THE PRINCIPLE OF RELATIVITY

By SARAH SANCHEZ

CONTENTS DIFFERENTIABLE MANIFOLDS CHARTS AND ATLASES TOPOLOGISATION SUBMANIFOLDS OF RM TANGENT VECTORS THE TANGENT SPACE GENERATION OF TANGENT VECTORS VECTOR FIELDS THE LIE BRACKET TENSORS INTRODUCTION MULTILINEAR FORMS COMPONENTS OPERATIONS WITH TENSORS TENSORS ON EUCLIDEAN SPACES SEMI-RIEMANNIAN MANIFOLDS TENSOR FIELDS RIEMANNIAN MANIFOLDS BILINEAR FORMS ORIENTATION SPACETIME THEORY OF SPECIAL RELATIVITY KINEMATICS DYNAMICS ELECTRODYNAMICS DIFFERENTIAL FORMS P-FORMS THE WEDGE PRODUCT THE HODGE-STAR OPERATOR OUTER DERIVATIVE THE MAXWELL EQUATIONS IN VACUUM THE COVARIANT DIFFERENTIATION OF VECTOR FIELDS THE DIRECTIONAL DERIVATIVE IN RN THE LEVI-CIVITA CONNECTION CHRISTOFFEL SYMBOLS THE COVARIANT DERIVATIVE ON HYPERSURFACES THE COVARIANT DERIVATIVE IN THE SCHWARZSCHILD SPACETIME CURVATURE THE CURVATURE TENSOR THE WEINGARTEN MAP THE RICCI TENSOR THE CURVATURE OF THE SCHWARZSCHILD SPACETIME CONNECTION FORMS AND CURVATURE FORMS MATTER MASS ENERGY AND MOMENTUM OF A FLOW THE ENERGY-MOMENTUM TENSOR CHARGE ENERGY AND MOMENTUM IN THE ELECTROMAGNETIC FIELD THE EINSTEIN FIELD EQUATION SPHERICALLY SYMMETRIC SOLUTIONS OUTER AND INNER SCHWARZSCHILD METRIC GEODESICS TIME THE EULER-LAGRANGE EQUATION THE GEODESIC EQUATION THE GEODESIC DEVIATION PERIHELION PRECESSION LIGHT DE?ECTION RED SHIFT COVARIANT DIFFERENTIATION OF TENSOR FIELDS PARALLEL TRANSPORT OF VECTORS PARALLEL TRANSPORT OF TENSORS CALCULATION RULES AND COMPONENT REPRESENTATION THE SECOND BIANCHI IDENTITY DIVERGENCE THE LIE DERIVATIVE THE FLOW AND ITS TANGENTS PULL-BACK AND PUSH-FORWARD AXIOMATIC SET UP THE DERIVATIVE FORMULA COMPONENT REPRESENTATION KILLING VECTORS THE LIE DERIVATIVE OF DIFFERENTIAL FORMS INTEGRATION ON MANIFOLDS PARTITION OF UNITY INTEGRALS MANIFOLDS WITH BOUNDARY INTEGRAL THEOREMS EXTREMAL PRINCIPLES NONROTATING BLACK HOLES THE SCHWARZSCHILD HALF PLANE OPTICS OF BLACK HOLES THE KRUSKAL PLANE COSMOLOGY SPACES OF CONSTANT CURVATURE THE ROBERTSON-WALKER METRIC UNIVERSE MODELS ROTATING BLACK HOLES THE KERR METRIC OTHER REPRESENTATIONS OF THE KERR METRIC CAUSAL STRUCTURE COVARIANT DERIVATIVE AND CURVATURE CONSERVATION THEOREMS A GLIMPSE OF STRING THEORY QUANTUM THEORY VERSUS RELATIVITY THEORY ELEMENTARY PARTICLES AS STRINGS THE EXTREMAL PRINCIPLE REFERENCES