Relativity: A Gentle Introduction

ABOUT THE COURSE:This course is an introduction to Einstein's theory of general relativity, and includes applications to early universe cosmology and the inflationary paradigm. The material is aimed at advanced undergraduate students and beginning graduate students. Special relativity will be reviewed in the first few lectures, to set the foundations for the remainder of the course. No prior knowledge of general relativity is expected.PREREQUISITES: Linear Algebra (taught in first year BTech)INDUSTRY SUPPORT: MOOCs (Coursera, edX)

Week 1: The need for Special Relativity; Michaelson-Morley Experiment, Galilean vs. Lorentz transformations, Simultaneity, Spacetime diagramsWeek 2:Lorentz invariance, scalars in special relativity, relativistic dynamics, acceleration in Special Relativity, the idea of a Metric, Minkowski metric and invarianceWeek 3:The Equivalence Principle, basics of why matter induces curvature, the need for Parallel Transport, an introduction to TensorsWeek 4:Reimannian geometry: space-time as curved manifold; coordinate transformations, Covariant Differentaition, Defining curvature using TensorsWeek 5:Lie Derivative, Geodesic Equation - its derivation and uses, Geodesic Deviation , The Stress-Energy TensorWeek 6:The march towards General Relativity - Einstein Equations, Riemann and Ricci Tensors, Bianchi Identities, Killing vectors and symmetryWeek 7:The Schwarzschild Solution - heuristic derivation; Physics in curved spacetime: particle and photon trajectoriesWeek 8:The General Relativistic Orbit Equation; stability of orbits in General RelativityWeek 9:Classical tests of General Relativity - light deflection by the sun, perihelion precession of Mercury, gravitational redshift of lightWeek 10:Schwarzschild Black Hole, Event Horizon, Hawking Radiation, Gravitational RadiationWeek 11:Robertson-Walker metric and Friedmann models, particle horizon; ? Λ – cosmologies; The Cosmic Microwave Background, Inflationary ParadigmWeek 12:Gravitational Waves - theory and origins, systems that exhibits gravitational waves, primordial GWs