Title of Paper: General Relativity I
Unit I: Review of the special theory of relativity and the Newtonian theory of gravitation.
Distinction between Newtonian space and relativistic space. The conflict between Newtonian
Theory of gravitation and special Relativity. Non-Euclidean space time. General Relativity and
gravitation, desirable features of gravitational theory. Principle of equivalence and principle of
covariance. 15 Lectures
Unit II: Transformation of co-ordinates. Tensor, Algebra of tensors. Symmetric and skew
symmetric tensors. Contraction of tensors and quotient law. Tensor Calculus: Christoffel
Symbols, Covariant derivative. Intrinsic derivative. Riemannian Christoffel Curvature tensor and
its symmetric properties. Bianchi identities and Einstein tensor. 15 Lectures
Unit III: Riemannian metric. Generalized Kronecker delta, alternating symbol and Levi-Civita
tensor, Dual tensor. Parallel transport and Lie derivative. Geodesic: i) geodesic as a curve of
unchanging direction ii) geodesic as the curve of shortest distance and iii) geodesic through
variational principle. The first integral of geodesic and types of geodesics. Geodesic deviation
and geodesic deviation equation. 15 Lectures
Unit IV: Killing vector fields. Isometry. Necessary and sufficient conditions for isometry.
Integrability condition, Homogeneity and isometry. Maximally symmetric space-time. Einstein
space. 15 Lectures
Unit V: Examples, seminars, group discussions on above four units. 15 Lectures
- Teacher: Laxman Katkar Maths