RELATIVISTIC COSMOLOGY AND DIFFERENTIAL FORMS
Paper Code:
MAT144 C
Credits:
4
Contact Hours:
60.00
Max. Marks:
100.00
Unit I:
I
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.
Unit II:
II
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.
Unit III:
III
Einstein-Space, Cosmological principles (perfect, ordinary and weak), Relativistic models not obeying Cosmological principle, Gödel universe and its properties.
Unit IV:
IV
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.
Unit V:
V
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.
Essential Readings:
- Albert Einstein, Relativity: The special and general theory, Createspace Independent Publication, 2015.
- Alan P. Lightman, Richard H. Price, Problem Book in Relativity and Gravitation, Princeton University Press, 1975.
- Bernard Schutz, A First Course in General Relativity, Cambridge University Press, 2012.
- Robert Wald, General Relativity, University of Chicago Press, 1984.
- Steven Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, 2008.
- Narlikar, Jayant Vishnu, Macmillan,General Relativity and Cosmology, 1979.
- J. V. Narlikar, An Introduction to Cosmology, Cambridge University Press, 2002.
Academic Year:
