- Access by Xinjiang University
Metric for rapidly spinning black holes suitable for strong-field tests of the no-hair theorem
Phys. Rev. D 83, 124015 – Published 7 June, 2011
DOI: https://doi.org/10.1103/PhysRevD.83.124015
Abstract
According to the no-hair theorem, astrophysical black holes are uniquely characterized by their masses and spins and are described by the Kerr metric. Several parametric deviations from the Kerr metric have been suggested to study observational signatures in both the electromagnetic and gravitational-wave spectra that differ from the expected Kerr signals. Because of the no-hair theorem, however, such spacetimes cannot be regular everywhere outside the event horizons, if they are solutions to the Einstein field equations; they are often characterized by naked singularities or closed timelike loops in the regions of the spacetime that are accessible to an external observer. For observational tests of the no-hair theorem that involve phenomena in the vicinity of the circular photon orbit or the innermost stable circular orbit around a black hole, these pathologies limit the applicability of the metrics only to compact objects that do not spin rapidly. In this paper, we construct a Kerr-like metric which depends on a set of free parameters in addition to its mass and spin and which is regular everywhere outside of the event horizon. We derive expressions for the energy and angular momentum of a particle on a circular equatorial orbit around the black hole and compute the locations of the innermost stable circular orbit and the circular photon orbit. We demonstrate that these orbits change significantly for even moderate deviations from the Kerr metric. The properties of our metric make it an ideally suited spacetime to carry out strong-field tests of the no-hair theorem in the electromagnetic spectrum using the properties of accretion flows around astrophysical black holes of arbitrary spin.
Article Text
References (41)
- W. Israel, Phys. Rev. 164, 1776 (1967); Commun. Math. Phys. 8, 245 (1968); B. Carter, Phys. Rev. Lett. 26, 331 (1971); S. W. Hawking, Commun. Math. Phys. 25, 152 (1972); D. C. Robinson, Phys. Rev. Lett. 34, 905 (1975).
- B. Carter, in Black Holes (Gordon and Breach, New York, 1973).
- R. Geroch, J. Math. Phys. (N.Y.) 11, 2580 (1970); R. O. Hansen, 15, 46 (1974).
- D. Psaltis, in Compact Stellar X-Ray Sources (Cambridge University Press, Cambridge, 2006).
- F. D. Ryan, Phys. Rev. D 52, 5707 (1995); 56, 1845 (1997); 56, 7732 (1997); L. Barack and C. Cutler, 69, 082005 (2004); J. Brink, 78, 102001 (2008); C. Li and G. Lovelace, 77, 064022 (2008); T. A. Apostolatos, G. Lukes-Gerakopoulos, and G. Contopoulos, Phys. Rev. Lett. 103, 111101 (2009).
- L. Barack and C. Cutler, Phys. Rev. D 75, 042003 (2007).
- N. A. Collins and S. A. Hughes, Phys. Rev. D 69, 124022 (2004).
- S. J. Vigeland and S. A. Hughes, Phys. Rev. D 81, 024030 (2010).
- K. Glampedakis and S. Babak, Classical Quantum Gravity 23, 4167 (2006).
- J. R. Gair, C. Li, and I. Mandel, Phys. Rev. D 77, 024035 (2008).
- T. Johannsen and D. Psaltis, Astrophys. J. 716, 187 (2010).
- T. Johannsen and D. Psaltis, Astrophys. J. 718, 446 (2010).
- T. Johannsen and D. Psaltis, Astrophys. J. 726, 11 (2011).
- T. Johannsen and D. Psaltis, Adv. Space Res. 47, 528 (2011); D. Psaltis and T. Johannsen, arXiv:1011.4078; C. Bambi and E. Barausse, Astrophys. J. 731, 121 (2011); C. Bambi, Phys. Rev. D 83, 103003 (2011).
- C. M. Will, Astrophys. J. 674, L25 (2008).
- D. Merritt, T. Alexander, S. Mikkola, and C. M. Will, Phys. Rev. D 81, 062002 (2010).
- N. Wex and S. M. Kopeikin, Astrophys. J. 514, 388 (1999).
- S. A. Hughes, arXiv:1002.2591; D. Psaltis and T. Johannsen, J. Phys. Conf. Ser. 283, 012030 (2011).
- V. S. Manko and I. D. Novikov, Classical Quantum Gravity 9, 2477 (1992).
- S. J. Vigeland, N. Yunes, and L. C. Stein, Phys. Rev. D 83, 104027 (2011).
- S. A. Hughes, AIP Conf. Proc. 873, 233 (2006).
- D. Psaltis, Living Rev. Relativity 11, 9 (2008).
- N. Yunes and F. Pretorius, Phys. Rev. D 79, 084043 (2009).
- C. F. Sopuerta and N. Yunes, Phys. Rev. D 80, 064006 (2009).
- T. Johannsen et al. (unpublished).
- C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, Cambridge, 1993).
- N. Yunes and L. C. Stein, Phys. Rev. D 83, 104002 (2011).
- D.-C. Dai and D. Stojkovic, arXiv:1004.3291.
- P. Pani and V. Cardoso, Phys. Rev. D 79, 084031 (2009).
- E. T. Newman and A. I. Janis, J. Math. Phys. (N.Y.) 6, 915 (1965); S. P. Drake and P. Szekeres, Gen. Relativ. Gravit. 32, 445 (2000).
- E. T. Newman and R. Penrose, J. Math. Phys. (N.Y.) 3, 566 (1962).
- D. Psaltis, J. Phys. Conf. Ser. 189, 012033 (2009).
- R. Beig, Gen. Relativ. Gravit. 12, 439 (1980); R. Beig and W. Simon, Proc. R. Soc. A 376, 333 (1981).
- M. Heusler, Black Hole Uniqueness Theorems (Cambridge University Press, Cambridge, 1996).
- D. Kennefick and N. Ó Murchadha, Classical Quantum Gravity 12, 149 (1995).
- C. M. Will, Living Rev. Relativity 9, 3 (2006).
- J. G. Williams, S. G. Turyshev, and D. H. Boggs, Phys. Rev. Lett. 93, 261101 (2004).
- B. Carter, Phys. Rev. 174, 1559 (1968).
- C. Bambi and K. Freese, Phys. Rev. D 79, 043002 (2009).
- J. M. Bardeen, in Black Holes (Gordon and Breach, New York, 1973).
- M. Shibata and M. Sasaki, Phys. Rev. D 58, 104011 (1998); E. Berti and N. Stergioulas, Mon. Not. R. Astron. Soc. 350, 1416 (2004).