General Relativity Explained in 7 Levels of Difficulty
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This video covers the General theory of Relativity, developed by Albert Einstein, from basic simple levels (it's gravity, curved space) through to the concepts of how curved spacetime is represented by psuedo-Riemannian manifolds with Lorentzian signature (that is, special relativity and minkowski space are the local tangent space), how matter and energy are represented by an energy-momentum tensor, and how these two together obey the Einstein Field Equations. The solutions to the Einstein Field Equations (including the schwarzschild metric, kerr metric, freedman-lemaitre-robertson-walker metric, etc) represent gravity around massive objects like the sun, earth, and black holes, but also the history and expansion and future evolution of the cosmos. The universe on a large scale is described by general relativity - on a small scale, quantum mechanics. And where they meet... there's still work to be done.
REFERENCES
Wald's textbook - General Relativity
Hartle's textbook - Gravity: An Introduction to Einstein's General Relativity
Carlo Rovelli History of Quantum Gravity: https://cds.cern.ch/record/442809/files/0006061.pdf
Leon Rosenfeld 1930 paper on quantum gravity: http://www.edoc.mpg.de/438547
Kerr Metric Solution - https://en.wikipedia.org/wiki/Eddington%E2%80%93Finkelstein_coordinates
Schwarzschild Metric - https://en.wikipedia.org/wiki/Schwarzschild_metric
Eddington-Finkelstein Coordinates - https://en.wikipedia.org/wiki/Eddington%E2%80%93Finkelstein_coordinates
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