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Books > Science & Mathematics > Physics > Relativity physics
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Mathematical Introduction To General Relativity, A (Hardcover)
Loot Price: R4,133
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Mathematical Introduction To General Relativity, A (Hardcover)
Expected to ship within 10 - 15 working days
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The book aims to give a mathematical presentation of the theory of
general relativity (that is, spacetime-geometry-based gravitation
theory) to advanced undergraduate mathematics students.
Mathematicians will find spacetime physics presented in the
definition-theorem-proof format familiar to them. The given precise
mathematical definitions of physical notions help avoiding
pitfalls, especially in the context of spacetime physics describing
phenomena that are counter-intuitive to everyday experiences.In the
first part, the differential geometry of smooth manifolds, which is
needed to present the spacetime-based gravitation theory, is
developed from scratch. Here, many of the illustrating examples are
the Lorentzian manifolds which later serve as spacetime models.
This has the twofold purpose of making the physics forthcoming in
the second part relatable, and the mathematics learnt in the first
part less dry. The book uses the modern coordinate-free language of
semi-Riemannian geometry. Nevertheless, to familiarise the reader
with the useful tool of coordinates for computations, and to bridge
the gap with the physics literature, the link to coordinates is
made through exercises, and via frequent remarks on how the two
languages are related.In the second part, the focus is on physics,
covering essential material of the 20th century spacetime-based
view of gravity: energy-momentum tensor field of matter, field
equation, spacetime examples, Newtonian approximation, geodesics,
tests of the theory, black holes, and cosmological models of the
universe.Prior knowledge of differential geometry or physics is not
assumed. The book is intended for self-study, and the solutions to
the (over 200) exercises are included.
General
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