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

TL;DR

This paper derives exact analytical vacuum solutions for a two-variable $ R^n $-gravity model, revealing both stationary and non-stationary configurations, advancing understanding of modified gravity solutions.

Contribution

It provides the first explicit exact solutions of $ R^n $-gravity depending on two variables, including traveling wave and stationary configurations.

Findings

Exact solutions for different $ n $ values

Presence of traveling wave configurations

Stationary solutions depending on radial variable

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.