Differential forms and the geometry of general relativity. (2014)

• Record Type: Book
• Further Information: Note: Tevian Dray.
• Authors: Dray, Tevian
• Contents: Spacetime Geometry; Spacetime; Line Elements; Circle Trig; Hyperbola Trig; The Geometry of Special Relativity Symmetries; Position and Velocity; Geodesics; Symmetries; Example: Polar Coordinates; Example: The Sphere Schwarzschild Geometry; The Schwarzschild Metric; Properties of the Schwarzschild Geometry; Schwarzschild Geodesics; Newtonian Motion; Orbits; Circular Orbits; Null Orbits; Radial Geodesics; Rain Coordinates; Schwarzschild Observers Rindler Geometry; The Rindler Metric; Properties of Rindler Geometry; Rindler Geodesics; Extending Rindler Geometry Black Holes; Extending Schwarzschild Geometry; Kruskal Geometry; Penrose Diagrams; Charged Black Holes; Rotating Black Holes; Problems General Relativity; Warmup; Differential Forms in a Nutshell; Tensors; The Physics of General Relativity; Problems Geodesic Deviation; Rain Coordinates II; Tidal Forces; Geodesic Deviation; Schwarzschild Connection; Tidal Forces Revisited Einstein's Equation; Matter; Dust; First Guess at Einstein's Equation; Conservation Laws; The Einstein Tensor; Einstein's Equation; The Cosmological Constant; Problems Cosmological Models; Cosmology; The Cosmological Principle; Constant Curvature; Robertson-Walker Metrics; The Big Bang; Friedmann Models; Friedmann Vacuum Cosmologies; Missing Matter; The Standard Models; Cosmological Redshift; Problems Solar System Applications; Bending of Light; Perihelion Shift of Mercury; Global Positioning Differential Forms; Calculus Revisited; Differentials; Integrands; Change of Variables ; Multiplying Differentials Vector Calculus Revisited; A Review of Vector Calculus; Differential Forms in Three Dimensions; Multiplication of Differential Forms; Relationships between Differential Forms; Differentiation of Differential Forms The Algebra of Differential Forms; Differential Forms; Higher Rank Forms; Polar Coordinates; Linear Maps and Determinants; The Cross Product; The Dot Product; Products of Differential Forms; Pictures of Differential Forms; Tensors; Inner Products; Polar Coordinates II Hodge Duality; Bases for Differential Forms; The Metric Tensor; Signature; Inner Products of Higher Rank Forms; The Schwarz Inequality; Orientation; The Hodge Dual; Hodge Dual in Minkowski 2-space; Hodge Dual in Euclidean 2-space; Hodge Dual in Polar Coordinates; Dot and Cross Product Revisited; Pseudovectors and Pseudoscalars; The General Case; Technical Note on the Hodge Dual; Application: Decomposable Forms; Problems Differentiation of Differential Forms; Gradient; Exterior Differentiation; Divergence and Curl; Laplacian in Polar Coordinates; Properties of Exterior Differentiation; Product Rules; Maxwell's Equations I; Maxwell's Equations II; Maxwell's Equations III; Orthogonal Coordinates; Div, Grad, Curl in Orthogonal Coordinates; Uniqueness of Exterior Differentiation; Problems Integration of Differential Forms; Vectors and Differential Forms; Line and Surface Integrals; Integrands Revisited; Stokes' Theorem; Calculus Theorems; Integration by Parts; Corollaries of Stokes' Theorem; Problems Connections; Polar Coordinates II; Differential Forms which are also Vector Fields; Exterior Derivatives of Vector Fields; Properties of Differentiation; Connections; The Levi-Civita Connection; Polar Coordinates III; Uniqueness of the Levi-Civita Connection; Tensor Algebra; Commutators; Problems Curvature; Curves; Surfaces; Examples in Three Dimensions; Curvature; Curvature in Three Dimensions; Components; Bianchi Identities; Geodesic Curvature; Geodesic Triangles; The Gauss-Bonnet Theorem; The Torus; Problems Geodesics; Geodesics; Geodesics in Three Dimensions; Examples of Geodesics; Solving the Geodesic Equation; Geodesics in Polar Coordinates; Geodesics on the Sphere Applications; The Equivalence Problem; Lagrangians; Spinors; Topology; Integration on the Sphere Appendix A: Detailed Calculations; Appendix B: Index Gymnastics Annotated Bibliography References
• Edition: 1st
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2014
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 530.11015153; General relativity (Physics); Black holes (Astronomy) -- Mathematics; Differential forms; Geometry
• Languages: English
• ISBNs: 9781466510326
• Related ISBNs: 9781466510005
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.