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Home > MAM4001W > Applied Mathematics Modules > General Relativity and Cosmology

General Relativity and Cosmology

Dr Julien Larena
Associate Professor Charles Hellaby
1st and 2nd semester 2018
20 credits / 30 lectures per semester

1st semester:

  • Mathematics of GR: differentiable manifolds; vector fields; one-form fields; tensor fields; Lie derivative; metrics; parallel transport and connections; curvature of a connection; gravity as geometry; the Einstein-Hilbert action.
  • The Schwarzschlid solution: exterior solutions, orbits and bending of light.
  • Black Holes: Properties of the Schwarzschild Black Hole; Carter-Penrose diagram; wormholes; other Black Holes.
  • Perturbation methods: gravitational waves
  • Cosmology: the homogeneous and isotropic universe; perturbations.

2nd semester:

  • Inhomogeneous Models - Lemaitre, Tolman and Szekeres
  • Singularities and Horizons
  • Observations in Homogeneous and Inhomogeneous Models
  • Junction Conditions

Prerequisites:

The undergraduate module 3GR (General Relativity), or equivalent, is required.