What is the relationship between light rays and the equations of motion in GR?

[lalbatros]

Hello,

Would you know a reference showing and deriving the equations of light rays in GR.
I would like to read that as well as to compare that to the equations of motion of test particles in a gravitaional field.

Thanks,

Michel

 

[Mark M]

Lalbatros, how is this?

 

[Naty1]

Idealized test particles, with no effect on an ambient gravitational field, follow null geodesics...actual light, that is photons, have some energy, so in fact they deviate slightly from geodesics in the real world...so a more energetic photon will follow a slightly different path than a low energy photon.

 

[Jonathan Scott]

Idealized test particles, with no effect on an ambient gravitational field, follow null geodesics...actual light, that is photons, have some energy, so in fact they deviate slightly from geodesics in the real world...so a more energetic photon will follow a slightly different path than a low energy photon.

Although this may be true as a theoretical limit, any such deviation is so tiny that I don't know of any way for it to have a measurable effect in our universe. We know for example that photons with a wide range of energies from a distant supernova arrive with indistinguishable speed and direction, and even when there is some variation in propagation of photons, it is clearly due to (electromagnetic) interactions with other matter in space rather than gravitational effects.

The normal assumption in GR is that anything whose gravitational effect is negligible compared with that of the source of the field can be treated as a test particle. If you compare the energy of a typical photon with that of a typical gravitational source it should be obvious that this assumption holds in such cases by many orders of magnitude.

 

[yuiop]

Idealized test particles, with no effect on an ambient gravitational field, follow null geodesics...actual light, that is photons, have some energy, so in fact they deviate slightly from geodesics in the real world...so a more energetic photon will follow a slightly different path than a low energy photon.

As Jonathan said, any such effect would be extremely difficult to detect. Additionally the equivalence principle suggests that locally and ignoring tidal effects that photons of all energies follow identical paths, because in the reference frame of a free falling lab, all photons from the same location follow an identical straight path no matter what their energy is.