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!

 

[Entropia]

The connection between general relativity and geometric refraction of light can be explained through the concept of spacetime curvature. In general relativity, gravity is not seen as a force between masses, but rather as a curvature in the fabric of spacetime caused by massive objects. This curvature affects the path of light, causing it to bend as it travels near massive objects like the sun.

In your attempt to obtain refraction of light by substituting the sun's gravitational field with a hypothetical aether with varying speeds of light, you are essentially trying to recreate the effects of spacetime curvature. However, this approach is not correct because the concept of aether has been disproven by experiments and is not a part of modern physics.

Furthermore, your proposed refraction law does not take into account the effects of spacetime curvature on the path of light. In general relativity, the bending of light is described by the geodesic equation, which takes into account the curvature of spacetime. This equation predicts a bending of light that is twice the value of your proposed refraction law.

In summary, your approach to obtaining refraction of light by substituting the sun's gravitational field with aether and using a refraction law that does not account for spacetime curvature is not correct. To fully understand the connection between general relativity and geometric refraction of light, one must consider the effects of spacetime curvature on the path of light.