Syllabus

(10 hrs) Galilean relativity and Galilean transformation, Michelson Morley experiment, Fizeau experiment, postulates of relativity, length contraction and time dilation, twin paradox, Lorentz transformation & velocity addition. Relativistic momentum and mass-energy relation. Doppler effect.

(8 hrs) Principle of equivalence and the geometrical description of gravity, uniformly accelerated observers and the Rindler spacetime. Diffeomorphism, Covariant and Contravariant tensors under general coordinate transformations, Tensor algebra in curved spacetime, metric tensor and its connection with gravity.

(8 hrs) Parallel transport, Christoffel symbols, geodesic equation. Parallel transport around a closed curve and the Riemann curvature tensor, connection of the Riemann tensor with spacetime curvature, algebraic and differential properties of the Riemann tensor, Ricci tensor.

(4 hrs) Einstein’s equations, deriving Poisson’s equations from Einstein’s equations. Schwarzchild solution, geodesics and particle trajectories in Schwarzschild spacetime.

(6 hrs) Observational verification and applications: Relativistic corrections to planetary orbits and perihelion precession of the planet mercury, bending of light, gravitational resdhift and comparison with Doppler shift, Shapiro time delay. Applications of relativity in the Global Positioning System.

To understand the role of relativity in defining the laws of physics.

To understand why non-inertial frames and gravitation are equivalent.

To understand gravity as the manifestation of curvature of spacetime, importance of tensors and appreciating why the laws of physics should be frame invariant.

Understanding the necessity to introduce the covariant derivative in curved spacetime, the concept of parallel transport and the symmetries of the metric tensor.

To understand Einstein’s equations, its solutions, its applications in accurately predicting the planetary motions and its role in the GPS.

CO1. On successful completion of this course, the students should be able to appreciate that relativity is indispensable in defining the physical laws.

CO2. They should be able to appreciate the counter-intuitive consequences of the postulates of relativity.

CO3. They should be able to explain how the classical laws of motion can be recovered from the relativistic momentum and energy.

CO4. On successful completion of this course, the students should be able to appreciate the inescapable connection between gravity and the curvature of spacetime.

CO5. They should be able to explain how light bends while moving in a curved spacetime and how planetary motions can be accurately predicted by incorporating general relativistic corrections.

Robert Resnick, Introduction to Special Relativity, Wiley

Jurgen Freund, Special Relativity For Beginners: A Textbook For Undergraduates, World Scientific

Bernard Schutz, A First Course in General Relativity, Cambridge University Press

J. Hartel, Gravity: An introduction to Einstein’s general relativity, Pearson-2014

Michael Tsamparlis, Special Relativity: An Introduction with 200 Problems and Solutions, Springer

David J Morin, Special Relativity: For the Enthusiastic Beginner, Self-published (to keep the cost low) through CreateSpace (2017)