- Bonnor beam
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 app-wave spacetime .The Bonnor beam is obtained by matching together two regions:
* a uniform plane wave
interior region , which is shaped like theworld tube of a solid cylinder, and models the electromagnetic and gravitational fields inside the beam,
* a vacuumexterior region , which models the gravitational field outside the beam.On the "cylinder" where they meet, the two regions are required to obey
matching conditions stating that themetric tensor andextrinsic curvature tensor must agree.The interior part of the solution is defined by
::
This is a
null dust solution and can be interpreted as incoherent electromagnetic radiation.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 vector s superimpose linearly, but pp-waves with nonparallel wave vectors (including antiparallel Bonnor beams) do not superimpose linearly, as we would expect from thenonlinear nature of theEinstein field equation .ee also
References
*. See also cite web | title= The gravitational interaction of light: from weak to strong fields| work=ArXiv | url=http://www.arxiv.org/abs/gr-qc/9811052 | accessmonthday=June 15 | accessyear=2005
*
External links
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