General Relativity & Cosmology (Optional Paper)
Mach’s principle, Newtonian approximation of equation of motion, Einstein’s field equation for matter and empty space, Reduction of Einstein’s field equation to Poisson’s equation.
Removal of clock paradox in General Relativity. Schwarzschild exterior metric, its isotropic form, Singularity and singularities in Schwarzschild exterior metric, Derivation of the formula GM = c2m, Mass of sun in gravitational unit,
Relativistic differential equation for the orbit of the planet. Three crucial tests in General Relativity and their detailed descriptions, Analogues of Kepler’s laws in General Relativity.
Trace of Einstein tensor, Energy-momentum tensor and its expression for perfect fluid, Schwarzschild interior metric and boundary condition.
Cosmology - Einstein’s field equation with cosmological term, Static cosmological models (Einstein & de-Sitter models) with physical and geometrical properties, Non-static form of de-Sitter line-element and Red shift in this metric, Einstein space, Hubble’s law, Weyl’s postulate.
1. Tolman R.C. Relativity, Thermodynamics and Cosmology, Oxford University Press.
2. Synge J.L.,Relativity the Special and General, North Holland Publishing Company,
Amsterdam.
3. Eddention A.S., The Mathematical Theory of Relativity, Cambridge University Press (2010
1. David Agmon, Paul Gluck: Classical and Relativistic Mechanics (2009)
2. Robert J. A. Lambourne, Relativity, Gravitation, and Cosmology , Cambridge University Press (2010).
3. S. Aranoff , Equilibrium in special relativity , Società Italiana di Fisica (1972).
