Modern General Relativity : Black Holes, Gravitational Waves, and Cosmology

Описание

Modern General Relativity
Black Holes, Gravitational Waves, and Cosmology
Einstein’s general theory of relativity is widely considered to be one of the most elegant and successful scientific theories ever developed, and it is increasingly being taught in a simplified form at advanced undergraduate level within both physics and mathematics departments. Due to the increasing interest in gravitational physics, in both the academic and the public sphere, driven largely by widely-publicised developments such as the recent observations of gravitational waves, general relativity is also one of the most popular scientific topics pursued through self-study. Modern General Relativity introduces the reader to the general theory of relativity using an example-based approach, before describing some of its most important applications in cosmology and astrophysics, such as gamma-ray bursts, neutron stars, black holes, and gravitational waves. With hundreds of worked examples, explanatory boxes, and end-of-chapter problems, this textbook provides a solid foundation for understanding one of the towering achievements of twentieth-century physics.
MIKE GUIDRY is Professor of Physics and Astronomy at the University of Tennessee, Knoxville. His current research is focused on the development of new algorithms to solve large sets of differential equations, and applications of Lie algebras to strongly-correlated electronic systems. He has written five textbooks and authored more than 120 journal publications on a broad variety of topics. He previously held the role of Lead Technology Developer for several major college textbooks in introductory physics, astronomy, biology, genetics, and microbiology. He has won multiple teaching awards and is responsible for a variety of important science outreach initiatives.
Modern General Relativity
Black Holes, Gravitational Waves, and Cosmology
MIKE GUIDRY
University of Tennessee, Knoxville
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Cambridge University Press is part of the University of Cambridge.
It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning, and research at the highest international levels of excellence.
DOI: 10.1017/9781108181938
First published 2019
Printed in the United Kingdom by TJ International Ltd. Padstow Cornwall
A catalog record for this publication is available from the British Library .
Library of Congress Cataloging-in-Publication Data
Names: Guidry, M. W., author.
Title: Modern general relativity : black holes, gravitational waves, and cosmology / Mike Guidry (University of Tennessee, Knoxville).
Description: Cambridge ; New York, NY : Cambridge University Press, 2019. | Includes bibliographical references and index.
Identifiers: LCCN 2018034213 | ISBN 9781107197893 (hardback : alk. paper)
Subjects: LCSH: General relativity (Physics)–Textbooks. | Astronomy–Textbooks. | Physics–Textbooks.
Classification: LCC QC173.6 .G84 2019 | DDC 523.01–dc23
ISBN 978-1-107-19789-3 Hardback
Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
For Jo Ann
Brief Contents
1Introduction
2Coordinate Systems and Transformations
3Tensors and Covariance
4Lorentz Covariance and Special Relativity
5Lorentz-Invariant Dynamics
6The Principle of Equivalence
7Curved Spacetime and General Covariance
8The General Theory of Relativity
9The Schwarzschild Spacetime
10Neutron Stars and Pulsars
11Spherical Black Holes
12Quantum Black Holes
13Rotating Black Holes
14Observational Evidence for Black Holes
15Black Holes as Central Engines
16The Hubble Expansion
17Energy and Matter in the Universe
18Friedmann Cosmologies
19Evolution of the Universe
20The Big Bang
21Extending Classical Big Bang Theory
22Gravitational Waves
23Weak Sources of Gravitational Waves
24Strong Sources of Gravitational Waves
25Tests of General Relativity
26Beyond Standard Models
Contents
Preface
Part I General Relativity
1Introduction
1.1Gravity and the Universe on Large Scales
1.2Classical Newtonian Gravity
1.3Transformations between Inertial Systems
1.4Maxwell, the Aether, and Galileo
1.5The Special Theory of Relativity
1.6Minkowski Space
1.7A New Theory of Gravity
1.8The Equivalence Principle
1.9General Relativity
Background and Further Reading
Problems
2Coordinate Systems and Transformations
2.1Coordinate Systems in Euclidean Space
2.1.1Parameterizing in Different Coordinate Systems
2.1.2Basis Vectors
2.1.3Expansion of Vectors and Dual Vectors
2.1.4Vector Scalar Product and the Metric Tensor
2.1.5Relationship of Vectors and Dual Vectors
2.1.6Properties of the Metric Tensor
2.1.7Line Elements
2.1.8Euclidean Line Element
2.2Integration
2.3Differentiation
2.4Non-euclidean Geometry
2.5Transformations
2.5.1Rotational Transformations
2.5.2Galilean Transformations
Background and Further Reading
Problems
3Tensors and Covariance
3.1Invariance and Covariance
3.2Spacetime Coordinates
3.3Vectors in Non-euclidean Space
3.4Coordinates in Spacetime
3.4.1Coordinate and Non-coordinate Bases
3.4.2Utility of Coordinate and Non-coordinate Bases
3.5Tensors and Coordinate Transformations
3.6Tensors as Linear Maps
3.6.1Linear Maps to Real Numbers

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