Book contents
- Frontmatter
- Contents
- Foreword
- Acknowledgments
- Introduction
- Notation
- 1 Superluminal motion in the quasar 3C273
- 2 Curved spacetime and SgrA*
- 3 Parallel transport and isometry of tangent bundles
- 4 Maxwell's equations
- 5 Riemannian curvature
- 6 Gravitational radiation
- 7 Cosmological event rates
- 8 Compressible fluid dynamics
- 9 Waves in relativistic magnetohydrodynamics
- 10 Nonaxisymmetric waves in a torus
- 11 Phenomenology of GRB supernovae
- 12 Kerr black holes
- 13 Luminous black holes
- 14 A luminous torus in gravitational radiation
- 15 GRB supernovae from rotating black holes
- 16 Observational opportunities for LIGO and Virgo
- 17 Epilogue: GRB/XRF singlets, doublets? Triplets!
- Appendix A Landau's derivation of a maximal mass
- Appendix B Thermodynamics of luminous black holes
- Appendix C Spin–orbit coupling in the ergotube
- Appendix D Pair creation in a Wald field
- Appendix E Black hole spacetimes in the complex plan
- Appendix F Some units, constants and numbers
- References
- Index
10 - Nonaxisymmetric waves in a torus
Published online by Cambridge University Press: 17 August 2009
- Frontmatter
- Contents
- Foreword
- Acknowledgments
- Introduction
- Notation
- 1 Superluminal motion in the quasar 3C273
- 2 Curved spacetime and SgrA*
- 3 Parallel transport and isometry of tangent bundles
- 4 Maxwell's equations
- 5 Riemannian curvature
- 6 Gravitational radiation
- 7 Cosmological event rates
- 8 Compressible fluid dynamics
- 9 Waves in relativistic magnetohydrodynamics
- 10 Nonaxisymmetric waves in a torus
- 11 Phenomenology of GRB supernovae
- 12 Kerr black holes
- 13 Luminous black holes
- 14 A luminous torus in gravitational radiation
- 15 GRB supernovae from rotating black holes
- 16 Observational opportunities for LIGO and Virgo
- 17 Epilogue: GRB/XRF singlets, doublets? Triplets!
- Appendix A Landau's derivation of a maximal mass
- Appendix B Thermodynamics of luminous black holes
- Appendix C Spin–orbit coupling in the ergotube
- Appendix D Pair creation in a Wald field
- Appendix E Black hole spacetimes in the complex plan
- Appendix F Some units, constants and numbers
- References
- Index
Summary
“I cannot do't without counters.”
William Shakespeare (1564–1616) The Winter's Tale, IV: iii.36.Waves are common in astrophysical fluids. They define the morphology of outflows, which are related to accretion disks surrounding compact objects. Waves often appear spontaneously, in response to instabilities commonly associated with shear flows. The canonical example of a shear-driven instability is the Kelvin–Helmholtz instability. Even in the absence of shear, stratified flows with different densities can become unstable in the presence of acceleration and/or gravity – the Rayleigh–Taylor instability. Such instabilities do not fundamentally depend on compressibility, and hence they are appropriately discussed in the approximation of incompressible flows. In rotating fluids, instabilities represent a tendency to redistribute angular momentum leading towards a lower energy state. These, likewise, can be studied in the limit of incompressible flows.
A torus around a black hole is a fluid bound to a central potential well. The fluid in the torus is a rotational shear flow, which is generally more rapidly rotating on the inner face than on the outer one. In particular, when driven by a spin-connection to the black hole, the inner face develops a super-Keplerian state, while the outer one develops a sub-Keplerian state by angular momentum loss in winds. The induced effective gravity – centrifugal on the inner face and centripetal on the outer face – allows surface waves to appear very similar to water waves in channels of finite depth.
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- Publisher: Cambridge University PressPrint publication year: 2005