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General Relativity & Cosmology (Optional Paper) [1]

Paper Code: 
MAT 426
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Unit I: 
I
15.00

Mach’s principle, Newtonian approximation of equation of motion, Einstein’s field equation for matter and empty space, Reduction of Einstein’s field equation to Poisson’s equation. 

Unit II: 
II
15.00
Removal of clock paradox in General Relativity. Schwarzschild exterior metric, its isotropic form, Singularity and singularities in Schwarzschild exterior metric, Derivation of the formula GM = c2m, Mass of sun in gravitational unit, 
 
Unit III: 
III
15.00
Relativistic differential equation for the orbit of the planet. Three crucial tests in General Relativity and their detailed descriptions, Analogues of Kepler’s laws in General Relativity.
 
Unit IV: 
IV
15.00
Trace of Einstein tensor, Energy-momentum tensor and its expression for perfect fluid, Schwarzschild interior metric and boundary condition. 
 
Unit V: 
V
15.00
Cosmology - Einstein’s field equation with cosmological term, Static cosmological models (Einstein & de-Sitter models) with physical and geometrical properties, Non-static form of de-Sitter line-element and Red shift in this metric, Einstein space, Hubble’s law, Weyl’s postulate.
 
Essential Readings: 
  1. Tolman R.C. : Relativity, Thermodynamics and Cosmology, Oxford University Press.
  2. Synge J.L. : Relativity the Special and General  North Holland Publishing Company, Amsterdam.
  3. Eddention A.S. : The Mathematical Theory of Relativity, Cambridge.
 
Academic Year: 
2014-2015 [2]

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Links:
[1] https://maths.iisuniv.ac.in/courses/subjects/general-relativity-cosmology-optional-paper-4
[2] https://maths.iisuniv.ac.in/academic-year/2014-2015