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General Relativity & Cosmology [1]

Paper Code: 
MAT 425A
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.

 

Course Outcomes (COs):

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

MAT 425A

 

 

 

 

General Relativity & Cosmology

 (Theory)

 

 

 

The students will be able to –

 

CO188: Formulate Einstein field equation for matter and empty space.

CO189: Understand the concept of clock paradox in general relativity.

CO190: Derive the differential equation for planetary orbit, analogues of kepler's law.

CO191: Derive Schwarzschild interior, exterior metric and their isitropic forms.

CO192: Calculate the Trace of Einstein tensor, Energy-momentum tensor and its expression for perfect fluid.

CO193: Apply the concepts of Einstein tensor, Energy-momentum tensor and its expression for perfect fluid.

 

Approach in teaching:

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Field trips

Quiz, Poster Presentations,

Power Point Presentations, Individual and group projects,

Open Book Test, 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=m c^2, 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. 
  • David Agmon, Paul Gluck, Classical and Relativistic Mechanics,2009.
References: 
  • 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, Dover Publications Inc, 1988.
  • J.L. Synge, Relativity the General Theory, North Holland Publishing Company, Amsterdam, 1971.
  • A.S. Eddention, The Mathematical Theory of Relativity, Cambridge University Press, 2010.
  • S. Aranoff, Equilibrium in Special Relativity: The Special Theory, North Holland Pub. Amsterdam, 1965.
Academic Year: 
2023-2024 [2]

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Source URL: https://maths.iisuniv.ac.in/courses/subjects/general-relativity-cosmology-1

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[1] https://maths.iisuniv.ac.in/courses/subjects/general-relativity-cosmology-1
[2] https://maths.iisuniv.ac.in/taxonomy/term/24