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1 The geometric approach to GWs

Michele Maggiore

in Gravitational Waves: Volume 1: Theory and Experiments

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198570745
eISBN:
9780191717666
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570745.003.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses how gravitational waves emerge from general relativity, and what their properties are. The most straightforward approach is ‘linearized theory’, where the Einstein equations ... More


GR as a geometric theory of gravity – I

Ta-Pei Cheng

in Relativity, Gravitation and Cosmology: A Basic Introduction

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199573639
eISBN:
9780191722448
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573639.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

A geometric description of equivalence principle physics of gravitational time dilation is presented. In this geometric theory, the metric plays the role of relativistic gravitational potential. ... More


GR as a geometric theory of gravity — II

Ta-Pei Cheng

in Relativity, Gravitation and Cosmology: A Basic Introduction

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199573639
eISBN:
9780191722448
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573639.003.0014
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

The mathematical realization of equivalence principle (EP) is the principle of general covariance. General relativity (GR) equations must be covariant with respect to general coordinate ... More


Parallel transport and geodesics

Andrew M. Steane

in Relativity Made Relatively Easy Volume 2: General Relativity and Cosmology

Published in print:
2021
Published Online:
December 2021
ISBN:
9780192895646
eISBN:
9780191943911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192895646.003.0013
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The mathematics of parallel transport and of affine and metric geodesics is presented. The geodesic equation is obtained in several different ways, bringing out its role both as a geometric statement ... More


Particle Motion in Curved Spacetime

Valeri P. Frolov and Andrei Zelnikov

in Introduction to Black Hole Physics

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199692293
eISBN:
9780191731860
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199692293.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Particle motion in a curved spacetime is considered. The Lagrangian and Hamiltonian form of the equation of motion of a relativistic particle are described. We discuss here also the Hamilton‐Jacobi ... More


Metric Spaces and Geodesic Motion

David D. Nolte

in Introduction to Modern Dynamics: Chaos, Networks, Space, and Time

Published in print:
2019
Published Online:
November 2019
ISBN:
9780198844624
eISBN:
9780191880216
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198844624.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The metric tensor uniquely defines the geometric properties of a metric space, while differential geometry is concerned with the derivatives of vectors and tensors within the metric space. ... More


Metric description of a curved space

Ta-Pei Cheng

in Relativity, Gravitation and Cosmology: A Basic Introduction

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199573639
eISBN:
9780191722448
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573639.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Einstein's new theory of gravitation is formulated in a geometric framework of curved spacetime. Here the subject of non-Euclidean geometry is introduced by way of Gauss's theory of curved surfaces. ... More


The elements of General Relativity

Andrew M. Steane

in Relativity Made Relatively Easy Volume 2: General Relativity and Cosmology

Published in print:
2021
Published Online:
December 2021
ISBN:
9780192895646
eISBN:
9780191943911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192895646.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter is a survey of central ideas and equations in general relativity. The basic equations are written down with a view to seeing where we are heading in the book, and in order to present ... More


Geodesics

Steven Carlip

in General Relativity: A Concise Introduction

Published in print:
2019
Published Online:
March 2019
ISBN:
9780198822158
eISBN:
9780191861215
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822158.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The generalization of a “straight line” in Euclidean geometry is a geodesic, the shortest distance between two points in a (possibly curved) space or spacetime. This chapter introduces geodesics, ... More


Classical Covariance

Moataz H. Emam

in Covariant Physics: From Classical Mechanics to General Relativity and Beyond

Published in print:
2021
Published Online:
May 2021
ISBN:
9780198864899
eISBN:
9780191897313
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198864899.003.0003
Subject:
Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

Classical mechanics, from point particles through rigid objects and continuum mechanics is reviewed based on the notions of tensors, transformations, and the metric, as developed in the first two ... More


Spacetime symmetries

Michael Kachelriess

in Quantum Fields: From the Hubble to the Planck Scale

Published in print:
2017
Published Online:
February 2018
ISBN:
9780198802877
eISBN:
9780191841330
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198802877.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter introduces tensor fields, covariant derivatives and the geodesic equation on a (pseudo-) Riemannian manifold. It discusses how symmetries of a general space-time can be found from the ... More


Gravity Reframed

David M. Wittman

in The Elements of Relativity

Published in print:
2018
Published Online:
August 2018
ISBN:
9780199658633
eISBN:
9780191863653
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199658633.003.0014
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The effects of gravity disappear in freely falling laboratories.Within such a laboratory, a freely falling particle appears to have no forces on it—it is an inertial particle following the rules of ... More


Conservation laws

Nathalie Deruelle and Jean-Philippe Uzan

in Relativity in Modern Physics

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198786399
eISBN:
9780191828669
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198786399.003.0045
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter studies how the ‘spacetime symmetries’ can generate first integrals of the equations of motion which simplify their solution and also make it possible to define conserved quantities, or ... More


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