Approaches to Numerical Relativity

by Edited by Ray d'Inverno

• ISBN13: 9780521017350
• ISBN10: 0521017351
• Format: Paperback
• Copyright: 2005-07-07
• Publisher: Cambridge University Press

Summary

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).

Table of Contents

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 Jõ

rg 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. Gó

mez 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. Ibá

nez, 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.