Introduction to Tensor Calculus, Relativity and CosmologyCourier Corporation, 01.01.2002 - 224 Seiten This elementary introduction pays special attention to aspects of tensor calculus and relativity that students tend to find most difficult. Its use of relatively unsophisticated mathematics in the early chapters allows readers to develop their confidence within the framework of Cartesian coordinates before undertaking the theory of tensors in curved spaces and its application to general relativity theory. Additional topics include black holes, gravitational waves, and a sound background in applying the principles of general relativity to cosmology. Numerous exercises advance the theoretical developments of the main text, thus enhancing this volume's appeal to students of applied mathematics and physics at both undergraduate and postgraduate levels. |
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An Introduction to Tensor Calculus: Relativity and Cosmology Derek F. Lawden Eingeschränkte Leseprobe - 2012 |
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4-velocity acceleration accordingly affinity angle assumed axes B₁ Calculate the component Cartesian coordinates Cartesian frame constant contravariant vector coordinate frame cosmical cosmos covariant derivative Deduce defined density derivative differentiation displacement vector distance dr² ds ds ds² dx¹ dx² dx³ Einstein's electromagnetic field employed energy energy-momentum tensor Euclidean follows force galactic galaxies gravitational field hence inertial frame invariant Lorentz transformation Maxwell's equations measured metric tensor momentum moving observed obtain orthogonal transformations parallel displacement particle particle's photon physical plane prove pseudotensor radius rectangular Cartesian coordinates reference frame region relative respect rest mass result Ricci tensor Schwarzschild Schwarzschild metric Show sin² skew-symmetric space space-time standard clock stationary symmetric t₁ theory transformation equations V₁ valid values vanish velocity world-line x-axis x-frame x₁ zero