Exact analytical vacuum solutions of $R^n$-gravity model depending on two variables

Abstract

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 contain both non-stationary configurations of the travelling wave type and stationary ones, in particular, depending on one radial variable.

19 pages, 8 figures

References in corpus (16)

• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• Low surface brightness galaxies rotation curves in the low energy limit of $R^n$ gravity : no need for dark matter?
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• The evolution of density perturbations in f(R) gravity
• Analysis of Rotation Curves in the framework of R^n gravity
• Further Exact Cosmological Solutions to Higher-Order Gravity Theories
• Power-law cosmic expansion in f(R) gravity models
• Non-Vacuum Bianchi Types I and V in f(R) Gravity
• Dynamical systems analysis of anisotropic cosmologies in $R^n$-gravity
• Early and late time cosmology: the $f(R)$ gravity perspective
• Probing the existence of the ZTF Casimir wormholes in the framework of $f(\mathcal{R})$ gravity
• A Geometrical Approach to Strong Gravitational Lensing in f(R) Gravity
• R^n gravity and the chameleon
• $f(R)$-Gravity Generated Post-inflationary Eras and their Effect on Primordial Gravitational Waves
• Phase Space of Anisotropic $R^n$ Cosmologies
• Smeared Mass Source Wormholes in Modified $f(R)$ Gravity with the Lorentzian Density Distribution Function

Cited by in corpus (1)

• Scheme of integration of vacuum $F(R)$ gravity in a travelling wave variable