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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:

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:

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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