Description. Einstein's theory of General Relativity (GR) models gravity in terms of curved space-time. One of its predictions is that gravity bends light, and this was famously confirmed in 1919, in observations of light bending around the edge of the Sun during a solar eclipse. In that case, the amount of bending was small. But a stronger gravitational field, such as that near a black hole, can cause light-rays to deviate very considerably. Recent research at Durham used gravitational lensing to discover an ultramassive black hole.

The project will begin by taking the equations describing light-rays passing near a compact massive object such as a star or a black hole, and investigating how the image of a source beyond that object gets deformed. Computing the angle by which light-rays get bent will enable you to generate pictures such as the right-hand one below. A later part of your work will be to give a brief account of GR and its geometrical framework, to explain the background and the mathematics of black holes, and derive the equations for light-rays.

Prerequisites. An acquaintance with the idea and the mathematics of space-time, in particular Special Relativity, for example via SREM II or its Physics equivalent.

Resources. There are many relevant books (and ebooks) in the Library, and many online resources.

The left-hand figure is a photograph of an Einstein ring: a lensed image of a distant galaxy. The right-hand figure is a numerically-generated example, using GR. The (red) disc at the centre is the unlensed object, and because of the lensing we instead see a ring (black).