Lagrangian Density for Perfect Fluids in General Relativity

Abstract

A previously discussed variational principle for a perfect fluid in general relativity was restricted to irrotational, isentropic motions of the fluid. It is proven that these restrictions can be dropped, and the original variational principle can be generalized to general motions of the perfect fluid. The form of the basic Lagrangian density is unchanged by these generalizations. An Eulerian fluid description is used throughout. As a by‐product of our variational principle, the 4‐velocity is required to have the generalized Clebsch form.