Edited by Ray d'Inverno
Publisher: Cambridge University Press
Print Publication Year: 1992
Online Publication Date:December 2009
Online ISBN:9780511524639
Hardback ISBN:9780521439763
Paperback ISBN:9780521017350
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511524639.018
Subjects: Cosmology, Relativity and Gravitation, Astrophysics
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Abstract. We present three-dimensional Newtonian and post-Newtonian codes, including the gravitational radiation damping effect, using a finite difference method. We follow the emission of gravitational radiation using the quadrupole approximation. Using these codes we calculate the coalescence of a neutron star binary. For Newtonian calculations the initial configuration is given as a hydrostatic equilibrium model of a close neutron-star binary. Calculations were performed for neutron stars of different masses as well as of the same masses. In order to evaluate general relativistic effects, we compare the results of the calculation of the coalescence of a binary comprising two spherical neutron stars using the post-Newtonian code with results using the Newtonian code.
INTRODUCTION
The most promising sources for laser-interferometric gravitational-wave detectors are catastrophic events such as the gravitational collapse of a star or the coalescence of a black-hole or neutron-star binary. We need to know the characteristics of the waves for design of detectors. It requires general relativistic calculations of stellar collapse and binary coalescence. In the last decade, 2 dimensional (2D) calculations were successfully performed for a head-on collision of two black holes (Smarr 1979) and axisymmetric collapse of a rotating star (Stark and Piran 1986). They found that the efficiency of gravitational wave emission (the ratio of the energy emitted in gravitational radiation to the total rest mass) is less than 0.1%. Nakamura, Oohara and Kojima (1987), on the other hand, pointed out that the efficiency may be much greater in non-axisymmetric black-hole collision.
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pp. xiii-xiv
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PART A - THEORETICAL APPROACHES : Read PDF
pp. 1-2
Numerical relativity on a transputer array : Read PDF
pp. 3-19
Some aspects of the characteristic initial value problem in numerical relativity : Read PDF
pp. 20-33
The characteristic initial value problem in general relativity : Read PDF
pp. 34-40
Algebraic approach to the characteristic initial value problem in general relativity : Read PDF
pp. 41-49
On hyperboloidal hypersurfaces : Read PDF
pp. 50-58
The initial value problem on null cones : Read PDF
pp. 59-68
Introduction to dual-null dynamics : Read PDF
pp. 69-78
On colliding plane wave space-times : Read PDF
pp. 79-82
Boundary conditions for the momentum constraint : Read PDF
pp. 83-93
On the choice of matter model in general relativity : Read PDF
pp. 94-102
A mathematical approach to numerical relativity : Read PDF
pp. 103-113
Making sense of the effects of rotation in general relativity : Read PDF
pp. 114-129
Stability of charged boson stars and catastrophe theory : Read PDF
pp. 130-140
PART B - PRACTICAL APPROACHES : Read PDF
pp. 141-142
Numerical asymptotics : Read PDF
pp. 143-162
Instabilities in rapidly rotating polytropes : Read PDF
pp. 163-181
Gravitational radiation from coalescing binary neutron stars : Read PDF
pp. 182-201
“Critical” behaviour in massless scalar field collapse : Read PDF
pp. 202-222
Godunov-type methods applied to general relativistic stellar collapse : Read PDF
pp. 223-229
Astrophysical sources of gravitational waves and neutrinos : Read PDF
pp. 230-246
Gravitational radiation from 3D gravitational stellar core collapse : Read PDF
pp. 247-257
A vacuum fully relativistic 3D numerical code : Read PDF
pp. 258-264
Solution of elliptic equations in numerical relativity using multiquadrics : Read PDF
pp. 265-280
Self-gravitating thin discs around rotating black holes : Read PDF
pp. 281-291
An ADI scheme for a black hole problem : Read PDF
pp. 292-296
Time-symmetric ADI and causal reconnection : Read PDF
pp. 297-307
The numerical study of topological defects : Read PDF
pp. 308-334
Computations of bubble growth during the cosmological quark-hadron transition : Read PDF
pp. 335-344
Initial data of axisymmetric gravitational waves with a cosmological constant : Read PDF
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