# Do gravitational lenses act as prisms?

Light creates gravity, and the greater the light's frequency, the greater this gravitational effect is. It stands to reason then that light of different colors would react slightly differently to gravitational fields. Namely, bluer light would bend more than red light, causing gravitational lenses to act like prisms.

• Gravitational lenses act equally on all kinds of electromagnetic radiation, not just visible light, but also in non-electromagnetic radiation, like gravitational waves. quote from; en.wikipedia.org/wiki/Gravitational_lens#Description Sep 18, 2020 at 10:12
• The optical terminology for the effect you are asking about is "chromatic aberration"; in the context of a lens this is the term for a wavelength-dependent focal length. Gravitational lenses have huge amounts of spherical aberration but no chromatic aberration in the geometric limit. Feb 22, 2021 at 11:15

In general relativity, any test particle's worldline (whether the particle is massive or massless) is determined entirely by its initial four-velocity $$u^\mu$$, and not by any other properties. This is manifested by the geodesic equation $$\frac{d u^\mu}{d\tau} = \Gamma^{\mu} {}_{\rho \sigma} u^\rho u^\sigma.$$ From the properties of ordinary differential equations, you can see that if you know $$u^\mu$$ at some initial time, then it determines the value of $$u^\mu$$ for the future of the particle.
• I wonder what the order of magnitude estimate for the dispersion would be? I suppose that the relevant scales would be $\Delta E$ the energy difference between two test photons, maybe the Ricci scalar, and a length $L$ that the photons travel over; perhaps the deviation in length between the two photons goes something like $\delta L \sim L R \Delta E \frac{8 \pi G}{c^4}$? I probably got my units wrong, but a derivation of a relation like this would be interesting to see Feb 15, 2021 at 18:03