Mathematical Introduction To General Relativity, A
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A01=Amol Sasane
Analysis on Manifolds
Author_Amol Sasane
Black Hole Thermodynamics
Black Holes
Category=PHR
Christoffel Symbols
Cosmological Constant
Cosmology
Curvature Tensor
Differential Geometry
Einstein
Einstein Field Equation
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Friedmann Universe
GAfA?del Spacetime
General Relativity
Geodesics
Global Analysis
Godel Spacetime
GravitationalWaves
Hawking Temperature
Hubble Law
Length Contraction
Levi-Civita Connection
Light Deflection
Lorentzian Manifolds
Mathematical Relativity
Minkowski Spacetime
Parallel Transport
Perihelion Shiftof Mercury
Red-Shift
Ricci Curvature
Schwarzschild Spacetime
Semi-Riemannian Geometry
Spacetime
Special Relativity
Speedof Light
Tensor Calculus
Tensor Fields
Time Dilation
Twin Paradox
Unruh Effect
Product details
- ISBN 9789811243776
- Publication Date: 31 Aug 2021
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
