Lectures on Introduction to General Relativity (original) (raw)
These lecture notes have been prepared as a rapid introduction to Einstein's General Theory of Relativity. Consequently, I have restricted to the standard four dimensional, metric theory of gravity with no torsion. A basic exposure to geometrical notions of tensors, their algebra and calculus, Riemann-Christoffel connection, curvature tensors, etc has been presupposed being covered by other lecturers. Given the time constraint, the emphasis is on explaining the concepts and the physical ideas. Calculational details and techniques have largely been given reference to. The First two lectures discuss the arguments leading to the beautiful synthesis of the idea of space-time geometry, the relativity of observers and the phenomenon of gravity. Heuristic 'derivations' of the Einstein Field equations are presented and some of their mathematical properties are discussed. The (simplest) Schwarzschild solution is presented. The next lecture discusses the standard solar system tests of Einstein's theory. The fourth lecture returns to static, spherically symmetric solutions namely the interiors of stars. This topic is discussed both to illustrate how non-vacuum solutions are constructed, how the Einstein's gravity affects stellar equilibria and hold out the possibility of complete, un-stoppable gravitational collapse. The concept of a black hole is introduced via the example of the Schwarzschild solution with the possibility of a physical realization justified by the interior solution. The fifth lecture describes the Kerr-Newman family of black holes. More general (nonstationary) black holes are defined and the laws of black hole mechanics are introduced. Their analogy with the laws of thermodynamics is discussed. This topic is of importance because it provides an arena from where the glimpses of interaction of GR and quantum theory can be hoped for. The cosmos is too large and too real to be ignored. So the last lecture is devoted to a view of the standard cosmology. Some additional material is included in an appendix. A collection of exercises meant for practice are also included.
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