Related papers: Exact solutions in two-dimensional metric $f(R)$-g…
In this paper we consider the metric power-law $f(R)\sim R^n $-gravity model for the four-dimensional metric tensor depending on two coordinates. We obtain exact analytical vacuum solutions for different values of $ n $. These solutions…
In this paper we present a number of examples of exact solutions for the Friedmann cosmological equation for metric $ F(R) $ gravity model. Emphasis was placed on the possibility of obtaining exact time dependences of the main cosmological…
In this paper we investigate spherically symmetric vacuum solutions of $f(R)$ gravity in a higher dimensional spacetime. With this objective we construct a system of non-linear differential equations, whose solutions depend on the explicit…
The main purpose of this paper is to investigate the exact solutions of cylindrically symmetric spacetime in the context of $f(R,T)$ gravity [1], where $f(R,T)$ is an arbitrary function of Ricci scalar $R$ and trace of the energy momentum…
In a recent paper we have established the form of the metric-torsional conformal gravitational field equations, and in the present paper we study their vacuum configurations; we will consider a specific situation that will enable us to look…
We construct the $F(R)$ gravity models with exact particular solutions using the conformal transformation and the superpotential method for the corresponding models in the Einstein frame. The functions $F(R)$ are obtained explicitly. We…
We find a new method for looking for the static and spherically symmetric solutions in $F(R)$ theory of gravity. With this method, a number of new solutions in terms of the analytic functions are obtained. We hope this investigation may be…
We review the exact solutions in modified gravity. It is one of the main problems of mathematical physics for the gravity theory. One can obtain an exact solution if the field equations reduce to a system of ordinary differential equations.…
In a recent paper \cite{1}, we have studied the vacuum solutions of Bianchi types I and V spacetimes in the framework of metric f(R) gravity. Here we extend this work to perfect fluid solutions. For this purpose, we take stiff matter to…
Axially symmetric static vacuum exact solution (ASSVES) in Weyl coordinates are studied in $f(R)$ theories of gravity. In particular, we obtain a general explicit expression for the dependence between $df(R)/dR$ and the $r$ and $z$…
Spherically symmetric static vacuum solutions have been built in $f(T)$ models of gravity theory. We apply some conditions on the metric components; then the new vacuum spherically symmetric solutions are obtained. Also, by extracting…
This paper is devoted to investigate the exact solutions of Bianchi types I and V spacetimes in the context of f(R, T) gravity [1]. For this purpose, we found two exact solutions in each case by using assumption of constant deceleration…
In this work, exact solutions of static and spherically symmetric space-times are analyzed in f(R) modified theories of gravity coupled to nonlinear electrodynamics. Firstly, we restrict the metric fields to one degree of freedom,…
We analyze an alternative theory of gravity characterized by metrics that are tensor density of rank(0,2)and weight-1/2.The metric compatibility condition is supposed to hold. The simplest expression for the action of gravitational field is…
There is a number of completely integrable gravity theories in two dimensions. We study the metric-affine approach on a 2-dimensional spacetime and display a new integrable model. Its properties are described and compared with the known…
In this article we propose the scheme of integration of two-dimensional $F(R)$ gravity vacuum equations in a travelling wave variable. The main emphasis is placed on the fundamental possibility of obtaining different forms of the function…
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…
Torsion and curvature could play a fundamental role in explaining cosmological dynamics. f(R)-gravity with torsion is an approach aimed to encompass in a comprehensive scheme all the Dark Side of the Universe (Dark Energy and Dark Matter).…
We investigate some exact static cylindrically symmetric solutions for a perfect fluid in the metric $f(R)$ theory of gravity. For this purpose, three different families of solutions are explored. We evaluate energy density, pressure, Ricci…
The modified theories of gravity, especially the $f(R)$ gravity, have attracted much attention in the last decade. This paper is devoted to exploring plane symmetric solutions in the context of metric $f(R)$ gravity. We extend the work on…