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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.

From the above one can immediately infer the existence of a time coordinate t2R such that all the events of constant time tcompose a 3-dimensional Euclidean space. The spacetime is topologically equivalent to R4 and admits a universal coordinate system (t;x 1;x2;x 3). Causal structure Given an event p occurring at time t

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