Inclusion of a perfect fluid term into the Einstein-Hilbert action

TL;DR

This paper presents a method to derive the stress-energy tensor of a perfect fluid directly from the Einstein-Hilbert action by adding a specific term and performing metric variation.

Contribution

It introduces a novel approach to obtain the perfect fluid stress-energy tensor through an action modification and metric variation.

Findings

Derived the perfect fluid stress-energy tensor from an extended Einstein-Hilbert action.

Provided a new variational method for incorporating perfect fluids into gravitational theories.

Clarified the role of additional terms in the action for modeling perfect fluids.

Abstract

I introduce a method to obtain the stress-energy tensor of the perfect fluid by adding a suitable term to the Einstein-Hilbert action. Variation should be understood with respect to the metric.