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

TL;DR

This paper introduces a method to integrate 2D vacuum $F(R)$ gravity equations using a travelling wave variable, allowing for the derivation of various $F(R)$ functions based on chosen metric components.

Contribution

It presents a novel scheme for solving $F(R)$ gravity equations in two dimensions by employing a travelling wave variable, enabling flexible determination of the gravity function.

Findings

Different forms of $F(R)$ can be obtained by selecting specific metric functions.

The scheme demonstrates the fundamental possibility of integrating $F(R)$ equations in a new way.

The approach provides a framework for exploring solutions in 2D $F(R)$ gravity.

Abstract

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 $F(R)$ by arbitrarily choosing a certain function through which all components of the metric tensor of the theory can be expressed.