Approaches to Numerical Relativity

doi:10.1017/CBO9780511524639

This volume includes contributions by leading workers in the field given at the workshop on Numerical Relativity held in Southampton in December 1991. Numerical Relativity, or the numerical solution of astrophysical problems using powerful computers to solve Einstein's equations, has grown rapidly over the last 15 years. It is now an important route to understanding the structure of the Universe, and is the only route currently available for approaching certain important astrophysical scenarios. The Southampton meeting was notable for the first full report of the new 2+2 approach and the related null or characteristic approaches, as well as for updates on the established 3+1 approach, including both Newtonian and fully relativistic codes. The contributions range from theoretical (formalisms, existence theorems) to the computational (moving grids, multiquadrics and spectral methods).

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Contents

Frontmatter
pp i-vi
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Contents
pp vii-ix
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Contributors
pp x-xii
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Introduction
pp xiii-xiv
- By Ray d'Inverno, Faculty of Mathematical Studies, University of Southampton, Southampton, UK
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Preface
pp xv-xx
- By C. J. S. Clarke, Faculty of Mathematical Studies, University of Southampton, Southampton, UK
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PART A - THEORETICAL APPROACHES
pp 1-2
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Numerical relativity on a transputer array
pp 3-19
- By Ray d'Inverno, Faculty of Mathematical Studies, University of Southampton, Southampton, UK
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Some aspects of the characteristic initial value problem in numerical relativity
pp 20-33
- By N. T. Bishop, Department of Mathematics, Applied Mathematics and Astronomy, University of South Africa, Pretoria, South Africa
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The characteristic initial value problem in general relativity
pp 34-40
- By J. M. Stewart, Department of Mathematics, Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK
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Algebraic approach to the characteristic initial value problem in general relativity
pp 41-49
- By Jörg Frauendiener, Max Planck Institute for Astrophysics, Munich, Germany
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On hyperboloidal hypersurfaces
pp 50-58
- By Helmut Friedrich, Max Planck Institute for Astrophysics, Munich, Germany
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The initial value problem on null cones
pp 59-68
- By J. A. Vickers, Faculty of Mathematical Studies, University of Southampton, Southampton, UK
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Introduction to dual-null dynamics
pp 69-78
- By S. A Hayward, Max Planck Institute for Astrophysics, Munich, Germany
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On colliding plane wave space-times
pp 79-82
- By J. B. Griffiths, Department of Mathematical Sciences, University of Technology, Loughborough, UK
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Boundary conditions for the momentum constraint
pp 83-93
- By Niall Ó Murchadha, Physics Department, University College, Cork, Ireland
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On the choice of matter model in general relativity
pp 94-102
- By A. D. Rendall, Max Planck Institute for Astrophysics, Munich, Germany
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A mathematical approach to numerical relativity
pp 103-113
- By J. W. Barrett, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK
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Making sense of the effects of rotation in general relativity
pp 114-129
- By J. C. Miller, Trieste Astronomical Observatory, Trieste, Italy
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Stability of charged boson stars and catastrophe theory
pp 130-140
- By Franz E. Schunck, Institute for Theoretical Physics, University of Cologne, Cologne, Germany, Fjodor V. Kusmartsev, Department of Physics, University of Oulu, Linnanmaa, Finland, Eckehard W. Mielke, Faculty of Mathematics, University of Kiel, Kiel, Germany
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PART B - PRACTICAL APPROACHES
pp 141-142
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Numerical asymptotics
pp 143-162
- By R. Gómez, Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, US, J. Winicour, Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, US
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Instabilities in rapidly rotating polytropes
pp 163-181
- By Scott C. Smith, Department of Physics and Atmospheric Science, Drexel University, Philadelphia, US, Joan M. Centrella, Department of Physics and Atmospheric Science, Drexel University, Philadelphia, US
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Gravitational radiation from coalescing binary neutron stars
pp 182-201
- By Ken-Ichi Oohara, National Laboratory for High Energy Physics, Oho, Japan, Takashi Nakamura, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan
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“Critical” behaviour in massless scalar field collapse
pp 202-222
- By M. W. Choptuik, Center for Relativity, University of Texas at Austin, Austin, US
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Godunov-type methods applied to general relativistic stellar collapse
pp 223-229
- By José M. Ibáñez, Department of Theoretical Physics, University of Valencia, Valencia, Spain, José M. Martí, Department of Theoretical Physics, University of Valencia, Valencia, Spain, Juan A. Miralles, Department of Theoretical Physics, University of Valencia, Valencia, Spain, J.V. Romero, Department of Theoretical Physics, University of Valencia, Valencia, Spain
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Astrophysical sources of gravitational waves and neutrinos
pp 230-246
- By Silvano Bonazzola, DARC, Meudon Observatory, Meudon, France, Eric Gourgoulhon, DARC, Meudon Observatory, Meudon, France, Pawel Haensel, DARC, Meudon Observatory, Meudon, France, Jean-Alain Marck, DARC, Meudon Observatory, Meudon, France
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Gravitational radiation from 3D gravitational stellar core collapse
pp 247-257
- By Jean-Alain Marck, DARC, Meudon Observatory, Meudon, France, Silvano Bonazzola, DARC, Meudon Observatory, Meudon, France
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A vacuum fully relativistic 3D numerical code
pp 258-264
- By C. Bona, Department of Physics, University of the Balearic lies, Palma de Mallorca, Spain, J. Massó, Department of Physics, University of the Balearic lies, Palma de Mallorca, Spain
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Solution of elliptic equations in numerical relativity using multiquadrics
pp 265-280
- By M. R. Dubal, Center for Relativity, University of Texas at Austin, Austin, US, S. R. Oliveira, Center for Relativity, University of Texas at Austin, Austin, US, R. A. Matzner, Center for Relativity, University of Texas at Austin, Austin, US
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Self-gravitating thin discs around rotating black holes
pp 281-291
- By A. Lanza, SISSA, Trieste, Italy
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