General relativistic shock waves in fluids for which pressure equals energy density

A shock wave in a self-gravitating fluid obeying the equation of state: pressure equal to energy density is shown to travel with the velocity of light in a space-time determined by the Einstein field equations. The jump conditions that must be satisfied by the hydrodynamic variables are derived and discussed as are those that must be satisfied by the metric tensor and its derivatives. The latter conditions are obtained by using a variational principle.