Relativity: A Gentle Introduction

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