Linearized perturbations of the Kerr spacetime and outer boundary conditions in numerical relativity

Classical and Quantum Gravity

Volumn 28, Issue 1, 2011, Pages

  Deadman, E ^a   Stewart, J M ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78650995730     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/28/1/015003     Document Type: Article

References (35)

1. Abramowitz M and Stegun I A 1964 Handbook of Mathematical Functions (Washington, DC: National Bureau of Standards)
2. Bai S, Cao Z, Gong X, Shang Y, Wu X and Lau y K 2007 Light cone structure near null infinity of the Kerr metric Phys. Rev. D 75 044003
3. Bayliss A and Turkel e 1980 Radiation boundary conditions for wave like equations Commun. Pure Appl. Math. 33 707-25
4. Boyer R H and Lindquist R W 1967 Maximal analytic extension of the Kerr metric J. Math. Phys. 8 265-81
5. Buchman L T and Sarbach O C A 2006 Towards absorbing outer boundaries in general relativity Class. Quantum Grav. 23 6709-44
6. Buchman L T and Sarbach O C A 2007 Improved outer boundaries for Einstein's field equations Class. Quantum Grav. 24 S307-26
7. Chandrasekhar S 1983 The Mathematical Theory of Black Holes (Oxford: Oxford University Press)
8. Chrzanowski P L 1975 Vector potential and metric perturbations of a rotating black hole Phys. Rev. D 11 2042-62
9. Cocke W J 1989 Table for constructing spin coefficients in general relativity Phys. Rev. D 40 650-1
10. Darboux G 1899 Leçons sur la Théorie Générale des Surfaces II (Paris: Gauthier)
11. Deadman e and Stewart J M 2009 Numerical relativity and asymptotic flatness Class. Quantum Grav. 26 065008
12. Geroch R, Held A and Penrose R P 1973 A space-time calculus based on pairs of null directions J. Math. Phys. 14 874-81
13. Givoli D 2004 High-order non-reflecting boundary conditions: a review Wave Motion 39 319-26
14. Givoli D and Neta B 2003 High-order non-reflecting boundary scheme for time-dependent waves J. Comput. Phys. 186 24-46
15. Hagstrom T and Warburton S I 2004 A new auxiliary variable formulation of high-order local radiation boundary conditions Wave Motion 39 327-38
16. Hertz H 1889 Die Kräfte elektrischer Schwingungen, behandelt nach derMaxwell'schen Theorie Ann. Phys. 36 1-22
17. Kegeles L S and Cohen J M 1979 Constructive procedure for perturbations of space-times Phys. Rev. D 19 1641-64
18. Kuipers L 1959 Generalized associated Legendre functions (integral theorems, recurrence formulas) Monatsh. Math. 63 24-31
19. Newman e T and Penrose R P 1962 An approach to gravitational radiation by a method of spin coefficients J. Math. Phys. 3 566-78
20. Newman e T and Unti T W J 1962 Behaviour of asymptotically flat empty spaces J. Math. Phys. 3 891-901
21. Núñez D, Degollado J C and Palanzuela C 2010 One-dimensional description of the gravitational perturbation in a Kerr background Phys. Rev. 81 064011
22. Penrose R 1965 Zero rest-mass fields including gravitation: asymptotic behaviour Proc. R. Soc. A 284 159-203
23. Penrose R and Rindler W 1984 Spinors and Space-Time vol 1 (Cambridge: Cambridge University Press)
24. Regge T and Wheeler J A 1957 Stability of a Schwarzschild singularity Phys. Rev. 108 1063-9
25. Rinne O, Buchman L T, Scheel M A and Pfeiffer H P 2009 Implementation of higher-order absorbing conditions for the Einstein equations Class. Quantum Grav. 26 075009
26. Sachs R and Bergman P G 1958 Structure of particles in linearised gravitation theory Phys. Rev. 112 674-80
27. Sasaki M and Tagoshi H 2003 Analytic black hole perturbation approach to gravitational radiation Living Rev. Rel. 6 www.livingreviews.org/lrr-2003-6
28. Stewart J M 1979 Hertz-Bromwich-Debye-Whittaker-Penrose potentials in general relativity Proc. R. Soc. A 367 527-38
29. Stewart J M 1990 Advanced General Relativity (Cambridge: Cambridge University Press)
30. Stewart J M 2009 The Euler-Poisson-Darboux equation for relativists Gen. Rel. Grav. 41 2045-71
31. Stewart J M and Walker M 1974 Perturbations of space-times in general relativity Proc. R. Soc. A 341 49-74
32. Teukolsky SA 1973 Perturbations of a rotating black hole: I. Fundamental equations for gravitational, electromagnetic, and neutrino-field perturbations Astrophys. J. 185 635-47
33. Virchenko N O and Fedotova I 2001 Generalized Associated Legendre Functions and Their Applications (Singapore: World Scientific)
34. Wald R M 1978 Construction of solutions of gravitational, electromagnetic, or other perturbation equations from solutions of decoupled equations Phys. Rev. Lett. 41 203-6
35. Zerilli F J 1970 Gravitational field of a particle falling in a Schwarzschild geometry analyzed in tensor harmonics Phys. Rev. 2 2141-60