \emph{every} Spatially Homogeneous vacuum model is…