Introducing general relativity / Mark Hindmarsh, Andrew Liddle.

Format:

Book

Author/Creator:

Hindmarsh, Mark, author.

Liddle, Andrew R., author.

Language:

English

Subjects (All):

General relativity (Physics)--Textbooks.

General relativity (Physics).

Physical Description:

xi, 271 pages : illustrations (some color) ; 23 cm

Place of Publication:

Hoboken, NJ : John Wiley & Sons, Inc., 2022.

Summary:

"This introductory textbook, which is positioned at an intermediate level between the more qualitative books at the low end and the many graduate-level standard textbooks, is an accessible introduction to general relativity primarily aimed at undergraduates studying mechanics, dynamics and special relativity. The text provides structured outlines to the concepts and applications of the topic, leading the reader from the basic ideas of relativity, such as the cosmological principle to the Friedmann equation, on to some more advanced ideas such as orbits in the Schwarzschild Geometry. At the end of each chapter there are appropriate problems. A wide-range of classical and modern topics are covered, exploring observational successes and particle physics to explain many popular principles including space-time, redshift, gravity, and fascinating topics such as black holes and dark matter. This timely textbook also provides a section of advanced topics that offers more detailed mathematical approaches and advanced ideas as a basis for further studies to prepare the reader for understanding more specialised texts"-- Provided by publisher.

Contents:

Preface

Constants and Symbols

Introducing General Relativity

A Special Relativity Reminder

The need for Special Relativity

The Lorentz transformation

Time dilation

Lorentz-Fitzgerald contraction

Addition of velocities

Simultaneity, colocality, and causality

Space-time diagrams

Tensors in Special Relativity

Coordinates

4-vectors

4-velocity, 4-momentum, and 4-acceleration

4-divergence and the wave operator

Tensors

Tensors in action: the Lorentz force

Towards General Relativity

Newtonian gravity

Special Relativity and gravity

Motivations for a General Theory of Relativity

Mach's Principle

Einstein's Equivalence Principle

Implications of the Equivalence Principle

Gravitational redshift

Gravitational time dilation

Principles of the General Theory of Relativity

Towards curved space-time

Curved space in two dimensions

Tensors and Curved Space-Time

General coordinate transformations

Tensor equations and the laws of physics

Partial differentiation of tensors

The covariant derivative and parallel transport

Christoffel symbols of a two-sphere

Parallel transport on a two-sphere

Curvature and the Riemann tensor

Riemann curvature of the two-sphere

More tensors describing curvature

Local inertial frames and local flatness

Describing Matter

The Correspondence Principle

The energy-momentum tensor

General properties

Conservation laws and 4-vector flux

Energy and momentum belong in a rank-2 tensor

Symmetry of the energy-momentum tensor

Energy-momentum of perfect fluids

The energy-momentum tensor in curved space-time

The Einstein Equation

The form of the Einstein equation

Properties of the Einstein equation

The Newtonian limit

The cosmological constant

The vacuum Einstein equation

The Schwarzschild Space-time

Christoffel symbols

Riemann tensor

Ricci tensor

The Schwarzschild solution

The Jebsen-Birkhoff theorem

Geodesics and Orbits

Geodesics

Non-relativistic limit of geodesic motion

Geodesic deviation

Newtonian theory of orbits

Orbits in the Schwarzschild space-time

Massive particles

Photon orbits

Tests of General Relativity

Precession of Mercury's perihelion

Gravitational light bending

Radar echo delays

Binary pulsar PSR 1913+

Direct detection of gravitational waves

Black Holes

The Schwarzschild radius

Singularities

Radial rays in the Schwarzschild space-time

Schwarzschild coordinate systems

The black hole space-time

Special orbits around black holes

Black holes in physics and in astrophysics

Cosmology

Constant-curvature spaces

The metric of the Universe

The matter content of the Universe

The Einstein equations

Cosmological Models

Simple solutions: matter and radiation

Light travel, distances, and horizons

Light travel in the cosmological metric

Cosmological redshift

The expansion rate

The age of the Universe

The distance-redshift relation and Hubble's law

Cosmic horizons

The luminosity and angular-diameter distances

Ingredients for a realistic cosmological model

Accelerating cosmologies

General Relativity: The Next 100 Years

Developing General Relativity

Beyond General Relativity

Into the future

Advanced Topic A1 Geodesics in the Schwarzschild Space-Time

Geodesics and conservation laws

Schwarzschild geodesics for massive particles

Schwarzschild geodesics for massless particles

Advanced Topic A2 The Solar System Tests in Detail

Newtonian orbits in detail

Perihelion shift in General Relativity

Light deflection

Time delay

Advanced Topic A3 Weak Gravitational Fields and Gravitational Waves

Nearly-flat space-times

Gravitational waves

Sources of gravitational waves

Advanced Topic A4 Gravitational Wave Sources and Detection

Gravitational waves from compact binaries

The energy in gravitational waves

Binary inspiral

Detecting gravitational waves

Laser interferometers

Pulsar timing

Interferometers in space

Bibliography

Answers to selected problems

Index.

Notes:

Includes bibliographical references and index.

Other Format:

Online version: Hindmarsh, Mark. Introducing general relativity

ISBN:

9781118600719

1118600711

OCLC:

1222894473

Publisher Number:

99993695383