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General Relativity

General RelativityStefanos AretakisJune 30, 20182 Contents1 Special Newtonian Physics .. The Birth of Special Relativity .. The Minkowski SpacetimeR3+1.. Theory .. Observers, Frames of Reference and Isometies .. and Special Covariance .. Mechanics .. Conformal Structure .. Double Null Foliation .. Penrose Diagram .. Electromagnetism and Maxwell Equations .. 232 Lorentzian Causality I .. Null Geometry .. Global Hyperbolicity .. Causality II .. 413 Introduction to General Equivalence Principle .. The Einstein Equations .. The Cauchy Problem .. Gravitational Redshift and Time Dilation .. Applications .. 484 Null Structure The Double Null Foliation .. Connection Coefficients .. Curvature Components.

all quantities as functions of (the space and) time t. Newton’s theory gives a very accurate theory for objects moving at slow speeds in absence of strong gravitational elds. However, in several circumstances di culties arise: 1.A more philosophical issue is that in Newtonian theory an observer is either at rest or in motion.

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