Book contents
- Frontmatter
- Contents
- Foreword
- Preface
- Notation
- Quotation acknowledgements
- 1 A zoo of astrophysical transient sources
- 2 Electromagnetic radiation processes
- 3 Curved spacetime and gravitational waves
- 4 Hadronic processes and neutrino emissions
- 5 Relativistic fluid dynamics
- 6 Winds and jets
- 7 Relativistic shock waves
- 8 Relativistic blast waves
- 9 Accretion disks and tori
- 10 Entropic attraction in black hole binaries
- 11 Transient sources from rotating black holes
- 12 Searching for long bursts in gravitational waves
- 13 Epilogue: the multimessenger Transient Universe
- Appendix A Some properties of Kerr black holes
- Appendix B Cosmological event rates
- Appendix C Relaxation limited evaporation
- Appendix D Some units and constants
- References
- Index
3 - Curved spacetime and gravitational waves
Published online by Cambridge University Press: 05 August 2012
- Frontmatter
- Contents
- Foreword
- Preface
- Notation
- Quotation acknowledgements
- 1 A zoo of astrophysical transient sources
- 2 Electromagnetic radiation processes
- 3 Curved spacetime and gravitational waves
- 4 Hadronic processes and neutrino emissions
- 5 Relativistic fluid dynamics
- 6 Winds and jets
- 7 Relativistic shock waves
- 8 Relativistic blast waves
- 9 Accretion disks and tori
- 10 Entropic attraction in black hole binaries
- 11 Transient sources from rotating black holes
- 12 Searching for long bursts in gravitational waves
- 13 Epilogue: the multimessenger Transient Universe
- Appendix A Some properties of Kerr black holes
- Appendix B Cosmological event rates
- Appendix C Relaxation limited evaporation
- Appendix D Some units and constants
- References
- Index
Summary
And these little things may not seem like much but after a while they take you off on a direction where you may be a long way off from what other people have been thinking about.
Roger Penrose (1931–)General relativity gives a complete description of gravitation as it follows from conservation of energy–momentum, general gauge covariance and causality. While it has unprecedented predictive power towards cosmology, gravitational collapse and gravitational waves, only recently has gravitation become an experimental science beyond Newton's law of attraction [22] and beyond gravitational redshift [489], with the advance of LAGEOS, LAGEOS II [155] and Gravity Probe B [199]. These controlled experiments provide the first direct measurements of geodetic and frame-dragging precessions combined, from which we can gain confidence in astrophysical models involving strong gravitational fields and their radiation processes.
In this chapter, we summarize the most immediate aspects in a geometrical way to facilitate applications to astrophysics. We follow the general idea that the essential properties of general relativity derive from the Riemann tensor [485, 141]. We use the tensor notation of [631] with Latin indices and use geometrical units in which Newton's constant and the velocity of light are set equal to 1 unless otherwise specified.
Curved spacetime
General relativity describes the motion of particles in terms of world-lines xb(τ) in a curved spacetime with coordinates xb, with the eigentime τ commonly used as the parameter of the world-line family.
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- Relativistic Astrophysics of the Transient UniverseGravitation, Hydrodynamics and Radiation, pp. 84 - 109Publisher: Cambridge University PressPrint publication year: 2012