Lagrangian formalism for adiabatic fluids on five-dimensional space-time

Abstract

The recently developed Lagrangian formalism on extended five-dimensional space-time that permits a unified description of general relativistic and gravitating nonrelativistic classical fields is applied to a model of an adiabatic perfect fluid described in terms of Lagrangian coordinates. The Lagrangian density is chosen as an arbitrary Lorentz- (or Galilei-) invariant function of the 5-current vector and leads, by variation with respect to frame fields, to a 5-stress-energy tensor, whose additional components are naturally interpreted as an entropy-flux vector.