Astronomy 4/5M: GR-II  Gravitation and Relativity II   Dr M. Hendry, Room 312 Kelvin Building 11 lectures, starting January 2009

Welcome to Gravitation and Relativity II. In these 11 lectures we will apply the mathematical and physical machinery developed in Gravitation and Relativity I to explore how general relativity influences a range of astrophysical phenomena -- from the interior structure of stars to the geometry of the Universe.

Course Content (11 lectures)

Resume of Gravitation and Relativity Part I
Foundations of General Relativity; properties of manifolds; transformation formulae for tensors; the metric tensor; covariant differentation of tensors; the geodesic principle; the energy-momentum tensor; the Riemann-Christoffel and Ricci tensors; conservation laws of energy and momentum; Einstein's field equations.

Static Models with Spherical Symmetry
Orthogonal metrics; spherically symmetric metrics in curved spacetime; evaluation of the Christoffel symbols and components of the Ricci tensor; derivation of the standard form of the Schwarzschild metric; derivation of the ordinary geodesics and identification with planetary orbits; classical tests of General Relativity: advance of pericentre, gravitational light deflection - applications to gravitational lensing and binary pulsars.

Einstein's Equations for Static, Spherically Symmetric Stars
Derivation of the Oppenheimer-Volkhoff equation; outline of a general numerical solution and derivation of the exact solution for constant density.

Gravitational Waves
Linearisation of Einstein's Equations for a weak gravitational field; establishment of the wave equation for gravitational radiation; example of plane gravitational radiation - its quadrupole nature and forms of polarisation. Example of a binary star system.

Black Holes
The infall of particles and photons towards the Schwarzschild horizon; behaviour of the coordinate time and radial coordinate inside and outside this horizon;  new form of the metric and interpretation of the spacetime diagram;  Hawking radiation.

GR and Cosmology
The cosmological principle and derivation of the Robertson-Walker metric;  (time permitting) observational tests of cosmological world models; luminosity and angular diameter distances;   connection to Cosmology II.

Recommended Books

Schutz, B. "A First Course in General Relativity", CUP (1985)
    This book is not essential for purchase, but is highly recommended

Books for consultation
Misner, Thorne and Wheeler,"Gravitation", Freeman (1973)
Wald, R.M. "General Relativity", University of Chicago (1984)
Rindler, W. "Essential Relativity", Springer (1977).
Berry, M. "Principles of Relativity and Cosmology", CUP (1976)
Papapetrou, A. "Lectures in General Relativity", Reidel (1974)
Ohanion, H.C. "Gravitation and Spacetime", Norton (1976)
d'Inverno R. "Introducing Einstein's Relativity", Oxford University Press (1992)

None of the above books is essential, or indeed worthwhile, for purchase but may be useful for occasional consultation and general background reading

Martin Hendry,
January 2009

Lecture Notes

Lecture notes for the course are provided below in pdf format. These notes are presented as a self-contained document (essentially like a short textbook) covering in detail all the material in the course syllabus.

These lecture notes are designed to avoid the need for students to copy down large amounts of text from the blackboard or OHP during the lectures.  They should not be seen as a substitute for attending the lectures themselves.
 

Lecture notes and other downloads

MP3 audio files of the GRG-II lectures

Example Sheets: Model Answers
 

You may also wish to consult the example sheets and lecture notes previously given for GR-I; these are available here
 

Please send any comments or questions on GR-II to Martin Hendry