Published on Mathematics (https://maths.iisuniv.ac.in)

Home > General Relativity & Cosmology

General Relativity & Cosmology [1]

Paper Code: 
25MAT425(A)
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 
This course will enable the students to -
1. Provide detailed knowledge of general relativity and its applications in cosmology.
2. Solve the problems and help with research in these broad areas.
 
Course Outcomes: 

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

25MAT

425(A)

 

 

 

General Relativity & Cosmology

 (Theory)

 

 

 

CO190: Formulate Einstein field equation for matter and empty space.

CO191: Understand the concept of clock paradox in general relativity. Derive Schwarzschild exterior metric and their isotropic forms.

CO192: Derive the differential equation for planetary orbit, analogues of kepler's law.

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

CO194: Apply the concepts of Einstein tensor, Energy-momentum tensor and its expression for perfect fluid.

CO195: Contribute effectively in course-specific interaction.

 

Approach in teaching:

Interactive Lectures, Discussion, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions,  Topic  presentation, Assigned tasks

 

 

Quiz, Class Test, Individual projects,

Open Book Test, Continuous Assessment, Semester End Examination

 

 

 

Unit I: 
Einstein’s field equation:
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: 
Schwarzschild Metric:
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: 
Kepler’s laws in general relativity:
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: 
Trace of Einstein tensor:
15.00

 Energy-momentum tensor and its expression for perfect fluid, Schwarzschild interior metric and boundary condition.

Unit V: 
Cosmology:
15.00
 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, Cambridge University Press, 2002.
  • Bernard F. Schutz, A First Course in General Relativity, Cambridge University 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, An Introduction to Relativity, Cambridge University 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: 
2025-2026 [10]

Follow Mathematics on:

IIS (Deemed to be University)

Gurukul Marg, SFS, Mansarovar, Jaipur 302020, (Raj.) India Phone:- +91-141-2400160-61, 2397906-07, Fax: 2395494, 2781158

Source URL: https://maths.iisuniv.ac.in/courses/subjects/general-relativity-cosmology-3

Links:
[1] https://maths.iisuniv.ac.in/courses/subjects/general-relativity-cosmology-3
[2] https://web.physics.ucsb.edu/~marolf/MasterNotes.pdf
[3] http://physics.mq.edu.au/~jcresser/Phys378/LectureNotes/VectorsTensorsSR.pdf
[4] https://nptel.ac.in/courses/115101011
[5] https://www.youtube.com/watch?v=e-W_omQ1FyA 
[6] https://iopscience.iop.org/journal/1475-7516
[7] https://www.springer.com/journal/10714
[8] https://www.nature.com/subjects/general-relativity-and-gravity/nphys 
[9] https://arxiv.org/list/gr-qc/current
[10] https://maths.iisuniv.ac.in/academic-year/2025-2026