General Relativity ,Fall 2012

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2 STUDENTS

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 Kruskal–Szekeres coordinates – Penrose diagrams – Wormholes – Formation of a black hole – Newton’s shell theorem – Newtonian – gravitational field – Continuity equation – Stress–energy 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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