GENERAL RELATIVITY & COSMOLOGY (Optional Paper)

Paper Code: 
MAT425A
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 
This course will enable the students to -
  1. Provide a detailed knowledge of  the general relativity and its applications in Cosmology.
  2. Solve the problems and help in research in these broad areas.

Learning Outcomes

Learning and teaching strategies

Assessment

After the completion of the course the students will be able to:

CLO143- Formulate Einstein field equation for matter and empty space.

 

CLO144- Understand the concept of clock paradox in general relativity.

 

CLO145- Derive the differential equation for planetary orbit, analogues of  kepler's law.

 

 

 

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, Reading assignments, Demonstration, Team teaching

Learning activities for the students:

Self learning assignments, Effective questions, Simulation, Seminar presentation, Giving tasks, Field practical

 

Presentations by Individual  Students

Class Tests at Periodic Intervals.

Written assignment(s)

Semester End Examination

 

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 and its isotropic form, Singularity and singularities in Schwarzschild exterior metric, Derivation of the formula GM=mc2,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: 
  • Jayant V. Narlikar, Introduction to Cosmology, CambridgeUniversity Press, 2002.
  • Bernard F. Schutz, A First Course in General Relativity, CambridgeUniversity Press, 2010.
  • Sushil Kumar Srivastava, General Relativity and Cosmology, Prentice hall India, 2008.
  • Raj Bali, General Relativity, JPH, 2005.
References: 
  • David Agmon, Paul Gluck, Classical and Relativistic Mechanics,2009.
  • Jayant V. Narlikar, AnIntroduction to Relativity, CambridgeUniversity Press, 2010.
  • Robert J. A. Lambourne, Relativity, Gravitation, and Cosmology, Cambridge University Press,2010.
  • R.C. Tolman,Relativity, Thermodynamics and Cosmology, Oxford University Press, 1934.
  • J.L. Synge,Relativity theGeneral Theory, North Holland Publishing Company,Amsterdam, 1971.
  • A.S.Eddention,The Mathematical Theory of Relativity, CambridgeUniversity Press, 2010.
  • S.Aranoff,Equilibrium in Special Relativity:The Special Theory,North Holland Pub. Amsterdam,1965.

 

 

Academic Year: 
2019-2020
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