Document Type



Available under a Creative Commons Attribution Non-Commercial Share Alike 4.0 International Licence


Applied mathematics

Publication Details

IAENG International Journal of Applied Mathematics Year: 2011 Vol: 41 Issue: 3 Pages/record No.: 177-190


Albert Einstein predicted the existence of `Einstein rings' as a consequence of his general theory of relativity. The phenomenon is a direct result of the idea that if a mass warps space-time then light (and other electromagnetic waves) will be `lensed' by the strong gravitational field produced by a large cosmological body such as a galaxy. Since 1998, when the first complete Einstein ring was observed, many more complete or partially complete Einstein rings have been observed in the radio and infrared spectra, for example, and by the Hubble Space Telescope in the optical spectrum. However, in the latter case, it is observed that the rings are blue providing the light is not red shifted. The gravitational lensing equation does not include dispersion (i.e. wavelength dependent effects) and thus, can not account for this `blue shift' and, to date, there has been no satisfactory explanation for this colour phenomenon. In this paper we provide an explanation for why Einstein rings are blue using a linear systems theory approach based on the idea that a gravitational field is generated by the scattering of very low frequency scalar waves in which the medium of propagation is space-time and that light waves can be both bent and difracted by this field. The latter effect provides a quantitative result that explains why an Einstein ring is blue.