Harmonic morphisms and shear-free perfect fluids coupled with gravity
The author considers a four-dimensional space-time (\(M,g\)) of Robertson-Walker type, modeling a relativistic perfect fluid (\(U,p,\rho\)), where \(U\) is a time-like future-pointing unit vector field on \(M\); \(p\) and \(\rho\) are the pressure and the mass density functions, respectively. The perfect fluid is supposed to be coupled with gravity (i.e., the Einstein's equations hold) and shear-free (i.e., \(\rho = -3p= \lambda^2\) for a special ``dilation'' function \(\lambda\)). Under these hypotheses, the author proves the known fact that the fluid is either irrotational or expansion-free. The novelty brought by the paper consists in the proof based on the classification of harmonic morphisms with one-dimensional fibers on four-dimensional Einstein manifolds.
scientific article; zbMATH DE number 6342897
scientific article