General Relativity and Gravitation
(MTH720U/MTHM033)


Last updated 14.12.2011
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Lecturer : Dr. A.G. Polnarev

e-mail : a.g.polnarev@qmul.ac.uk
website page : http://www.maths.qmul.ac.uk/~agp
Office : Room 356, Maths Building

Office Hours : Room 356, Maths Building, Tuesday 16.30 - 17.30, Wednesday 12.30 - 13.30

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This course is an introduction to General Relativity and includes:

Explanation of the fundamental principles of GR.
The motion of particles in a given gravitational field.
The propagation of electromagnetic waves in a gravitational field.
The derivation of Einstein's field equations from the basic principles.
The derivation of the Schwarzschild solution.
Analysis of the Kerr solution.
A discussion of physical aspects of strong gravitational fields around black holes.
The generation, propagation and detection of gravitational waves.
The weak general relativistic effects in the Solar System and binary pulsars.
The experimental tests of General Relativity.

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KEY OBJECTIVES

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LECTURE NOTES//

Lecture 1. Introduction
A. About this course // B. The principle of equivalence //
C. Gravity as a space-time geometry // D. The principle of covariance

Lecture 2. Tensors
A. The principle of covariance and tensor // B. Transformation of coordinates//
C. Contravariant and covariant tensors // D. Reciprocal tensors // E. Examples //

Lecture 3. Physical Geometry of Space-Time

A. Proper time // B. Physical distance //
C. Synchronization of clocks // D. Invariant 4-volume //

Lecture 4. Covariant differentiation
A. Parallel translation // B. Covariant derivatives and Christoffel symbols //
C. The Christoffel symbols and the metric tensor // D. Physical applications //

Lecture 5. Motion of a Test Particle in a Gravitational Field
A. Hamilton-Jacobi equation // B. Eikonal equation //
C. The motion in a spherically symmetric static gravitational field //

Lecture 6. Curvature of space-time
A. The Riemann curvature tensor // B. Symmetry properties of the Riemann tensor //
C. Bianchi Identity // D. The Ricci tensor and the scalar curvature //
E. Geodesic deviation equation // F. Stress-Energy Tensor //
G. Heuristic Derivation of EFEs //

Lecture 7. Rigorous Derivation of EFEs
A. The principle of the least action // B. The action function for the gravitational field //
C. The action function for matter // D. The stress-energy tensor and the action density //
E. The final EFEs //

Lecture 8. Solving EFEs
A. Weak field and slow motion approximation // B. The Schwarzschild metric as an exact solution of EFEs //
C. Physical singularity versus coordinate singularity in the Schwarzschild metric //

Lecture 9. Black Holes
A. Limit of stationarity // B. Event horizon //
C. Schwarzschild black holes // D. Kerr Black Holes //
E. "Ergosphere" and Penrose process //

Lecture 10. In vicinity of the Schwarzschild Black Hole
A. Test particles in the Schwarzschild Metric // B. Stable and Unstable Circular Orbits //
C. Propagation of light in the Schwarzschild metric //

Lecture 11. Experimental Con rmation of GR and Gravitational Waves (GWs)
A. Relativistic experiments in the Solar system and Binary pulsar // B. Propagation of GWs //
C. Detection of GWs // D. Generation of GWs // E. Examples and problems //


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COURSE WORKS//

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PAST EXAMINATION PAPERS //

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Textbooks

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