From the form of the general coordinate basis expression given above, it is apparent that the stress–energy tensor has precisely the same isotropy group as the null vector field . It is generated by two parabolic Lorentz transformations (pointing in the direction) and one rotation (about the axis), and it is isometric to the three-dimensional Lie group , the isometry group of the euclidean plane. Examples Null dust solutions include two large and important families of exact solutions: pp-wave spacetimes (which model generalizations of the plane waves familiar from electromagnetism), Robinson–Trautman null dusts (which model radiation expanding from a radiating object). The pp-waves include the gravitational plane waves and the monochromatic electromagnetic plane wave. A specific example of considerable interest is the Bonnor beam, an exact solution modeling an infinitely long beam of light surrounded by a vacuum region. Robinson–Trautman null dusts include the Kinnersley–Walker photon rocket solutions, which include the Vaidya null dust, which includes the Schwarzschild vacuum. See also Vaidya metric Lorentz group References . This standard monograph gives many examples of null dust solutions. Exact solutions in general relativity