Introducing General Relativity

Introducing General Relativity
 
An accessible and engaging introduction to general relativity for undergraduates
 
In Introducing General Relativity, the authors deliver a structured introduction to the core concepts and applications of General Relativity. The book leads readers from the basic ideas of relativity--including the Equivalence Principle and curved space-time--to more advanced topics, like Solar System tests and gravitational wave detection.
 
Each chapter contains practice problems designed to engage undergraduate students of mechanics, electrodynamics, and special relativity. A wide range of classical and modern topics are covered in detail, from exploring observational successes and astrophysical implications to explaining many popular principles, like space-time, redshift, black holes, gravitational waves and cosmology. Advanced topic sections introduce the reader to more detailed mathematical approaches and complex ideas, and prepare them for the exploration of more specialized and sophisticated texts.
 
Introducing General Relativity also offers:
* Structured outlines to the concepts of General Relativity and a wide variety of its applications
* Comprehensive explorations of foundational ideas in General Relativity, including space-time curvature and tensor calculus
* Practical discussions of classical and modern topics in relativity, from space-time to redshift, gravity, black holes, and gravitational waves
* Optional, in-depth sections covering the mathematical approaches to more advanced ideas
 
Perfect for undergraduate physics students who have studied mechanics, dynamics, and Special Relativity, Introducing General Relativity is an essential resource for those seeking an intermediate level discussion of General Relativity placed between the more qualitative books and graduate-level textbooks.

Sommario

Preface ix
 
Constants and Symbols x
 
1 Introducing General Relativity 1
 
2 A Special Relativity Reminder 3
 
2.1 The need for Special Relativity 4
 
2.2 The Lorentz transformation 6
 
2.3 Time dilation 8
 
2.4 Lorentz-Fitzgerald contraction 9
 
2.5 Addition of velocities 11
 
2.6 Simultaneity, colocality, and causality 12
 
2.7 Space-time diagrams 13
 
3 Tensors in Special Relativity 17
 
3.1 Coordinates 18
 
3.2 4-vectors 20
 
3.3 4-velocity, 4-momentum, and 4-acceleration 24
 
3.4 4-divergence and the wave operator 26
 
3.5 Tensors 28
 
3.6 Tensors in action: the Lorentz force 30
 
4 Towards General Relativity 37
 
4.1 Newtonian gravity 37
 
4.2 Special Relativity and gravity 39
 
4.3 Motivations for a General Theory of Relativity 41
 
4.3.1 Mach's Principle 42
 
4.3.2 Einstein's Equivalence Principle 42
 
4.4 Implications of the Equivalence Principle 44
 
4.4.1 Gravitational redshift 45
 
4.4.2 Gravitational time dilation 46
 
4.5 Principles of the General Theory of Relativity 47
 
4.6 Towards curved space-time 49
 
4.7 Curved space in two dimensions 50
 
5 Tensors and Curved Space-Time 57
 
5.1 General coordinate transformations 57
 
5.2 Tensor equations and the laws of physics 59
 
5.3 Partial differentiation of tensors 59
 
5.4 The covariant derivative and parallel transport 60
 
5.5 Christoffel symbols of a two-sphere 65
 
5.6 Parallel transport on a two-sphere 66
 
5.7 Curvature and the Riemann tensor 68
 
5.8 Riemann curvature of the two-sphere 71
 
5.9 More tensors describing curvature 72
 
5.10 Local inertial frames and local flatness 73
 
6 Describing Matter 79
 
6.1 The Correspondence Principle 79
 
6.2 The energy-momentum tensor 80
 
6.2.1 General properties 80
 
6.2.2 Conservation laws and 4-vector flux 81
 
6.2.3 Energy and momentum belong in a rank-2 tensor 83
 
6.2.4 Symmetry of the energy-momentum tensor 84
 
6.2.5 Energy-momentum of perfect fluids 84
 
6.2.6 The energy-momentum tensor in curved space-time 87
 
7 The Einstein Equation 91
 
7.1 The form of the Einstein equation 91
 
7.2 Properties of the Einstein equation 93
 
7.3 The Newtonian limit 93
 
7.4 The cosmological constant 95
 
7.5 The vacuum Einstein equation 96
 
8 The Schwarzschild Space-time 99
 
8.1 Christoffel symbols 100
 
8.2 Riemann tensor 101
 
8.3 Ricci tensor 102
 
8.4 The Schwarzschild solution 103
 
8.5 The Jebsen-Birkhoff theorem 104
 
9 Geodesics and Orbits 109
 
9.1 Geodesics 109
 
9.2 Non-relativistic limit of geodesic motion 112
 
9.3 Geodesic deviation 113
 
9.4 Newtonian theory of orbits 115
 
9.5 Orbits in the Schwarzschild space-time 117
 
9.5.1 Massive particles 117
 
9.5.2 Photon orbits 120
 
10 Tests of General Relativity 123
 
10.1 Precession of Mercury's perihelion 123
 
10.2 Gravitational light bending 125
 
10.3 Radar echo delays 127
 
10.4 Gravitational redshift 129
 
10.5 Binary pulsar PSR 1913+16 131
 
10.6 Direct detection of gravitational waves 135
 
11 Black Holes 139
 
11.1 The Schwarzschild radius 139
 
11.2 Singularities 140
 
11.3 Radial rays in the Schwarzschild space-time 141
 
11.4 Schwarzschild coordinate systems 143
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Info autore

Mark Hindmarsh is Professor of Theoretical Physics with joint appointments at the University of Sussex, UK and the University of Helsinki, Finland. His research is focused on the physics of the Big Bang, and he is a member of the LISA consortium with particular expertise in the cosmological production of gravitational waves. He has taught at all levels of the undergraduate and postgraduate curriculum.
Andrew Liddle is a Principal Researcher at the University of Lisbon in Portugal, with joint affiliations at the University of Edinburgh, UK, and the Perimeter Institute for Theoretical Physics, Waterloo, Canada. He researches the properties of our Universe and how these relate to fundamental physical laws, especially through understanding astronomical observations. He is involved in several international projects, including the Planck Satellite and the Dark Energy Survey.

Riassunto

Introducing General Relativity

An accessible and engaging introduction to general relativity for undergraduates

In Introducing General Relativity, the authors deliver a structured introduction to the core concepts and applications of General Relativity. The book leads readers from the basic ideas of relativity--including the Equivalence Principle and curved space-time--to more advanced topics, like Solar System tests and gravitational wave detection.

Each chapter contains practice problems designed to engage undergraduate students of mechanics, electrodynamics, and special relativity. A wide range of classical and modern topics are covered in detail, from exploring observational successes and astrophysical implications to explaining many popular principles, like space-time, redshift, black holes, gravitational waves and cosmology. Advanced topic sections introduce the reader to more detailed mathematical approaches and complex ideas, and prepare them for the exploration of more specialized and sophisticated texts.

Introducing General Relativity also offers:
* Structured outlines to the concepts of General Relativity and a wide variety of its applications
* Comprehensive explorations of foundational ideas in General Relativity, including space-time curvature and tensor calculus
* Practical discussions of classical and modern topics in relativity, from space-time to redshift, gravity, black holes, and gravitational waves
* Optional, in-depth sections covering the mathematical approaches to more advanced ideas

Perfect for undergraduate physics students who have studied mechanics, dynamics, and Special Relativity, Introducing General Relativity is an essential resource for those seeking an intermediate level discussion of General Relativity placed between the more qualitative books and graduate-level textbooks.

Dettagli sul prodotto

• Autori: M Hindmarsh, Mark Hindmarsh, Mark Liddle Hindmarsh, Andrew Liddle, Liddle Andrew
• Editore: Wiley, John and Sons Ltd
• Lingue: Inglese
• Formato: Tascabile
• Pubblicazione: 30.11.2021
• EAN: 9781118600719
• ISBN: 978-1-118-60071-9
• Pagine: 288
• Categorie: Saggistica > Natura, tecnica > Astronomia: tematiche generali, opere di consultazione; Scienze naturali, medicina, informatica, tecnica > Fisica, astronomia > Fisica atomica, fisica nucleare; Physik, Astronomie, Theoretische Physik, Physics, allgemeine relativitätstheorie, Theoretical Physics, Astronomie u. Astrophysik, Astronomy & Astrophysics