General Relativity ,Fall 2012

Overview

The equivalence principle - Accelerated reference frames - Curvilinear coordinate transformations - Effect of gravity on light - Tidal forces - Euclidean geometry - Riemannian geometry - Metric tensor - Distance measurement in a curved geometry - Intrinsic geometry - Flat spacetime - Einstein summation convention - Covariant and contravariant vectors and tensors - Flat space - Metric tensor - Scalar and tensor fields - Tensor analysis - Tensor mathematics: addition, multiplication, contraction - Riemannian geometry - Metric tensor - Gaussian normal coordinates - Covariant derivatives - Christoffel symbols - Curvature tensor - Cones - Parallel transport - Tangent vectors - Geodesics - Spacetime - Special relativity - Uniform acceleration - Uniform gravitational fields - Space-like, time-like, and light-like intervals - Light cone - Black holes

Schwarzschild metric - Event horizon - Schwarzschild metric - Schwarzschild Radius - Black hole event horizon - Light ray orbiting a black hole - Photon sphere - Hyperbolic coordinates - Black hole singularity - Schwarzschild metric - Event horizon - Singularity KruskalSzekeres coordinates - Penrose diagrams - Wormholes - Formation of a black hole - Newton's shell theorem - Newtonian - gravitational field - Continuity equation - Stressenergy tensor (also known as the energy-momentum tensor) - Curvature scalar - Ricci tensor - Einstein tensor - Einstein field equations - Weak gravitational fields - Gravitational radiation - Gravity waves - Einstein-Hilbert action for general relativity