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/CBO9780511524639.013
Subjects: Cosmology, Relativity and Gravitation, Astrophysics
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Abstract. This article contains some proposals for the construction of an algorithm for the evolution of initial data in general relativity which will apply to generic initial values. One of the main issues is to allow a dynamic refinement of the discretisation which will be local and vary according to local values of the initial data. I outline some of the main problems which will have to be addressed in any implementation of the general scheme. There are also some suggestions for a construction of a smooth solution of the Einstein equations which is near to the discrete evolution.
INTRODUCTION
At the present time, computer codes for general relativity are written specifically for particular problems such as stellar collapse or coalescing binary systems. In the longer run relativists are interested in using the computer as a mathematical tool to investigate the properties of solutions which seem inaccessible by analytic means, or to formulate hypotheses which may then be attacked analytically. This requires the construction of an algorithm which applies to generic initial data and which also has a sufficiently solid framework which allows analytic investigation of the error of the approximation.
The approach I would like to suggest is based on triangulations. One of the problems of numerical relativity is that the degree of discretisation that is required to approximate given data well is dependent on that data. However one cannot predict — in advance — how this will evolve as the data evolves with time.
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pp. vii-ix
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pp. xiii-xiv
pp. xv-xx
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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