 The degree of generality reached at this point is not lessened by introducing matter; matter is written into the metric and contributes 4 new coordinate functions necessary to describe the initial distribution of its density and the 3 components of its velocity.This makes possible to determine matter evolution merely from the laws of its movement in an "a priori" given gravitational field which are the [[Fluid dynamics|hydrodynamic]] equations

where "ui" is the 4-dimensional velocity, ε and σ are the densities of energy and [[entropy]] of matter.For the [[ultrarelativistic limit|ultrarelativistic]] [[equation of state]] "p" = ε/3 the entropy σ ~ ε1/4.