Book contents
- Frontmatter
- Contents
- Preface to the second edition
- Preface to the first edition
- 1 Special relativity
- 2 Vector analysis in special relativity
- 3 Tensor analysis in special relativity
- 4 Perfect fluids in special relativity
- 5 Preface to curvature
- 6 Curved manifolds
- 7 Physics in a curved spacetime
- 8 The Einstein field equations
- 9 Gravitational radiation
- 10 Spherical solutions for stars
- 11 Schwarzschild geometry and black holes
- 12 Cosmology
- Appendix A Summary of linear algebra
- References
- Index
4 - Perfect fluids in special relativity
- Frontmatter
- Contents
- Preface to the second edition
- Preface to the first edition
- 1 Special relativity
- 2 Vector analysis in special relativity
- 3 Tensor analysis in special relativity
- 4 Perfect fluids in special relativity
- 5 Preface to curvature
- 6 Curved manifolds
- 7 Physics in a curved spacetime
- 8 The Einstein field equations
- 9 Gravitational radiation
- 10 Spherical solutions for stars
- 11 Schwarzschild geometry and black holes
- 12 Cosmology
- Appendix A Summary of linear algebra
- References
- Index
Summary
Fluids
In many interesting situations in astrophysical GR, the source of the gravitational field can be taken to be a perfect fluid as a first approximation. In general, a ‘fluid’ is a special kind of continuum. A continuum is a collection of particles so numerous that the dynamics of individual particles cannot be followed, leaving only a description of the collection in terms of ‘average’ or ‘bulk’ quantities: number of particles per unit volume, density of energy, density of momentum, pressure, temperature, etc. The behavior of a lake of water, and the gravitational field it generates, does not depend upon where any one particular water molecule happens to be: it depends only on the average properties of huge collections of molecules.
Nevertheless, these properties can vary from point to point in the lake: the pressure is larger at the bottom than at the top, and the temperature may vary as well. The atmosphere, another fluid, has a density that varies with position. This raises the question of how large a collection of particles to average over: it must clearly be large enough so that the individual particles don't matter, but it must be small enough so that it is relatively homogeneous: the average velocity, kinetic energy, and interparticle spacing must be the same everywhere in the collection. Such a collection is called an ‘element’.
- Type
- Chapter
- Information
- A First Course in General Relativity , pp. 84 - 110Publisher: Cambridge University PressPrint publication year: 2009