Rindler type acceleration in f(R) gravity

TL;DR

This paper demonstrates that a specific $f(R)$ gravity model with a logarithmic correction can produce a Rindler acceleration term in the metric, satisfying certain energy conditions.

Contribution

It introduces a new $f(R)$ gravity model that naturally incorporates Rindler acceleration and analyzes the energy conditions within this framework.

Findings

The model yields a Rindler acceleration term in the metric.

Weak and strong energy conditions are satisfied in certain domains.

The chosen $f(R)$ form links Rindler acceleration with modified gravity.

Abstract

By choosing a fluid source in $f(R)$ gravity, defined by $f\left(R\right) =R-12a\xi \ln \left\ | R\right\ | $, where $a$ (=Rindler acceleration) and $\xi $ are both constants, the field equations correctly yield the Rindler acceleration term in the metric. We identify domains in which the weak energy conditions (WEC) and the strong energy conditions (SEC) are satisfied.