School of Mathematics
MA4448 - General Relativity 2011-12 (SS Theoretical Physics
SS Mathematics )
Lecturer: Prof. Peter Taylor
Requirements/prerequisites:
Duration: Hilary Term, 11 weeks
Number of lectures per week:
Assessment:
ECTS credits: 5
End-of-year Examination: This module will be examined jointly with MA3429 in a 3-hour examination in Trinity term, except that those taking just one of the two modules will have a 2 hour examination. However there will be separate grades for MA3429 and MA4448.

Description:

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.

Feb 15, 2012

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On 15 Feb 2012, 17:09.