General Relativity ,Fall 2012

Stanford Course , Fall 2012 , Prof. Leonard Susskind

Lecture 1:

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Lecture Details :

(December 3, 2012) Leonard Susskind demonstrates that Einstein's field equations become wave equations in the approximation of weak gravitational fields. The solutions for these equations create the theory of gravity waves.This series is the fourth installment of a six-quarter series that explore the foundations of modern physics. In this quarter Susskind focuses on Einstein's General Theory of Relativity.Originally presented in the Stanford Continuing Studies Program.Stanford University:http://www.stanford.edu/Stanford Continuing Studies Program:https://continuingstudies.stanford.edu/Stanford University Channel on YouTube:http://www.youtube.com/stanford

Course Description :

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

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