Course Details
Subject {L-T-P / C} : PH6123 : Introduction To General Theory of Relativity { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Dr. Subhash Chandra Mahapatra
Syllabus
Principle of equivalence, Diffeomorphism, Covariant and Contravariant tensors under general coordinate transformations, parallel transport, Christoffel symbols, Riemannian geometry.
The curvature and stress-energy tensors Einstein’s equations.
Vacuum solution of Einstein’s equations: Schwarzchild solution geodesics and particle trajectories, experimental tests of the general theory of relativity (Perihelion precession, Bending of light, gravitational redshift).
Black hole physics, Kruskal-Szekers coordinate, Penrose diagram, Surface gravity, Hawking temperature, Hawking radiation, Elements of Black hole mechanics.
Reissner Nordstrom geometry, Kerr Geometry, Penrose process.
Geodesic congruence and Raychaudhuri equation.
Cosmological principle, Friedman-Robertson-Walker metric, Friedman’s equations, Luminosity distance, Hubble’s law, Cosmological constant and dark energy.
Einstein Equation with matter, Tolman-Oppenheimer-Volkoff Equation.
Gravitational waves: Linearized Gravity.
Course Objectives
- Understanding the concept of the covariant derivative, parallel transport, <br />covariant Lagrangian dynamics, geodesic curves.
- To understand gravity as the manifestation of curvature of spacetime. <br />Solving Einstein’s gravitation field equations.
- Solutions of Einstein’s equation and black-hole physics and its properties.
- Applications of general relativity in cosmology
Course Outcomes
To introduce students to the field of general relativity. On successful completion of this course, students should be able to apply the physical and mathematical ideas of general relativity to study various systems in cosmology.
Essential Reading
- S. Carroll, Space time and geometry: an introduction to general relativity, Pearson-2003
- T. Padmanabhan, Gravitation, CAMBRIDGE UNIVERSITY PRESS
Supplementary Reading
- Bernard Schutz, A First Course in General Relativity, CAMBRIDGE UNIVERSITY PRESS
- J. Hartel, Gravity: An introduction to Einstein’s general relativity, Pearson-2014