Introductory description

Einstein's general theory of relativity (GR) is the basis for our understanding of black holes and the Universe on its largest scales. In GR the Newtonian concept of a gravitational force is abolished, to be replaced by a new notion, that of the curvature of space-time. This leads to predictions of phenomena such as the bending of light and gravitational time dilation that are well tested, and others, such as gravitational waves, which have only recently been directly detected.

The module starts with a recap of Special Relativity, emphasizing its geometrical significance. The formalism of curved coordinate systems is then developed. Einstein's equivalence principle is used to link the two to arrive at the field equations of GR. The remainder of the module looks at the application of general relativity to stellar collapse, neutron stars and black-holes, gravitational waves, including their detection, and finally to cosmology where the origin of the "cosmological constant" - nowadays called "dark energy" - becomes apparent.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

The geometry of space-time and the invariant “interval” in special relativity; geodesics and equations of motion applied to circular orbits within the Schwarzschild metric; 4-vector formulation of special relativity; metric of special relativity; the equivalence principle and local inertial frames; motivation for considering curved space-time; vectors and tensors in curved coordinate systems; geodesic motion revisited; motion in almost-flat space-time: the Newtonian limit; the curvature and stress-energy tensors; how the metric is determined: Einstein's field equations; Schwarzschild metric; observable consequences; black-holes; stability of orbits; extraction of energy; gravitational radiation and its detection; cosmology: the Robertson-Walker metric

Learning outcomes

By the end of the module, students should be able to:

• Explain the metric nature of special and general relativity, how the metric determines the motion of particles
• Undertake calculations involving the Schwarzschild metric
• Describe features of black-holes
• Demonstrate knowledge of current attempts to detect gravitational waves

Indicative reading list

BF Schutz A first course in general relativity, Cambridge University Press,
M.P Hobson, G. Efstathiou, A.N. Lasenby, General Relativity - An Introduction for Physicists, CUP,
L. D. Landau, E. M. Lifshit︠s︡, The Classical Theory of Fields

View reading list on Talis Aspire

Interdisciplinary

The theory of General Relativity, like quantum theory, has been the result of collaboration between people working in physics and in mathematics with insights flowing in both directions. At its core is a simple hypothesis about observations (the equivalence principle), which leads to a theory of gravity based on the differential geometry of curved spaces. This module covers the necessary mathematics and computes some of the consequences of the theory for the physical Universe.

Subject specific skills

Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking.

Transferable skills

Analytical, communication, problem-solving, self-study