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MAU44404 General relativity

Module Code MAU44404
Module Title General relativity
Semester taught Semester 2
ECTS Credits 5
Module Lecturer Prof. Andrei Parnachev
Module Prerequisites
 
MAU34301 Differential geometry and
MAU34402 Classical electrodynamics

Assessment Details

  • This module is examined in a 2-hour examination at the end of Semester 2.
  • Continuous assessment contributes 15% towards the overall mark.
  • Re-assessment, if needed, consists of 100% exam.

Contact Hours

11 weeks of teaching with 3 lectures and 1 tutorial per week.

Learning Outcomes

On successful completion of this module, students will be able to

  • Define the Einstein-Hilbert action and derive Einstein's equations from an action principle.
  • Define the stress-energy-momentum tensor, obtain its components in an orthonormal tetrad, and obtain explicit expressions for the stress-energy-momentum tensor describing a perfect fluid matter distribution.
  • Derive the canonical form of the Schwarzschild solution to the vacuum field equations under the sole assumption of spherical symmetry, and hence state Birkhoff's Theorem.
  • Derive expressions for the gravitational redshift, perihelion advance of the planets, and light deflection in the Schwarzschild space-time and hence discuss solar system tests of general relativity.
  • Obtain the geodesic equations in arbitrary space-times and hence describe various trajectories such as radially in-falling particles or circular geodesics etc.
  • Obtain the maximal extension of the Schwarzschild solution in Kruskal coordinates and hence discuss the Schwarzschild black hole.
  • Define spatial isotropy with respect to a universe filled with a congruence of time-like world-lines, discuss the consequences of global isotropy on the shear, vorticity and expansion of the congruence and hence construct the Friedmann-Robertson-Walker metric.
  • Obtain the Friedmann and Raychaudhuri equations from the Einstein field equations, solve these equations for the scale factor and discuss the cosmogonical and eschatological consequences of the solutions.
  • Derive the Einstein equations in the linear approximation and discuss the Newtonian limit in the weak-field, slow-moving approximation.
  • Use the gauge freedom to show that, in the Einstein-deDonder gauge, the perturbations satisfy an inhomogeneous wave-equation, to solve in terms of plane-waves, and to use the residual gauge freedom to show that for waves propagating in the positive z-direction there are only two linearly independent non-zero components.
  • Derive the Reissner-Nordstrom solution of the Einstein-Maxwell field equations, obtain its maximal extension and discuss the Reissner-Nordstrom black hole solution.

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