Approaches to Numerical Relativity

Contributions by leading workers in the field given at an international workshop on Numerical Relativity held in Southampton in December 1991.

Ray d'Inverno (Edited by)

9780521017350, Cambridge University Press

Paperback, published 7 July 2005

400 pages, 108 b/w illus. 7 tables
24.5 x 17.1 x 2.3 cm, 0.64 kg

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).

Introduction Ray d'Inverno
Preface C. J. S. Clarke
Part I. Theoretical Approaches: 1. Numerical relativity on a transputer array Ray d'Inverno
2. Some aspects of the characteristic initial value problem in numerical relativity Nigel Bishop
3. The characteristic initial value problem in general relativity J. M. Stewart
4. Algebraic approachs to the characteristic initial value problem in general relativity Jõrg Frauendiener
5. On hyperboidal hypersurfaces Helmut Friedrich
6. The initial value problem on null cones J. A. Vickers
7. Introduction to dual-null dynamics S. A. Hayward
8. On colliding plane wave space-times J. B. Griffiths
9. Boundary conditions for the momentum constraint Niall O Murchadha
10. On the choice of matter model in general relativity A. D. Rendall
11. A mathematical approach to numerical relativity J. W. Barrett
12. Making sense of the effects of rotation in general relativity J. C. Miller
13. Stability of charged boson stars and catastrophe theory Franz E. Schunck, Fjodor V. Kusmartsev and Eckehard W. Mielke
Part II. Practical Approaches: 14. Numerical asymptotics R. Gómez and J. Winicour
15. Instabilities in rapidly rotating polytropes Scott C. Smith and Joan M. Centrella
16. Gravitational radiation from coalescing binary neutron stars Ken-Ichi Oohara and Takashi Nakamura
17. 'Critical' behaviour in massless scalar field collapse M. W. Choptuik
18. Goudunov-type methods applied to general relativistic gravitational collapse José Ma. Ibánez, José Ma. Martí, Juan A. Miralles and J. V. Romero
19. Astrophysical sources of gravitational waves and neutrinos Silvano Bonazzola, Eric Gourgoulhon, Pawel Haensel and Jean-Alain Marck
20. Gravitational radiation from triaxial core collapse Jean-Alain Marck and Silvano Bonazzola
21. A vacuum fully relativistic 3D numerical code C. Bona and J. Massó
22. Solution of elliptic equations in numerical relativity using multiquadrics M. R. Dubal, S. R. Oliveira and R. A. Matzner
23. Self-gravitating thin disks around rotating black holes A. Lanza
24. An ADI and causal reconnection Gabrielle D. Allen and Bernard F. Schutz
25. Time-symmetric ADI and causal reconnection Miguel Alcubierre and Bernard F. Schutz
26. The numerical study of topological defects E. P. S. Shellard
27. Computations of bubble growth during the cosmological quark-hadron transition J. C. Miller and O. Pantano
28. Initial data of axisymmetric gravitational waves with a cosmological constant Ken-Ichi Nakao, Kei-Ichi Maeda, Takashi Nakamura and Ken-Ichi Oohara.

Subject Areas: Relativity physics [PHR]