About this Journal Submit a Manuscript Table of Contents
Advances in Astronomy
Volume 2012 (2012), Article ID 486750, 9 pages
http://dx.doi.org/10.1155/2012/486750
Review Article

Testing the No-Hair Theorem with Sgr A*

Physics Department, University of Arizona, 1118 E. 4th Street, Tucson, AZ 85721, USA

Received 16 May 2011; Accepted 5 July 2011

Academic Editor: Francesco Shankar

Copyright © 2012 Tim Johannsen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. Israel, “Event horizons in static vacuum space-times,” Physical Review, vol. 164, no. 5, pp. 1776–1779, 1967. View at Publisher · View at Google Scholar · View at Scopus
  2. W. Israel, “Event horizons in static electrovac space-times,” Communications in Mathematical Physics, vol. 8, no. 3, pp. 245–260, 1968. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. B. Carter, “Axisymmetric black hole has only two degrees of freedom,” Physical Review Letters, vol. 26, no. 6, pp. 331–333, 1971. View at Publisher · View at Google Scholar · View at Scopus
  4. S. W. Hawking, “Black holes in general relativity,” Communications in Mathematical Physics, vol. 25, p. 152, 1972.
  5. B. Carter, Black Holes, Gordon and Breach, New York, NY, USA, 1973.
  6. D. C. Robinson, “Uniqueness of the Kerr black hole,” Physical Review Letters, vol. 34, no. 14, pp. 905–906, 1975. View at Publisher · View at Google Scholar · View at Scopus
  7. R. Geroch, “Multipole moments. II. Curved space,” Journal of Mathematical Physics, vol. 11, no. 8, pp. 2580–2588, 1970. View at Scopus
  8. R. O. Hansen, “Multipole moments of stationary spacetimes,” Journal of Mathematical Physics, vol. 15, no. 1, pp. 46–53, 1974. View at Publisher · View at Google Scholar
  9. D. Psaltis, Compact Stellar X-Ray Sources, Cambridge University Press, Cambridge, Mass, USA, 2006.
  10. F. D. Ryan, “Gravitational waves from the inspiral of a compact object into a massive, axisymmetric body with arbitrary multipole moments,” Physical Review D, vol. 52, no. 10, pp. 5707–5718, 1995. View at Publisher · View at Google Scholar
  11. F. D. Ryan, “Accuracy of estimating the multipole moments of a massive body from the gravitational waves of a binary inspiral,” Physical Review D, vol. 56, no. 4, pp. 1845–1855, 1997. View at Publisher · View at Google Scholar
  12. F. D. Ryan, “Scalar waves produced by a scalar charge orbiting a massive body with arbitrary multipole moments,” Physical Review D, vol. 56, no. 12, pp. 7732–7739, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  13. L. Barack and C. Cutler, “LISA capture sources: approximate waveforms, signal-to-noise ratios, and parameter estimation accuracy,” Physical Review D, vol. 69, no. 8, Article ID 082005, 2004. View at Publisher · View at Google Scholar
  14. L. Barack and C. Cutler, “Using LISA extreme-mass-ratio inspiral sources to test off-Kerr deviations in the geometry of massive black holes,” Physical Review D, vol. 75, no. 4, Article ID 042003, 2007. View at Publisher · View at Google Scholar
  15. J. Brink, “Spacetime encodings. I. A spacetime reconstruction problem,” Physical Review D, vol. 78, Article ID 102001, 8 pages, 2008. View at Publisher · View at Google Scholar
  16. C. Li and G. Lovelace, “Generalization of Ryan's theorem: probing tidal coupling with gravitational waves from nearly circular, nearly equatorial, extreme-mass-ratio inspirals,” Physical Review D, vol. 77, Article ID 064022, 10 pages, 2008. View at Publisher · View at Google Scholar
  17. T. A. Apostolatos, G. Lukes-Gerakopoulos, and G. Contopoulos, “How to observe a non-kerr spacetime using gravitational waves,” Physical Review Letters, vol. 103, no. 11, Article ID 111101, 2009. View at Publisher · View at Google Scholar
  18. N. A. Collins and S. A. Hughes, “Towards a formalism for mapping the spacetimes of massive compact objects: bumpy black holes and their orbits,” Physical Review D, vol. 69, Article ID 124022, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  19. S. J. Vigeland and S. A. Hughes, “Spacetime and orbits of bumpy black holes,” Physical Review D, vol. 81, no. 2, Article ID 024030, 2010. View at Publisher · View at Google Scholar
  20. K. Glampedakis and S. Babak, “Mapping spacetimes with LISA: inspiral of a test body in a “quasi-Kerr” field,” Classical and Quantum Gravity, vol. 23, no. 12, article 013, pp. 4167–4188, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. J. R. Gair, C. Li, and I. Mandel, “Observable properties of orbits in exact bumpy spacetimes,” Physical Review D, vol. 77, no. 2, Article ID 024035, 23 pages, 2008. View at Publisher · View at Google Scholar
  22. T. Johannsen and D. Psaltis, “Testing the no-hair theorem with observations in the electromagnetic spectrum. I. Properties of a Quasi-Kerr spacetime,” Astrophysical Journal, vol. 716, no. 1, pp. 187–197, 2010. View at Publisher · View at Google Scholar · View at Scopus
  23. T. Johannsen and D. Psaltis, “Testing the no-hair theorem with observations in the electromagnetic spectrum. II. Black hole images,” Astrophysical Journal, vol. 718, no. 1, p. 446, 2010. View at Publisher · View at Google Scholar
  24. T. Johannsen and D. Psaltis, “Testing the no-hair theorem with observations in the electromagnetic spectrum. III. Quasi-periodic variability,” Astrophysical Journal, vol. 726, no. 1, p. 11, 2011. View at Publisher · View at Google Scholar
  25. T. Johannsen and D. Psaltis, “Testing the no-hair theorem with observations of black holes in the electromagnetic spectrum,” Advances in Space Research, vol. 47, p. 528, 2011.
  26. D. Psaltis and T. Johannsen, “A ray-tracing algorithm for spinning compact object spacetimes with arbitrary quadrupole moments. I. Quasi-kerr black holes,” Astrophysical Journal. In press.
  27. C. Bambi and E. Barausse, “Constraining the quadrupole moment of stellar-mass black hole candidates with the continuum fitting method,” Astrophysical Journal, vol. 731, p. 121, 2011. View at Publisher · View at Google Scholar
  28. C. Bambi, “Constraint on the quadrupole moment of super-massive black hole candidates from the estimate of the mean radiative efficiency of AGN,” Physical Review D, vol. D 83, Article ID 103003, 4 pages, 2011. View at Publisher · View at Google Scholar
  29. C. M. Will, “Testing the general relativistic “no-hair” theorems using the galactic center black hole Sgr A*,” Astrophysical Journal, vol. 674, p. L25, 2008.
  30. D. Merritt, T. Alexander, S. Mikkola, and C. M. Will, “Testing properties of the Galactic center black hole using stellar orbits,” Physical Review D, vol. 81, no. 6, Article ID 062002, 2010. View at Publisher · View at Google Scholar
  31. N. Wex and S. M. Kopeikin, “Frame dragging and other precessional effects in black hole pulsar binaries,” Astrophysical Journal, vol. 514, no. 1, pp. 388–401, 1999. View at Scopus
  32. V. S. Manko and I. D. Novikov, “Generalizations of the Kerr and Kerr-Newman metrics possessing an arbitrary set of mass-multipole moments,” Classical and Quantum Gravity, vol. 9, no. 11, article 013, pp. 2477–2487, 1992. View at Publisher · View at Google Scholar · View at Scopus
  33. S. J. Vigeland, N. Yunes, and L. C. Stein, “Bumpy black holes in alternative theories of gravity,” Physical Review D, vol. 83, Article ID 104027, 16 pages, 2011. View at Publisher · View at Google Scholar
  34. T. Johannsen and D. Psaltis, “Metric for rapidly spinning black holes suitable for strong-field tests of the no-hair theorem,” Physical Review D, vol. 83, Article ID 124015, 16 pages, 2011. View at Publisher · View at Google Scholar
  35. S. A. Hughes, “(Sort of) testing relativity with extreme mass ratio inspirals,” in Proceedings of the AIP Conference, vol. 873, pp. 233–240, November 2006. View at Publisher · View at Google Scholar
  36. D. Psaltis and T. Johannsen, “Sgr A*: the optimal testbed of strong-field gravity,” Journal of Physics, vol. 283, Article ID 102030, 2011. View at Publisher · View at Google Scholar
  37. A. M. Ghez, S. Salim, N. N. Weinberg et al., “Measuring distance and properties of the milky way's central supermassive black hole with stellar orbits,” Astrophysical Journal, vol. 689, no. 2, pp. 1044–1062, 2008. View at Publisher · View at Google Scholar · View at Scopus
  38. S. Gillessen, F. Eisenhauer, S. Trippe, et al., “Monitoring stellar orbits around the massive black hole in the galactic center,” Astrophysical Journal, vol. 692, p. 1075, 2009. View at Publisher · View at Google Scholar
  39. S. S. Doeleman, J. Weintroub, A. E. E. Rogers et al., “Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre,” Nature, vol. 455, no. 7209, pp. 78–80, 2008. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  40. K. Schwarzschild, “Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie,” Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften, vol. 1, pp. 189–196, 1916.
  41. R. P. Kerr, “Gravitational field of a spinning mass as an example of algebraically special metrics,” Physical Review Letters, vol. 11, no. 5, pp. 237–238, 1963. View at Publisher · View at Google Scholar
  42. J. B. Hartle, “Slowly Rotating Relativistic Stars. I. Equations of Structure,” Astrophysical Journal, vol. 150, p. 1005, 1967.
  43. J. B. Hartle and K. S. Thorne, “Slowly Rotating Relativistic Stars. II. Models for Neutron Stars and Supermassive Stars,” Astrophysical Journal, vol. 153, p. 807, 1968.
  44. A. Tomimatsu and H. Sato, “New exact solution for the gravitational field of a spinning mass,” Physical Review Letters, vol. 29, no. 19, pp. 1344–1345, 1972. View at Publisher · View at Google Scholar · View at Scopus
  45. A. Tomimatsu and H. Sato, “New series of exact solutions for gravitational fields of spinning masses,” Progress of Theoretical Physics, vol. 50, no. 1, pp. 95–110, 1973. View at Publisher · View at Google Scholar
  46. H. Stephani, D. Kramer, M. A. H. MacCallum, C. Hoenselaers, and E. Herlt, Exact Solutions of Einstein’s Field Equations, Cambridge University Press, Cambridge, Mass, USA, 2003.
  47. I. Hauser and F. J. Ernst, “Proof of a Geroch conjecture,” Journal of Mathematical Physics, vol. 22, no. 5, pp. 1051–1063, 1981. View at Scopus
  48. C. Hoenselaers, W. Kinnersley, and B. C. Xanthopoulos, “Symmetries of the stationary Einstein–Maxwell equations. VI. Transformations which generate asymptotically flat spacetimes with arbitrary multipole moments,” Journal of Mathematical Physics, vol. 20, no. 8, p. 2530, 1979. View at Publisher · View at Google Scholar
  49. R. Geroch, “A method for generating solutions of Einstein's equations,” Journal of Mathematical Physics, vol. 12, no. 6, pp. 918–924, 1971. View at Scopus
  50. R. Geroch, “A method for generating new solutions of Einstein's equation. II,” Journal of Mathematical Physics, vol. 13, no. 3, pp. 394–404, 1972. View at Scopus
  51. R. Beig and W. Simon, “Proof of a multipole conjecture due to Geroch,” Communications in Mathematical Physics, vol. 78, p. 75, 1980.
  52. R. Beig and W. Simon, “On the multipole expansion for stationary space-times,” Proceedings of the Royal Society A, vol. 376, pp. 333–341, 1981. View at Publisher · View at Google Scholar
  53. N. R. Sibgatullin, Oscillations and Waves in Strong Gravitational and Electromagnetic Fields, Springer, Berlin, Germany, 1991.
  54. V. S. Manko and N. R. Sibgatullin, “Construction of exact solutions of the Einstein-Maxwell equations corresponding to a given behaviour of the Ernst potentials on the symmetry axis,” Classical and Quantum Gravity, vol. 10, no. 7, article 014, pp. 1383–1404, 1993. View at Publisher · View at Google Scholar · View at Scopus
  55. E. M. Butterworth and J. R. Ipser, “On the structure and stability of rapidly rotating fluid bodies in general relativity. I - The numerical method for computing structure and its application to uniformly rotating homogeneous bodies,” Astrophysical Journal, vol. 204, pp. 200–223, 1976. View at Publisher · View at Google Scholar
  56. N. Stergioulas and J. L. Friedman, “Comparing models of rapidly rotating relativistic stars constructed by two numerical methods,” Astrophysical Journal, vol. 444, no. 1, pp. 306–311, 1995. View at Scopus
  57. W. G. Laarakkers and E. Poisson, “Quadrupole moments of rotating neutron stars,” Astrophysical Journal, vol. 512, no. 1, pp. 282–287, 1999. View at Scopus
  58. E. Berti, F. White, A. Maniopoulou, and M. Bruni, “Rotating neutron stars: an invariant comparison of approximate and numerical space-time models,” Monthly Notices of the Royal Astronomical Society, vol. 358, no. 3, pp. 923–938, 2005. View at Publisher · View at Google Scholar · View at Scopus
  59. C. Cadeau, S. M. Morsink, D. Leaky, and S. S. Campbell, “Light curves for rapidly rotating neutron stars,” Astrophysical Journal, vol. 654, no. 1 I, pp. 458–469, 2007. View at Publisher · View at Google Scholar · View at Scopus
  60. C. F. Sopuerta and N. Yunes, “Extreme- and intermediate-mass ratio inspirals in dynamical Chern-Simons modified gravity,” Physical Review D, vol. 80, no. 6, Article ID 064006, 2009. View at Publisher · View at Google Scholar
  61. D.-C. Dai and D. Stojkovic, “Analytic solution for a static black hole in RSII model,” submitted to General Relativity and Quantum Cosmology.
  62. N. Yunes and L. C. Stein, “Effective gravitational wave stress-energy tensor in alternative theories of gravity,” Physical Review D, vol. 83, p. 4002, 2011.
  63. E. Barausse, T. Jacobson, and T. P. Sotiriou, “Black holes in Einstein-aether and Horava-Lifshitz gravity,” General Relativity and Quantum Cosmology, vol. 83, Article ID 124043, 2011. View at Publisher · View at Google Scholar
  64. P. Figueras and T. Wiseman, “Gravity and large black holes in Randall-Sundrum II braneworlds,” submitted to High Energy Physics.
  65. T. Johannsen, et al., in preparation.
  66. A. E. Broderick, V. L. Fish, S. S. Doeleman, and A. Loeb, “Estimating the parameters of sagittarius A*'s accretion flow via millimeter vlbi,” Astrophysical Journal, vol. 697, no. 1, pp. 45–54, 2009. View at Publisher · View at Google Scholar · View at Scopus
  67. A. E. Broderick, V. L. Fish, S. S. Doeleman, and A. Loeb, “Evidence for low black hole spin and physically motivated accretion models from millimeter-VLBI observations of sagittarius A*,” Astrophysical Journal, vol. 735, p. 110, 2011. View at Publisher · View at Google Scholar
  68. J. M. Bardeen, Black Holes, Gordon and Breach, New York, NY, USA, 1973.
  69. H. Falcke, F. Melia, and E. Agol, “Viewing the shadow of the black hole at the Galactic center,” Astrophysical Journal, vol. 528, no. 1, pp. L13–L16, 2000. View at Scopus
  70. A. E. Broderick and A. Loeb, “Imaging bright-spots in the accretion flow near the black hole horizon of Sgr A*,” Monthly Notices of the Royal Astronomical Society, vol. 363, no. 2, pp. 353–362, 2005. View at Publisher · View at Google Scholar · View at Scopus
  71. A. E. Broderick and A. Loeb, “Imaging optically-thin hotspots near the black hole horizon of Sgr A* at radio and near-infrared wavelengths,” Monthly Notices of the Royal Astronomical Society, vol. 367, no. 3, pp. 905–916, 2006. View at Publisher · View at Google Scholar · View at Scopus
  72. V. L. Fish and S. S. Doeleman, IAU Symp. 261, Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis, Cambridge University Press, Cambridge, UK, 2009.
  73. A. E. Broderick and A. Loeb, “Imaging optically-thin hotspots near the black hole horizon of Sgr A* at radio and near-infrared wavelengths,” Monthly Notices of the Royal Astronomical Society, vol. 367, no. 3, pp. 905–916, 2006. View at Publisher · View at Google Scholar · View at Scopus
  74. A. E. Broderick and A. Loeb, “Imaging the black hole silhouette of M87: implications for jet formation and black hole spin,” Astrophysical Journal, vol. 697, no. 2, pp. 1164–1179, 2009. View at Publisher · View at Google Scholar · View at Scopus
  75. R. Takahashi, “Shapes and positions of black hole shadows in accretion disks and spin parameters of black holes,” Astrophysical Journal, vol. 611, no. 2, pp. 996–1004, 2004. View at Publisher · View at Google Scholar · View at Scopus
  76. J. D. Schnittman and J. H. Krolik, “X-ray polarization from accreting black holes: the thermal state,” Astrophysical Journal, vol. 701, no. 2, pp. 1175–1187, 2009. View at Publisher · View at Google Scholar · View at Scopus
  77. J. D. Schnittman and J. H. Krolik, “X-ray polarization from accreting black holes: coronal emission,” Astrophysical Journal, vol. 712, no. 2, pp. 908–924, 2010. View at Publisher · View at Google Scholar · View at Scopus
  78. K. Beckwith and C. Done, “Extreme gravitational lensing near rotating black holes,” Monthly Notices of the Royal Astronomical Society, vol. 359, no. 4, pp. 1217–1228, 2005. View at Publisher · View at Google Scholar · View at Scopus
  79. C. M. Will, Theory and Experiment in Gravitational Physics, Cambridge University Press, Cambridge, Mass, USA, 1993.
  80. L. Sadeghian and C. M. Will, “Testing the black hole no-hair theorem at the galactic center: perturbing effects of stars in the surrounding cluster,” submitted to General Relativity and Quantum Cosmology.
  81. H. Bartko, G. Perrin, W. Brandner et al., “GRAVITY: astrometry on the galactic center and beyond,” New Astronomy Reviews, vol. 53, no. 11-12, pp. 301–306, 2009. View at Publisher · View at Google Scholar · View at Scopus
  82. J.-P. MacQuart, N. Kanekar, D. A. Frail, and S. M. Ransom, “A high-frequency search for pulsars within the central parsec of Sgr A*,” Astrophysical Journal, vol. 715, no. 2, pp. 939–946, 2010. View at Publisher · View at Google Scholar · View at Scopus