Exact solutions in two-dimensional metric $f(R)$-gravity

TL;DR

This paper derives exact analytical vacuum solutions in two-dimensional metric $f(R)$-gravity models, expanding understanding of cosmological solutions with arbitrary functions in the metric.

Contribution

It provides new exact solutions for two-dimensional $f(R)$-gravity with arbitrary functions, enhancing the analytical understanding of such models.

Findings

Exact vacuum solutions for different $f(R)$ forms.

Solutions expressed in terms of arbitrary functions.

Potential for new variable choices under specific conditions.

Abstract

In this paper we consider the two-dimensional metric $f(R)$-gravity model for the metric tensor depending on two variable: time and one spacelike coordinate. We obtain exact analytical vacuum solutions for different forms of function $ f(R) $ which are solutions of cosmological type. These solutions are expressed in terms of arbitrary functions, which, under certain conditions, can be chosen as new variables.