Relativity

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Relativity
Special
relativity
Background Principle of relativity (Galilean relativity • Galilean transformation) • Special relativity • Doubly special relativity
Fundamental
concepts
Frame of reference • Speed of light • Hyperbolic orthogonality • Rapidity • Maxwell's equations • Proper length • Proper time • Relativistic mass
Formulation Lorentz transformation
Phenomena Time dilation • Mass-energy equivalence • Length contraction • Relativity of simultaneity • Relativistic Doppler effect • Thomas precession • Ladder paradox • Twin paradox • Terrell rotation
Spacetime Light cone • World line • Minkowski diagram • Biquaternions • Minkowski space
General
relativity
Background Introduction • Mathematical formulation
Fundamental
concepts
Equivalence principle • Riemannian geometry • Penrose diagram • Geodesics • Mach's principle
Formulation ADM formalism • BSSN formalism • Einstein field equations • Linearized gravity • Post-Newtonian formalism • Raychaudhuri equation • Hamilton-Jacobi-Einstein equation • Ernst equation
Phenomena Black hole • Event horizon • Singularity • Two-body problem • Gravitational waves: astronomy • detectors (LIGO and collaboration • Virgo • LISA Pathfinder • GEO) • Hulse-Taylor binary • Other tests: precession of Mercury • lensing (together with Einstein cross and Einstein rings) • redshift • Shapiro delay • frame-dragging / geodetic effect (Lense-Thirring precession) • pulsar timing arrays
Advanced
theories
Brans-Dicke theory • Kaluza-Klein • Quantum gravity
Solutions Cosmological: Friedmann-Lemaître-Robertson-Walker (Friedmann equations) • Lemaître-Tolman • Kasner • BKL singularity • Gödel • Milne • Spherical: Schwarzschild (interior • Tolman-Oppenheimer-Volkoff equation) • Reissner-Nordström • Axisymmetric: Kerr (Kerr-Newman) • Weyl−Lewis−Papapetrou • Taub-NUT • van Stockum dust • discs • Others: pp-wave • Ozsváth-Schücking • Alcubierre • In computational physics: Numerical relativity
Scientists Poincaré • Lorentz • Einstein • Hilbert • Schwarzschild • de Sitter • Weyl • Eddington • Friedmann • Lemaître • Milne • Robertson • Chandrasekhar • Zwicky • Wheeler • Choquet-Bruhat • Kerr • Zel'dovich • Novikov • Ehlers • Geroch • Penrose • Hawking • Taylor • Hulse • Bondi • Misner • Yau • Thorne • Weiss • others
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