Book contents
- Frontmatter
- Contents
- Preface
- 1 The special theory of relativity
- 2 From the special to the general theory of relativity
- 3 Vectors and tensors
- 4 Covariant differentiation
- 5 Curvature of spacetime
- 6 Spacetime symmetries
- 7 Physics in curved spacetime
- 8 Einstein's equations
- 9 The Schwarzschild solution
- 10 Experimental tests of general relativity
- 11 Gravitational radiation
- 12 Relativistic astrophysics
- 13 Black holes
- 14 The expanding Universe
- 15 Friedmann models
- 16 The early Universe
- 17 Observational cosmology
- 18 Beyond relativity
- References
- Index
7 - Physics in curved spacetime
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 The special theory of relativity
- 2 From the special to the general theory of relativity
- 3 Vectors and tensors
- 4 Covariant differentiation
- 5 Curvature of spacetime
- 6 Spacetime symmetries
- 7 Physics in curved spacetime
- 8 Einstein's equations
- 9 The Schwarzschild solution
- 10 Experimental tests of general relativity
- 11 Gravitational radiation
- 12 Relativistic astrophysics
- 13 Black holes
- 14 The expanding Universe
- 15 Friedmann models
- 16 The early Universe
- 17 Observational cosmology
- 18 Beyond relativity
- References
- Index
Summary
Introduction
Having acquainted ourselves with the trials and tribulations of working in non-Euclidean spacetimes we are now prepared for the next step, that of describing physics in such curved spacetimes. For we recall from Chapter 2 that the Einstein programme for general relativity consists of replacing the Newtonian perception of gravitation as a force by the notion that its effect makes the geometry of spacetime ‘suitably non-Euclidean’. What we mean by ‘suitably’ will be clear in the next two chapters. But given that the geometry is non-Euclidean we first need to know how the rest of physics is described in it.
For example, how do we describe the motion of a particle under a non-gravitational force? How do we write Maxwell's equations? What is the role of energy-momentum tensors? Can a dynamical action principle be written in curved spacetime? Such questions need our attention before we turn to the basic issue of how gravity actually leads to curved spacetime.
To this end we will introduce a concept that Einstein took as a basic principle in formulating general relativity. It is known as the principle of equivalence.
The principle of equivalence
Let us go back to the purely mathematical result embodied in the relations shown in Section 4.6 and attempt to describe their physical meaning. These relations tell us that special (locally inertial) coordinates that behave like the coordinates (t, x, y, z) of special relativity exist in the neighbourhood of any point P in spacetime.
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- Information
- An Introduction to Relativity , pp. 100 - 115Publisher: Cambridge University PressPrint publication year: 2010