Lectures on general relativity

This monograph is based on lectures given to MSc and PhD students of Rangoon (Yangon) University between 1994 and 2006. There are four chapters : Chapter I Elementary principles and tensor calculus,Chapter II The law of gravitation,Chapter III The Hamiltonian formulation of general relativity, Chapter IV The singularities and blackholes. Some of the topics covered are 1.2 The Riemann spacetime 1.3 Curved space 1.4 Christoffel symbols 1.5 The principle of least action and the geodesic equation 16 The covariant derivative 1.7 Parallel displacement of a vector 1.8 Geodesics 1.9 Material energy tensor 2.1 The Newtonian solution 2.2 The Ricci tensor 2.3 The Schwarschild line element 2.4 The orbital motion in general relativity 2.5 The deflection of light 2.6 The precessional motion of planets 2.7 Gravitational lenses 3.1 The Lagrangian density for gravitation 3.2 The momentum of the gravitational field 3.4 The Hamiltonian of the gravitational field 3.4 The weak field approximation 3.5 Gravitational waves 3.6 The energy of the gravitational waves 3.7 The polarization of the gravitational waves 4.1 Light dragging by massive collapsing bodies 4.2 Penrose diagrams and singularities 4.3 The Hawking radiation 4.4 The Dirac-Lemaitre metric . The readers will find the influence of Eddington's 1922 Cambridge monograph "Mathematical Theory of Relativity" regarding notation and the backbone. The rather strong influence of Dirac's classic papers on Hamiltonian formulation of general relativity that he presented in the 1958 issue of Proc Roy Soc A vol 246,333 ,in the 1959 issue of Phys Rev vol 114 , 924 and the 1959 issue of Phys Rev Lett vol 2,368 will be apparent in Chapter III. These papers played a huge role in persuading physicists -or at least one third world physicist- of the physical reality of the gravitational waves and of the quantum aspect of the gravitational radiation called the graviton which as has spin 2. The material on polarization of gravitational waves is based on Dirac's treatment as expounded in his slim book on general relativity that he published in 1975. The chapter on singularities rely heavily on the work of Penrose and Hawking as described in the 1973 classic Cambridge monograph of of Hawking and Ellis. For the treatment of of quantum aspects of blackhole evaporation we based our discussions on the 1976 Phys Rev D vol 13, 2188 paper of Hartle and Hawking and on R Wald's 1994 excellent and meticulous Chicago lectures on Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics. The general philosophy of the choice of topics and the treatment is based on my concept of what a third world PhD in physics should "know" quite independent of the topic of his thesis research lasting 3 to 4 years.