Selected Topics on Gravitation[MatSciRep:49]

Abstract

This report is based on the series of 10 lectures given by the visiting scientist Pr.P.C. Vaidya, for which the Notes prepared by A.R. Prasanna. Gravitational phenomenon by means of Newton's law of Universal Gravitation is discussed along with a revision of basic concepts of Newtonian Mechanics. As a result of which the special theory of Relativity, emerged based on postulates with respect to Invariance, and Homogeneous Euclidean Background prevailing the entire space-time. This is just a general background and the particles, charges, forces were all entraneous entities, which are to be superposed on this background, and interactions have to be further postulated. With spherical symmetry, Schwarzschild's solution is the only solution of vacuum field equations, and because it is static there are no strictly spherical waves; Hence a cylindrical symmetry is considered in Lecture 2. Plane Waves, Waves from bounded sources are also discussed in this lecture. The Equation "R(i,j) = 0" is too complicated to yield any general results, giving general properties of gravitational waves. Geometrical approach leading to such general properties is considered for discussions in the Lecture 3. Lecture 4 on 'Radiation through matter' talks about gravitational radiation within matter. Gravitational Collapse, Schwarzschild Singularity, and some properties of the limiting radius-Gravitational radius of a spherical distribution with respect to general relativity are discussed in Lectures 5 and 6 respectively. Lecture 7 talks about 'Collapse with emission of radiation', and Radiation solutions. 'Field inside a radiating collapsing sphere' is discussed in the eighth lecture. Lecture 9 deals with 'Non Isotropic Cosmological models'; and Lecture 10 deals with Generalizations.