# Does light have gravity?

## Main Question or Discussion Point

I know light is affected by gravity, but does light have its own gravitational pull? Does light attract other light?

## Answers and Replies

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In general relativity, light does have gravity. The gravity depends on the energy density and momentum flow.

But how to calculate the gravity between two lights ?we know light is massiveless when v=0,but v=c !

Light has no gravitational field around it..light is bent because space-time is curved as per GR...

jtbell
Mentor
No, Snazzy is correct. In general relativity, two light beams can affect each other gravitationally. It's been discussed here before, with some details, but right now I can't think of the right keywords to pull up that thread in a search.

I've moved this to the relativity forum so maybe someone there will help out.

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Light has no gravitational field around it..light is bent because space-time is curved as per GR...
That is not quite true. Although the spacetime is curved around, say, a star it is not curved spacetime that is the cause. For example; a beam of light is deflected by the sun due to the gravitational attraction on the light. The amount of delfection is determined by that acceleration and the amount of spatial contraction caused by the mass of the sun.

To illustrate this concept consider a uniform gravitational field. A beam of light is also deflected by such a field. However the spacetime curvature for such a field is zero!

It is quite true that a beam of light has a gravitational field around it. I'm curious as to why you'd conclude otherwise?? The derivation can be found on the internet or in the physics literature. E.g. look in Relativity, Thermodynamics and Cosmology, Richard C. Tolman, Dover Pub. page 273-288.

Pete

i dont understand uniform gravitational field and curvature is zero...how can a curvature be zero in uniform gravitational field...

i dont understand uniform gravitational field and curvature is zero...how can a curvature be zero in uniform gravitational field...
Its pretty simple. Eintein never said that gravity was a curvature in spacetime. Actually he stated quite clearly that he disagreed with such an interpretation. The assumption that he said so is probably the worst misconception in all of physics. Consider Einstein's equivalence principle (weak form)
A uniform gravitational field is equivalent to a uniformly accelerating frame of reference in flat spacetime.
If the spacetime is flat then it is impossible to introduce spacetime curvature by changing the spacetime coordinate from that of an inertial frame in a flat spacetime to coordinates corresponding to a uniformly accelerating frame of reference.

Consider what curved spacetime really is; spacetime curvature and tidal gradients are the exact same phenomena expressed in different languages.

Since a uniform gravitational field, by definition, has zero tidal forces then the spacetime curvature must also be zero. There is no way around this. It seems to have been Max Von Laue who associated spacetime curvature with a gravitational field. Perhaps the reason was that you can't transform spacetime curvature away and thus you can tell if you're in an accelerating frame in flat spacetime or in a gravitational field which has tidal gradients present. I guess Von Laue didn't like the notion of a gravitational field having a relative existance.

However the non-existance of tidal forces does not imply that there are no gravitational field present. This is stated quite clearly in Gravitation by Misner, Thorne and Wheeler. I.e. on page 467, i.e.
One can always find in any given locality in which all local "gravitational fields" (all Christofell symbols: all $\Gamma^{\alpha}_{\mu\nu}$) disappear. No $\Gamma$ means no "gravitational field" ...
The Christoffel symbols for an observer in a uniform gravitational field are non-zero. For this reason particles, as well as light, are deflected.

Pete