General Relativity for the Gifted Amateur

Auteur
Tom Lancaster is Professor of Physics at Durham University. His research interests include using muons to investigate low-dimensional and molecular magnetism. Stephen Blundell is a Professor of Physics at the University of Oxford, and a Professorial Fellow of Mansfield College. His research interests include muon-spin rotation, density functional techniques, and spin liquids.

Texte du rabat

Using numerous worked examples, diagrams and careful physically motivated explanations this book will smooth the path towards understanding the radically different and revolutionary view of the physical world that general relativity provides and which all physicists should have the opportunity to experience.

Résumé
General relativity is one of the most profound statements in science. It is a theory of gravity that allows us to model the large-scale structure of the Universe, to understand and explain the motions and workings of stars, to reveal how gravity interacts with light waves and even how it hosts its own gravitational waves. It is central to our notions of where the Universe comes from and what its eventual fate might be. For those wishing to learn physics, general relativity enjoys a dubious distinction. It is frequently viewed as a difficult theory, whose mastery is a rite of passage into the world of advanced physics and is described in an array of unforgiving, weighty textbooks aimed firmly at aspiring professionals. Written by experimental physicists and aimed at providing the interested amateur with a bridge from undergraduate physics to general relativity, this book is designed to be different. The imagined reader is a gifted amateur possessing a curious and adaptable mind looking to be told an entertaining and intellectually stimulating story, but who will not feel patronised if a few mathematical niceties are spelled out in detail. Using numerous worked examples, diagrams and careful physically motivated explanations, this book will smooth the path towards understanding the radically different and revolutionary view of the physical world that general relativity provides and which all physicists should have the opportunity to experience.

Contenu

• 0: Overture

• I Geometry and mechanics in at spacetime

• 1: Special relativity

• 2: Vectors in at spacetime

• 3: Coordinates

• 4: Linear slot machines

• 5: The metric

• II Curvature and general relativity

• 6: Finding a theory of gravitation

• 7: Parallel lines and the covariant derivative

• 8: Free fall and geodesics

• 9: Geodesic equations and connection coecients

• 10: Making measurements in relativity

• 11: Riemann curvature and the Ricci tensor

• 12: The energy-momentum tensor

• 13: The gravitational field equations

• 14: The triumphs of general relativity

• III Cosmology

• 15: An introduction to cosmology

• 16: Robertson-Walker spaces

• 17: The Friedmann equations

• 18: Universes of the past and future

• 19: Causality, infinity and horizons

• IV Orbits, stars and black holes

• 20: Newtonian orbits

• 21: The Schwarzschild geometry

• 22: Motion in the Schwarzschild geometry

• 23: Orbits in the Schwarzschild geometry

• 24: Photons in the Schwarzschild geometry

• 25: Black holes

• 26: Black-hole singularities

• 27: Kruskal-Szekeres coordinates

• 28: Hawking radiation

• 29: Charged and rotating black holes

• V Geometry

• 30: Classical curvature

• 31: A reintroduction to geometry

• 32: Differential forms

• 33: Exterior and Lie derivatives

• 34: Geometry of the connection

• 35: Riemann curvature revisited

• 36: Cartan's method

• 37: Duality and the volume form

• 38: Forms, chains and Stokes' theorem

• VI Classical and quantum fields

• 39: Fluids as dry water

• 40: Lagrangian field theory

• 41: Inflation

• 42: The electromagnetic field

• 43: Charge conservation and the Bianchi identity

• 44: Gauge fields

• 45: Weak gravitational fields

• 46: Gravitational waves

• 47: The properties of gravitons

• 48: Higher-dimensional spacetime

• 49: From classical to quantum gravity

• 50: The Big-Bang singularity

• A: Further reading

• B: Conventions and notation

• C: Manifolds and bundles

• D: Embedding

• E: Answers to selected problems