**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