In general relativity, the Bonnor beam is an exact solution which models an infinitely long, straight beam of light. It is an explicit example of a pp-wave spacetime. It is named after William B. Bonnor who first described it.
The Bonnor beam is obtained by matching together two regions:
- a uniform plane wave interior region, which is shaped like the world tube of a solid cylinder, and models the electromagnetic and gravitational fields inside the beam,
- a vacuum exterior region, which models the gravitational field outside the beam.
The interior part of the solution is defined by
The exterior part of the solution is defined by
The Bonnor beam can be generalized to several parallel beams traveling in the same direction. Perhaps surprisingly, the beams do not curve toward one another. On the other hand, "anti-parallel" beams (traveling along parallel trajectories, but in opposite directions) do attract each other. This reflects a general phenomenon: two pp-waves with parallel wave vectors superimpose linearly, but pp-waves with nonparallel wave vectors (including antiparallel Bonnor beams) do not superimpose linearly, as we would expect from the nonlinear nature of the Einstein field equation.
- Faraoni, V. & Dumse, R. M. (1999). "The gravitational interaction of light: from weak to strong fields". Gen. Rel. Grav. 31 (1): 91–105. arXiv: . Bibcode:1999GReGr..31...91F. doi:10.1023/A:1018867405133.. See also Faraoni; Dumse (1998). "The gravitational interaction of light: from weak to strong fields". arXiv: [gr-qc].
- Bonnor, W. B. (1969). "The gravitational field of light". Comm. Math. Phys. 13 (3): 163–174. Bibcode:1969CMaPh..13..163B. doi:10.1007/BF01645484.
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