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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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