Gravitational radiation, luminous black holes, and gamma-ray burst supernovae / Maurice H.P.M. van Putten.

Format:

Book

Author/Creator:

Van Putten, Maurice H. P. M.

Contributor:

Craig M. Merrihue Memorial Fund.

Language:

English

Subjects (All):

Gravitational waves.

Black holes (Astronomy).

Supernovae.

Physical Description:

xvii, 308 pages : illustrations ; 26 cm

Place of Publication:

Cambridge, UK ; New York : Cambridge University Press, 2005.

Summary:

Black holes and gravitational radiation are two of the most dramatic predictions of general relativity. The quest for rotating black holes-discovered by Roy P. Kerr as exact solutions to the Einstein equations - is one of the most exciting challenges currently facing physicists and astronomers.

Gravitational Radiation, Luminous Black Holes and Gamma-Ray Burst Supernovae takes the reader through the theory of gravitational radiation and rotating black holes, and the phenomenology of GRB-supernovae. Topics covered include Kerr black holes and the frame-dragging of spacetime, luminous black holes, compact tori around black holes, and black hole spin-interactions. It concludes with a discussion of prospects for gravitational-wave detections of a long-duration burst in gravitational waves as a method of choice for identifying Kerr black holes in the Universe.

This book is ideal for a special topics graduate course on gravitational-wave astronomy and as an introduction to those interested in this contemporary development in physics.

Contents:

1 Superluminal motion in the quasar 3C273 1

1.1 Lorentz transformations 1

1.2 Kinematic effects 5

1.3 Quasar redshifts 6

1.4 Superluminal motion in 3C273 7

1.5 Doppler shift 9

1.6 Relativistic equations of motion 9

2 Curved spacetime and SgrA* 13

2.1 The accelerated letter "L" 14

2.2 The length of timelike trajectories 15

2.3 Gravitational redshift 16

2.4 Spacetime around a star 18

2.5 Mercury's perihelion precession 20

2.6 A supermassive black hole in SgrA* 22

3 Parallel transport and isometry of tangent bundles 26

3.1 Covariant and contravariant tensors 27

3.2 The metric g[subscript ab] 29

3.3 The volume element 30

3.4 Geodesic trajectories 31

3.5 The equation of parallel transport 32

3.6 Parallel transport on the sphere 34

3.7 Fermi-Walker transport 34

3.8 Nongeodesic observers 35

3.9 The Lie derivative 39

4 Maxwell's equations 43

4.1 p-forms and duality 43

4.2 Geometrical interpretation of F[subscript ab] 44

4.3 Two representations of F[subscript ab] 46

4.4 Exterior derivatives 47

4.5 Stokes' theorem 48

4.6 Some specific expressions 49

4.7 The limit of ideal MHD 50

5 Riemannian curvature 55

5.1 Derivations of the Riemann tensor 55

5.2 Symmetries of the Riemann tensor 57

5.3 Foliation in spacelike hypersurfaces 58

5.4 Curvature coupling to spin 59

5.5 The Riemann tensor in connection form 62

5.6 The Weyl tensor 64

5.7 The Hilbert action 64

6 Gravitational radiation 67

6.1 Nonlinear wave equations 69

6.2 Linear gravitational waves in h[subscript ij] 72

6.3 Quadrupole emissions 75

6.4 Summary of equations 79

7 Cosmological event rates 81

7.1 The cosmological principle 82

7.2 Our flat and open universe 83

7.3 The cosmological star-formation rate 85

7.4 Background radiation from transients 85

7.5 Observed versus true event rates 86

8 Compressible fluid dynamics 89

8.1 Shocks in 1D conservation laws 91

8.2 Compressible gas dynamics 94

8.3 Shock jump conditions 95

8.4 Entropy creation in a shock 98

8.5 Relations for strong shocks 98

8.6 The Mach number of a shock 100

8.7 Polytropic equation of state 101

8.8 Relativistic perfect fluids 103

9 Waves in relativistic magnetohydrodynamics 110

9.1 Ideal magnetohydrodynamics 112

9.2 A covariant hyperbolic formulation 113

9.3 Characteristic determinant 115

9.4 Small amplitude waves 117

9.5 Right nullvectors 118

9.6 Well-posedness 122

9.7 Shock capturing in relativistic MHD 125

9.8 Morphology of a relativistic magnetized jet 132

10 Nonaxisymmetric waves in a torus 138

10.1 The Kelvin-Helmholtz instability 139

10.2 Multipole mass-moments in a torus 141

10.3 Rayleigh's stability criterion 142

10.4 Derivation of linearized equations 142

10.5 Free boundary conditions 144

10.6 Stability diagram 145

10.7 Numerical results 146

10.8 Gravitational radiation-reaction force 148

11 Phenomenology of GRB supernovae 152

11.1 True GRB energies 162

11.2 A redshift sample of 33 GRBs 164

11.3 True GRB supernova event rate 165

11.4 Supernovae: the endpoint of massive stars 168

11.5 Supernova event rates 174

11.6 Remnants of GRB supernovae 175

11.7 X-ray flashes 176

11.8 Candidate inner engines of GRB/XRF supernovae 177

12 Kerr black holes 179

12.1 Kerr metric 180

12.2 Mach's principle 183

12.3 Rotational energy 183

12.4 Gravitational spin-orbit energy E = [omega]J 185

12.5 Orbits around Kerr black holes 187

12.6 Event horizons have no hair 189

12.7 Penrose process in the ergosphere 192

13 Luminous black holes 197

13.1 Black holes surrounded by a torus 197

13.2 Horizon flux of a Kerr black hole 199

13.3 Active black holes 202

14 A luminous torus in gravitational radiation 215

14.1 Suspended accretion 216

14.2 Magnetic stability of the torus 217

14.3 Lifetime and luminosity of black holes 222

14.4 Radiation channels by the torus 222

14.5 Equations of suspended accretion 224

14.6 Energies emitted by the torus 226

14.7 A compactness measure 228

15 GRB supernovae from rotating black holes 231

15.1 Centered nucleation at low kick velocities 233

15.2 Branching ratio by kick velocities 237

15.3 Single and double bursters 237

15.4 Radiatively driven supernovae 238

15.5 SN1998bw and SN2002dh 240

15.6 True GRB afterglow energies 241

16 Observational opportunities for LIGO and Virgo 245

16.1 Signal-to-noise ratios 249

16.2 Dimensionless strain amplitudes 250

16.3 Background radiation from GRB-SNe 251

16.4 LIGO and Virgo detectors 253

16.5 Signal-to-noise ratios for GRB-SNe 256

16.6 A time-frequency detection algorithm 260

17 Epilogue: GRB/XRF singlets, doublets? Triplets! 266

Appendix A Landau's derivation of a maximal mass 269

Appendix B Thermodynamics of luminous black holes 271

Appendix C Spin-orbit coupling in the ergotube 273

Appendix D Pair creation in a Wald field 275

Appendix E Black hole spacetimes in the complex plane 280

Appendix F Some units, constants and numbers 283.

Notes:

Includes bibliographical references (pages 285-299) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Craig M. Merrihue Memorial Fund.

ISBN:

0521849608

OCLC:

60371184

Publisher Number:

9780521849609 (hbk.)