Lecturer: Elizabeth Stanway

Weighting: 15 CATS

Aims:
The module presents Einstein's general theory of relativity and its applications in modern astrophysics. It is a follow-on to the third year module PX389 Cosmology.

To present the theory of General Relativity and its applications in modern astronomy, and to give an understanding of black-holes.

Objectives:
At the end of this module you should:

• understand the metric nature of special and general relativity, how the metric determines the motion of particles
• be able to undertake elementary calculations involving the Schwarzschild metric
• be able to describe the key features of black-holes
• be able to demonstrate knowledge of current attempts to detect gravitational waves

Syllabus:

• The geometry of space-time and the invariant “interval” in special relativity
• The 4-vector formulation of special relativity; the metric of special relativity
• The equivalence principle and local inertial frames; the motivation for considering curved space-time
• Vectors and tensors in curved coordinate systems
• Geodesics: how the metric determines equations of motion
• Motion in almost-flat space-time: the Newtonian limit
• The curvature and stress-energy tensors
• How the metric is determined: Einstein's field equations
• The Schwarzschild metric; observable consequences
• Black-holes; stability of orbits; extraction of energy
• Gravitational radiation and its detection
• Cosmology: the Robertson-Walker metric

Commitment: 25 Lectures (and 5 problems classes)

Assessment: 3 hour examination

Recommended Texts: 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.

Leads from: PX389 Cosmology