Connection of General relativity and geometric Refraction of light

[exponent137]

I tried to obtain refraction of light by sun's gravity by substitution of sun's gravitational field by aether with different speeds of light.
I do not get right result. Where I am wrong?

For light which travel close to the sun by direct trajectory, I get the following speed of light in dependence of angle phi.


C=c0 (1-g cos(phi)/(1-g cos(phi)^3)^(1/2)

g=2GM/(r c^2).
r is the closest radius to the sun.

I suppose that refraction law is

dc = d(alpha) * tg(phi)

Where alpha is small refraction and phi is angle regarding sun.



But this do not give right solution in the first approximation, which is alpha = 2g.

Equation for c I get from Schwarzschild equation.

c0^2 dt^2 (1-2g cos(phi)) - dx^2/(1-2g cos(phi))-r cos(phi)^2...=0

 

[Chris Hillman]

This idea has been extensively discussed in the literature. Try using the searchbar at http://math.ucr.edu/home/baez/RelWWW/ to search the arXiv using the search key "refraction lensing gr-qc". This turns up lots of relevant eprints, including one which is hardly a week old http://arxiv.org/abs/0704.3485 Enjoy!