The Bonnor Beam as an Exact Realization of Curvature Sourced by Pure Radiation

The Bonnor Beam as an Exact Realization of Curvature Sourced by Pure Radiation Abstract This paper examines the Bonnor beam—an exact solution of the Einstein equations first obtained by W. B. Bonnor in 1969—as a concrete classical illustration of the thesis that spacetime curvature is sourced by the stress-energy tensor rather than by rest mass. The solution describes a steady, uniform beam of light of circular cross-section. Its interior is a null-dust region (interpretable as incoherent electromagnetic radiation) matched to a vacuum exterior; both regions are pp-waves. The construction demonstrates that a pure radiation stress-energy tensor, carrying zero rest mass, generates a non-flat metric of Petrov type N. Parallel co-directed beams do not attract, while the beam itself is gravitationally stable. These properties supply a precise, globally regular (within the idealization of infinite length) example of gravity without rest mass within classical general relativity.