The Bonnor Beam


Subject: The Bonnor Beam
Date: Sat, 31 May 2008 11:50:23 EDT

This is an exact solution of the Einstein field equation due to W. B. Bonnor, Comm. Math. Phys., 13, 163 (1969). It is written in Brinkman coordinates and models an infinitely long, straight beam of light. It is an example of a pp wave spacetime. It has a uniform plane wave interior region, which is a null dust interpreted as incoherent electromagnetic radiation. I also has an exterior region claimed to be the gravitational field outside the beam. The line elements are:

a) ds squared = – 8 pi m r squared du squared – 2 du dv + dr squared + r squared d theta squared

where

-infinity
b) ds squared = – A du squared – 2 du dv + dr squared + r squared d theta squared

where

A = – 8 pi m r sub 0 sqaured (1 + 2 loge sub e (r / r sub 0))

and the same boundary conditions.

I think that these two solutions will again fail the test of the dual Bianchi identity. The latter must be used to work out how light interacts with gravitation, as in the 112 ECE papers to date.