Lie derivative of a tensor field, Scalar Function, Contravariant and covariant vectors, Covariant tensor of rank two, Symmetry and Killing equations, Integrability of Killing equation, Geodesic deviation.

 

Conformal curvature tensor and its properties, Algebraic classification of conformal curvature tensor, Basic equation of isotropic cosmology, Singularity and singularities in isotropic models, Red shift in non-static form of de-Sitter universe.

 

Einstein-Space, Cosmological principles (perfect, ordinary and weak), Relativistic models not obeying Cosmological principle, Gödel universe and its properties.

 

Non-static cosmology models, Robertson-Walker model and its derivation and geometrical properties, Fredmann-Robertson-Walker model and its scale factor, Three different forms of scale factor, Doppler effect in Robertson-Walker model, Big Bang theory, Steady state theory, Brans-Dicke theory as an alternative theory of gravitation, Derivation of its field equation and solution based on Brans-Dicke theory. 

 

Differential forms: Exterior differentiation, Connection 1-form, Ricci rotation coefficients, Cartan's    equation of structure, Calculation of Riemann Curvature tensor using differential forms, Curvature 2- form for Vaidya metric.