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 and its isotropic form, Singularity and singularities in Schwarzschild exterior metric, Derivation of the formula GM=mc2 , 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.
- Jayant V. Narlikar, Introduction to Cosmology, Cambridge University Press, 2002.
- Bernard F. Schutz, A First Course in General Relativity, Cambridge University Press, 2010.
- Sushil Kumar Srivastava, General Relativity and Cosmology, Prentice hall India, 2008.
- Raj Bali, General Relativity, JPH, 2005.
- David Agmon, Paul Gluck, Classical and Relativistic Mechanics, 2009.
- Jayant V. Narlikar, An Introduction to Relativity, Cambridge University Press, 2010.
- Robert J. A. Lambourne, Relativity, Gravitation, and Cosmology, Cambridge University Press, 2010.
- R.C. Tolman, Relativity, Thermodynamics and Cosmology, Oxford University Press, 1934.
