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Tensors in general relativity

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/9780199573639.003.0013
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Differentiation of tensor components in a curved space must be handled with extra care. By adding another term (related to Christoffel symbols) to the ordinary derivative operator, we can form a ... More


Curved Space

Nicholas Manton and Nicholas Mee

in The Physical World: An Inspirational Tour of Fundamental Physics

Published in print:
2017
Published Online:
July 2017
ISBN:
9780198795933
eISBN:
9780191837111
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198795933.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

This chapter develops the mathematical technology required to understand general relativity by taking the reader from the traditional flat space geometry of Euclid to the geometry of Riemann that ... More


Distances, angles and the real and reciprocal spaces

Paolo G. Radaelli

in Symmetry in Crystallography: Understanding the International Tables

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199550654
eISBN:
9780191775093
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199550654.003.0006
Subject:
Physics, Crystallography: Physics, Condensed Matter Physics / Materials

This chapter explains the concept of a metric, which enables distances and angles to be measured. In the crystallographic coordinate framework, this is done by introducing a metric tensor. The ... 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


Riemannian manifolds

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/9780198786399.003.0042
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter introduces the Riemann tensor characterizing curved spacetimes, and then the metric tensor, which allows lengths and durations to be defined. As shown in the preceding chapter, ... More


Manifolds and tensors

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/9780198822158.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The mathematical basis of general relativity is differential geometry. This chapter establishes the starting point of differential geometry: manifolds, tangent vectors, cotangent vectors, tensors, ... More


Radical Structural Essentialism for the Spacetime Substantivalist

Tomasz Bigaj

in The Foundation of Reality: Fundamentality, Space, and Time

Published in print:
2020
Published Online:
May 2020
ISBN:
9780198831501
eISBN:
9780191869273
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198831501.003.0013
Subject:
Philosophy, Metaphysics/Epistemology

Spacetime substantivalists insist that spatiotemporal points are fundamental entities and thus are ontologically independent from the physical objects occupying these points.This chapter argues that ... More


Curvilinear coordinates

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/9780198786399.003.0003
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter presents a discussion on curvilinear coordinates in line with the introduction on Cartesian coordinates in Chapter 1. First, the chapter introduces a new system C of curvilinear ... More


Basics of crystallography, part 1

Ulrich Müller

in Symmetry Relationships between Crystal Structures: Applications of Crystallographic Group Theory in Crystal Chemistry

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199669950
eISBN:
9780191775086
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199669950.003.0002
Subject:
Physics, Crystallography: Physics, Condensed Matter Physics / Materials

A crystal can be considered to be a finite section from an infinite ideal crystal (a crystal pattern). This is an infinite periodic, three-dimensional array of atoms. A shift by a translation vector ... More


Hamiltonian Field Theory

Peter Mann

in Lagrangian and Hamiltonian Dynamics

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198822370
eISBN:
9780191861253
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822370.003.0026
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses classical electromagnetism. As an example of a classical field theory, electrodynamics is framed using a Lagrangian density. Until pioneers such as Faraday and Maxwell, ... More


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