Book contents
- Frontmatter
- Contents
- Preface
- Background: what you need to know before you start
- 1 Gravity on Earth:
- 2 And then came Newton
- 3 Satellites
- 4 The Solar System
- 5 Tides and tidal forces
- 6 Interplanetary travel
- 7 Atmospheres
- 8 Gravity in the Sun
- 9 Reaching for the stars
- 10 The colors of stars
- 11 Stars at work
- 12 Birth to death
- 13 Binary stars
- 14 Galaxies
- 15 Physics at speed
- 16 Relating to Einstein
- 17 Spacetime geometry
- 18 Einstein's gravity
- 19 Einstein's recipe
- 20 Neutron stars
- 21 Black holes
- 22 Gravitational waves
- 23 Gravitational lenses
- 24 Cosmology
- 25 The Big Bang
- 26 Einstein's Universe
- 27 Ask the Universe
- Appendix: values of useful constants
- Glossary
- Index
19 - Einstein's recipe
Fashioning the geometry of gravity
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Background: what you need to know before you start
- 1 Gravity on Earth:
- 2 And then came Newton
- 3 Satellites
- 4 The Solar System
- 5 Tides and tidal forces
- 6 Interplanetary travel
- 7 Atmospheres
- 8 Gravity in the Sun
- 9 Reaching for the stars
- 10 The colors of stars
- 11 Stars at work
- 12 Birth to death
- 13 Binary stars
- 14 Galaxies
- 15 Physics at speed
- 16 Relating to Einstein
- 17 Spacetime geometry
- 18 Einstein's gravity
- 19 Einstein's recipe
- 20 Neutron stars
- 21 Black holes
- 22 Gravitational waves
- 23 Gravitational lenses
- 24 Cosmology
- 25 The Big Bang
- 26 Einstein's Universe
- 27 Ask the Universe
- Appendix: values of useful constants
- Glossary
- Index
Summary
We are now ready to go to the heart of general relativity, to learn how matter generates gravity. This subject is usually left out of discussions of general relativity below the level of an advanced university course. The reason is mathematics, not physics: Einstein formulated his field equations, his gravity-generating equations, using the language of differential geometry. This is the mathematical discipline that deals with curvature, and it is far from elementary. The physical ideas that Einstein expressed in this mathematical language are simply too important, however, to pass over. In this chapter we whittle down the mathematics to a form that is as close as possible to the algebra we used in our earlier chapters on Newton's gravity. This allows us to share in Einstein's thinking, to see what general relativity really predicts about the world we live in.
In this chapter: we study the equations that show how matter generates gravity in general relativity. We identify four properties of matter and gravity that act as sources of gravity, and we show how these different sources produce different gravitational effects. Using only little algebra, we compute the curvature of space and get the observed deflection of light as it passes the Sun. We show how special relativity and the curvature of time lead to something called the dragging of inertial frames. We examine the special properties of the cosmological constant as a source of gravity.
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- Chapter
- Information
- Gravity from the Ground UpAn Introductory Guide to Gravity and General Relativity, pp. 239 - 260Publisher: Cambridge University PressPrint publication year: 2003