B Gravitational Lensing: Refraction or Something Else?

[Paige_Turner]

TL;DR

Does 4D spacetime, bent by mass, act like "compressed space" in 3D?

It seems like a strong gravitational field acts like spacetime is denser in some sense. Light passing through a gravitational lens is delayed, just like in a glass lens (which refracts because it's denser than air).

 

[PeterDonis]

While there are similarities between gravitational lensing and refraction by an ordinary glass lens, they are only similarities and can't be taken too far. There is nothing in the actual mathematical model in GR that corresponds to "density of spacetime", so that part of the analogy does not hold.

 

[Dale]

Summary:: Does 4D spacetime, bent by mass, act like "compressed space" in 3D?

It seems like a strong gravitational field acts like spacetime is denser in some sense. Light passing through a gravitational lens is delayed, just like in a glass lens (which refracts because it's denser than air).

I have never seen any paper that made that analogy.

 

[DaveC426913]

Summary:: Does 4D spacetime, bent by mass, act like "compressed space" in 3D?

It seems like a strong gravitational field acts like spacetime is denser in some sense. Light passing through a gravitational lens is delayed, just like in a glass lens (which refracts because it's denser than air).

Light follows similar geometry if you only consider a convex (converging) lens (left-side diagrams).

If this analogy really held, you could theoretically find a galaxy or galaxy cluster that is concave in shape. One would naively expect light passing through volume of space with a concave-shaped mass to diverge (right-side diagrams).

 

[vanhees71]

Summary:: Does 4D spacetime, bent by mass, act like "compressed space" in 3D?

It seems like a strong gravitational field acts like spacetime is denser in some sense. Light passing through a gravitational lens is delayed, just like in a glass lens (which refracts because it's denser than air).

As was stressed before, it is not literally the same to have refraction, which is usually naming the phenomena related to the interaction of the electromagnetic field with matter, i.e., due to scattering of em. waves with charged particles, and empty space is not considered as any kind of matter anymore since Einstein got rid of the aether.

Mathematically in some sense there's an analogy, because to describe "lensing" you can use for both usual refraction as well as the "bending of light" by gravitational fields using geometrical optics, which is the eikonal approximation of Maxwell's equations. It turns out that the light rays as defined by geometrical optics follow from Fermat's principle, and in matter-free space within GR, this leads formally to a geodesic equation for "massless particles". Fermat's principle of course is also a valid description of light propation in matter in the eikonal approximation. In this sense mathematically both effects are a bit analogous.