MAU44404 General relativity
Module Code | MAU44404 |
---|---|
Module Title | General relativity |
Semester taught | Semester 2 |
ECTS Credits | 5 |
Module Lecturer | Prof. Manya Sahni |
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 25% 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.
Recommended Reading
- Sean M. Carroll, Spacetime and geometry: An introduction to general relativity.
- Sean M. Carroll, Lecture notes on general relativity.
- Robert M. Wald, General relativity.