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Physics - Theoretical, Mathematical & Computational Physics | Einstein in Matrix Form - Exact Derivation of the Theory of Special and General Relativity without

Einstein in Matrix Form

Exact Derivation of the Theory of Special and General Relativity without Tensors

Ludyk, Günter

2013, XIV, 194 p. 11 illus.

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  • Derives the fundamental equations of Einstein's theory of special and general relativity using matrix calculus, without the help of tensors
  • Provides necessary mathematical tools in a user-friendly way, either directly in the text or in the appendices
  • Appendices contain an introduction to classical dynamics as a refresher of known fundamental physics
  • Rehearses vector and matrix calculus, differential geometry, and some special solutions of general relativity in the appendices
This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einsteins theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the "Black Hole" phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.

Content Level » Graduate

Keywords » Black Holes - Galilei Transformation - Lorentz Transformation - Matrix Calculus - Motion in a Gravity Field - Relativistic Electrodynamics - Riemannian Geometry - Schwarzschild Solution - Theory of General Relativity - Theory of Special Relativity

Related subjects » Classical Continuum Physics - Mechanics - Theoretical, Mathematical & Computational Physics - Theoretical and Computational Chemistry

Table of contents 

Special Relativity.-  The Galilei Transformation.- The Lorentz Transformation.- The Invariance of Quadratic Forms.- Velocity Addition.- Lorentz Transformation of Velocities.- Lorentz Transformation of Impulses.- Acceleration and Force.- Relativistic Electrodynamics.- Energy Momentum Matrix.- General Relativity.- General Relativity and Riemannian Geometry.- Some Mathematics: Derivation of a function, vector, and matrix with respect  to time.- Motion in a Gravity Field.- Geodesic Path.- Exampel: Rotating System.- General Transformations of Coordinates.- Some Differential Geometry.- Parallel Displacement.- Riemannian Curvature Matrix.- Properties of the Riemannian Curvature Matrix.- The Ricci Matrix and its Properties.- General Theory of Gravitation.- Summary.- Hilbert Functional.- Gravitation of a Spherical Body.- Schwarzschild Solution.- The Influence of a Body upon its Vicinity.- The Interior Schwarzschild Solution.- Black Holes.- Rotating Masses.

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