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

Here, I introduce a method to obtain the stress-energy tensor of the perfect fluid by adding a suitable term to the Einstein-Hilbert action. This term has the physical interpretation of pressure and variation should be understood with respect to the metric. In this derivation, velocity potentials are not needed.

Automated summary

This article introduces a method for obtaining the stress-energy tensor of a perfect fluid by adding a suitable term to the Einstein-Hilbert action. This term has the physical interpretation of pressure, and its variation should be understood with respect to the metric. Velocity potentials are not required in this derivation.