| Advances in Astronomy | |
| Testing the No-Hair Theorem with Sgr A* | |
| Review Article | |
| Tim Johannsen1  | |
| [1] Physics Department, University of Arizona, 1118 E. 4th Street, Tucson, AZ 85721, USA, arizona.edu | |
| Others : 1267893 DOI : 10.1155/2012/486750 |
|
| received in 2011-05-16, accepted in 2011-07-05, 发布年份 2011 | |
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【 摘 要 】
The no-hair theorem characterizes the fundamental nature of black holes in general relativity. This theorem can be tested observationally by measuring the mass and spin of a black hole as well as its quadrupole moment, which may deviate from the expected Kerr value. Sgr A*, the supermassive black hole at the center of the Milky Way, is a prime candidate for such tests thanks to its large angular size, high brightness, and rich population of nearby stars. In this paper, I discuss a new theoretical framework for a test of the no-hair theorem that is ideal for imaging observations of Sgr A* with very long baseline interferometry (VLBI). The approach is formulated in terms of a Kerr-like spacetime that depends on a free parameter and is regular everywhere outside of the event horizon. Together with the results from astrometric and timing observations, VLBI imaging of Sgr A* may lead to a secure test of the no-hair theorem.
【 授权许可】
CC BY
Copyright © 2012 Tim Johannsen. 2012
【 预 览 】
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【 参考文献 】
- [1]W. Israel. (1967). Event horizons in static vacuum space-times. Physical Review.164(5):1776-1779. DOI: 10.1103/PhysRev.164.1776.
- [2]W. Israel. (1968). Event horizons in static electrovac space-times. Communications in Mathematical Physics.8(3):245-260. DOI: 10.1103/PhysRev.164.1776.
- [3]B. Carter. (1971). Axisymmetric black hole has only two degrees of freedom. Physical Review Letters.26(6):331-333. DOI: 10.1103/PhysRev.164.1776.
- [4]S. W. Hawking. (1972). Black holes in general relativity. Communications in Mathematical Physics.25:152. DOI: 10.1103/PhysRev.164.1776.
- [5]B. Carter. (1973). Black Holes. DOI: 10.1103/PhysRev.164.1776.
- [6]D. C. Robinson. (1975). Uniqueness of the Kerr black hole. Physical Review Letters.34(14):905-906. DOI: 10.1103/PhysRev.164.1776.
- [7]R. Geroch. (1970). Multipole moments. II. Curved space. Journal of Mathematical Physics.11(8):2580-2588. DOI: 10.1103/PhysRev.164.1776.
- [8]R. O. Hansen. (1974). Multipole moments of stationary spacetimes. Journal of Mathematical Physics.15(1):46-53. DOI: 10.1103/PhysRev.164.1776.
- [9]D. Psaltis. (2006). Compact Stellar X-Ray Sources. DOI: 10.1103/PhysRev.164.1776.
- [10]F. D. Ryan. (1995). Gravitational waves from the inspiral of a compact object into a massive, axisymmetric body with arbitrary multipole moments. Physical Review D.52(10):5707-5718. DOI: 10.1103/PhysRev.164.1776.
- [11]F. D. Ryan. (1997). Accuracy of estimating the multipole moments of a massive body from the gravitational waves of a binary inspiral. Physical Review D.56(4):1845-1855. DOI: 10.1103/PhysRev.164.1776.
- [12]F. D. Ryan. (1997). Scalar waves produced by a scalar charge orbiting a massive body with arbitrary multipole moments. Physical Review D.56(12):7732-7739. DOI: 10.1103/PhysRev.164.1776.
- [13]L. Barack, C. Cutler. (2004). LISA capture sources: approximate waveforms, signal-to-noise ratios, and parameter estimation accuracy. Physical Review D.69(8). DOI: 10.1103/PhysRev.164.1776.
- [14]L. Barack, C. Cutler. (2007). Using LISA extreme-mass-ratio inspiral sources to test off-Kerr deviations in the geometry of massive black holes. Physical Review D.75(4). DOI: 10.1103/PhysRev.164.1776.
- [15]J. Brink. (2008). Spacetime encodings. I. A spacetime reconstruction problem. Physical Review D.78-8. DOI: 10.1103/PhysRev.164.1776.
- [16]C. Li, G. Lovelace. (2008). Generalization of Ryan's theorem: probing tidal coupling with gravitational waves from nearly circular, nearly equatorial, extreme-mass-ratio inspirals. Physical Review D.77-10. DOI: 10.1103/PhysRev.164.1776.
- [17]T. A. Apostolatos, G. Lukes-Gerakopoulos, G. Contopoulos. (2009). How to observe a non-kerr spacetime using gravitational waves. Physical Review Letters.103(11). DOI: 10.1103/PhysRev.164.1776.
- [18]N. A. Collins, S. A. Hughes. (2004). Towards a formalism for mapping the spacetimes of massive compact objects: bumpy black holes and their orbits. Physical Review D.69. DOI: 10.1103/PhysRev.164.1776.
- [19]S. J. Vigeland, S. A. Hughes. (2010). Spacetime and orbits of bumpy black holes. Physical Review D.81(2). DOI: 10.1103/PhysRev.164.1776.
- [20]K. Glampedakis, S. Babak. (2006). Mapping spacetimes with LISA: inspiral of a test body in a “quasi-Kerr” field. Classical and Quantum Gravity.23(12, article 013):4167-4188. DOI: 10.1103/PhysRev.164.1776.
- [21]J. R. Gair, C. Li, I. Mandel. (2008). Observable properties of orbits in exact bumpy spacetimes. Physical Review D.77(2)-23. DOI: 10.1103/PhysRev.164.1776.
- [22]T. Johannsen, D. Psaltis. (2010). Testing the no-hair theorem with observations in the electromagnetic spectrum. I. Properties of a Quasi-Kerr spacetime. Astrophysical Journal.716(1):187-197. DOI: 10.1103/PhysRev.164.1776.
- [23]T. Johannsen, D. Psaltis. (2010). Testing the no-hair theorem with observations in the electromagnetic spectrum. II. Black hole images. Astrophysical Journal.718(1):446. DOI: 10.1103/PhysRev.164.1776.
- [24]T. Johannsen, D. Psaltis. (2011). Testing the no-hair theorem with observations in the electromagnetic spectrum. III. Quasi-periodic variability. Astrophysical Journal.726(1):11. DOI: 10.1103/PhysRev.164.1776.
- [25]T. Johannsen, D. Psaltis. (2011). Testing the no-hair theorem with observations of black holes in the electromagnetic spectrum. Advances in Space Research.47:528. DOI: 10.1103/PhysRev.164.1776.
- [26]D. Psaltis, T. Johannsen. A ray-tracing algorithm for spinning compact object spacetimes with arbitrary quadrupole moments. I. Quasi-kerr black holes. . DOI: 10.1103/PhysRev.164.1776.
- [27]C. Bambi, E. Barausse. (2011). Constraining the quadrupole moment of stellar-mass black hole candidates with the continuum fitting method. Astrophysical Journal.731:121. DOI: 10.1103/PhysRev.164.1776.
- [28]C. Bambi. (2011). Constraint on the quadrupole moment of super-massive black hole candidates from the estimate of the mean radiative efficiency of AGN. Physical Review D.D 83-4. DOI: 10.1103/PhysRev.164.1776.
- [29]C. M. Will. (2008). Testing the general relativistic “no-hair” theorems using the galactic center black hole Sgr A*. Astrophysical Journal.674:L25. DOI: 10.1103/PhysRev.164.1776.
- [30]D. Merritt, T. Alexander, S. Mikkola, C. M. Will. et al.(2010). Testing properties of the Galactic center black hole using stellar orbits. Physical Review D.81(6). DOI: 10.1103/PhysRev.164.1776.
- [31]N. Wex, S. M. Kopeikin. (1999). Frame dragging and other precessional effects in black hole pulsar binaries. Astrophysical Journal.514(1):388-401. DOI: 10.1103/PhysRev.164.1776.
- [32]V. S. Manko, I. D. Novikov. (1992). Generalizations of the Kerr and Kerr-Newman metrics possessing an arbitrary set of mass-multipole moments. Classical and Quantum Gravity.9(11, article 013):2477-2487. DOI: 10.1103/PhysRev.164.1776.
- [33]S. J. Vigeland, N. Yunes, L. C. Stein. (2011). Bumpy black holes in alternative theories of gravity. Physical Review D.83-16. DOI: 10.1103/PhysRev.164.1776.
- [34]T. Johannsen, D. Psaltis. (2011). Metric for rapidly spinning black holes suitable for strong-field tests of the no-hair theorem. Physical Review D.83-16. DOI: 10.1103/PhysRev.164.1776.
- [35]S. A. Hughes. (Sort of) testing relativity with extreme mass ratio inspirals. .873:233-240. DOI: 10.1103/PhysRev.164.1776.
- [36]D. Psaltis, T. Johannsen. (2011). Sgr A*: the optimal testbed of strong-field gravity. Journal of Physics.283. DOI: 10.1103/PhysRev.164.1776.
- [37]A. M. Ghez, S. Salim, N. N. Weinberg, J. R. Lu. et al.(2008). Measuring distance and properties of the milky way's central supermassive black hole with stellar orbits. Astrophysical Journal.689(2):1044-1062. DOI: 10.1103/PhysRev.164.1776.
- [38]S. Gillessen, F. Eisenhauer, S. Trippe. (2009). Monitoring stellar orbits around the massive black hole in the galactic center. Astrophysical Journal.692:1075. DOI: 10.1103/PhysRev.164.1776.
- [39]S. S. Doeleman, J. Weintroub, A. E. E. Rogers, R. Plambeck. et al.(2008). Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre. Nature.455(7209):78-80. DOI: 10.1103/PhysRev.164.1776.
- [40]K. Schwarzschild. (1916). Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften.1:189-196. DOI: 10.1103/PhysRev.164.1776.
- [41]R. P. Kerr. (1963). Gravitational field of a spinning mass as an example of algebraically special metrics. Physical Review Letters.11(5):237-238. DOI: 10.1103/PhysRev.164.1776.
- [42]J. B. Hartle. (1967). Slowly Rotating Relativistic Stars. I. Equations of Structure. Astrophysical Journal.150:1005. DOI: 10.1103/PhysRev.164.1776.
- [43]J. B. Hartle, K. S. Thorne. (1968). Slowly Rotating Relativistic Stars. II. Models for Neutron Stars and Supermassive Stars. Astrophysical Journal.153:807. DOI: 10.1103/PhysRev.164.1776.
- [44]A. Tomimatsu, H. Sato. (1972). New exact solution for the gravitational field of a spinning mass. Physical Review Letters.29(19):1344-1345. DOI: 10.1103/PhysRev.164.1776.
- [45]A. Tomimatsu, H. Sato. (1973). New series of exact solutions for gravitational fields of spinning masses. Progress of Theoretical Physics.50(1):95-110. DOI: 10.1103/PhysRev.164.1776.
- [46]H. Stephani, D. Kramer, M. A. H. MacCallum, C. Hoenselaers. et al.(2003). Exact Solutions of Einstein’s Field Equations. DOI: 10.1103/PhysRev.164.1776.
- [47]I. Hauser, F. J. Ernst. (1981). Proof of a Geroch conjecture. Journal of Mathematical Physics.22(5):1051-1063. DOI: 10.1103/PhysRev.164.1776.
- [48]C. Hoenselaers, W. Kinnersley, B. C. Xanthopoulos. (1979). Symmetries of the stationary Einstein–Maxwell equations. VI. Transformations which generate asymptotically flat spacetimes with arbitrary multipole moments. Journal of Mathematical Physics.20(8):2530. DOI: 10.1103/PhysRev.164.1776.
- [49]R. Geroch. (1971). A method for generating solutions of Einstein's equations. Journal of Mathematical Physics.12(6):918-924. DOI: 10.1103/PhysRev.164.1776.
- [50]R. Geroch. (1972). A method for generating new solutions of Einstein's equation. II. Journal of Mathematical Physics.13(3):394-404. DOI: 10.1103/PhysRev.164.1776.
- [51]R. Beig, W. Simon. (1980). Proof of a multipole conjecture due to Geroch. Communications in Mathematical Physics.78:75. DOI: 10.1103/PhysRev.164.1776.
- [52]R. Beig, W. Simon. (1981). On the multipole expansion for stationary space-times. Proceedings of the Royal Society A.376:333-341. DOI: 10.1103/PhysRev.164.1776.
- [53]N. R. Sibgatullin. (1991). Oscillations and Waves in Strong Gravitational and Electromagnetic Fields. DOI: 10.1103/PhysRev.164.1776.
- [54]V. S. Manko, N. R. Sibgatullin. (1993). 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.10(7, article 014):1383-1404. DOI: 10.1103/PhysRev.164.1776.
- [55]E. M. Butterworth, J. R. Ipser. (1976). 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.204:200-223. DOI: 10.1103/PhysRev.164.1776.
- [56]N. Stergioulas, J. L. Friedman. (1995). Comparing models of rapidly rotating relativistic stars constructed by two numerical methods. Astrophysical Journal.444(1):306-311. DOI: 10.1103/PhysRev.164.1776.
- [57]W. G. Laarakkers, E. Poisson. (1999). Quadrupole moments of rotating neutron stars. Astrophysical Journal.512(1):282-287. DOI: 10.1103/PhysRev.164.1776.
- [58]E. Berti, F. White, A. Maniopoulou, M. Bruni. et al.(2005). Rotating neutron stars: an invariant comparison of approximate and numerical space-time models. Monthly Notices of the Royal Astronomical Society.358(3):923-938. DOI: 10.1103/PhysRev.164.1776.
- [59]C. Cadeau, S. M. Morsink, D. Leaky, S. S. Campbell. et al.(2007). Light curves for rapidly rotating neutron stars. Astrophysical Journal.654(1 I):458-469. DOI: 10.1103/PhysRev.164.1776.
- [60]C. F. Sopuerta, N. Yunes. (2009). Extreme- and intermediate-mass ratio inspirals in dynamical Chern-Simons modified gravity. Physical Review D.80(6). DOI: 10.1103/PhysRev.164.1776.
- [61]D.-C. Dai, D. Stojkovic. Analytic solution for a static black hole in RSII model. . DOI: 10.1103/PhysRev.164.1776.
- [62]N. Yunes, L. C. Stein. (2011). Effective gravitational wave stress-energy tensor in alternative theories of gravity. Physical Review D.83:4002. DOI: 10.1103/PhysRev.164.1776.
- [63]E. Barausse, T. Jacobson, T. P. Sotiriou. (2011). Black holes in Einstein-aether and Horava-Lifshitz gravity. General Relativity and Quantum Cosmology.83. DOI: 10.1103/PhysRev.164.1776.
- [64]P. Figueras, T. Wiseman. Gravity and large black holes in Randall-Sundrum II braneworlds. . DOI: 10.1103/PhysRev.164.1776.
- [65]T. Johannsen. . DOI: 10.1103/PhysRev.164.1776.
- [66]A. E. Broderick, V. L. Fish, S. S. Doeleman, A. Loeb. et al.(2009). Estimating the parameters of sagittarius A*'s accretion flow via millimeter vlbi. Astrophysical Journal.697(1):45-54. DOI: 10.1103/PhysRev.164.1776.
- [67]A. E. Broderick, V. L. Fish, S. S. Doeleman, A. Loeb. et al.(2011). Evidence for low black hole spin and physically motivated accretion models from millimeter-VLBI observations of sagittarius A*. Astrophysical Journal.735:110. DOI: 10.1103/PhysRev.164.1776.
- [68]J. M. Bardeen. (1973). Black Holes. DOI: 10.1103/PhysRev.164.1776.
- [69]H. Falcke, F. Melia, E. Agol. (2000). Viewing the shadow of the black hole at the Galactic center. Astrophysical Journal.528(1):L13-L16. DOI: 10.1103/PhysRev.164.1776.
- [70]A. E. Broderick, A. Loeb. (2005). Imaging bright-spots in the accretion flow near the black hole horizon of Sgr A*. Monthly Notices of the Royal Astronomical Society.363(2):353-362. DOI: 10.1103/PhysRev.164.1776.
- [71]A. E. Broderick, A. Loeb. (2006). 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.367(3):905-916. DOI: 10.1103/PhysRev.164.1776.
- [72]V. L. Fish, S. S. Doeleman. (2009). IAU Symp. 261, Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis. DOI: 10.1103/PhysRev.164.1776.
- [73]A. E. Broderick, A. Loeb. (2006). 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.367(3):905-916. DOI: 10.1103/PhysRev.164.1776.
- [74]A. E. Broderick, A. Loeb. (2009). Imaging the black hole silhouette of M87: implications for jet formation and black hole spin. Astrophysical Journal.697(2):1164-1179. DOI: 10.1103/PhysRev.164.1776.
- [75]R. Takahashi. (2004). Shapes and positions of black hole shadows in accretion disks and spin parameters of black holes. Astrophysical Journal.611(2):996-1004. DOI: 10.1103/PhysRev.164.1776.
- [76]J. D. Schnittman, J. H. Krolik. (2009). X-ray polarization from accreting black holes: the thermal state. Astrophysical Journal.701(2):1175-1187. DOI: 10.1103/PhysRev.164.1776.
- [77]J. D. Schnittman, J. H. Krolik. (2010). X-ray polarization from accreting black holes: coronal emission. Astrophysical Journal.712(2):908-924. DOI: 10.1103/PhysRev.164.1776.
- [78]K. Beckwith, C. Done. (2005). Extreme gravitational lensing near rotating black holes. Monthly Notices of the Royal Astronomical Society.359(4):1217-1228. DOI: 10.1103/PhysRev.164.1776.
- [79]C. M. Will. (1993). Theory and Experiment in Gravitational Physics. DOI: 10.1103/PhysRev.164.1776.
- [80]L. Sadeghian, C. M. Will. Testing the black hole no-hair theorem at the galactic center: perturbing effects of stars in the surrounding cluster. . DOI: 10.1103/PhysRev.164.1776.
- [81]H. Bartko, G. Perrin, W. Brandner, C. Straubmeier. et al.(2009). GRAVITY: astrometry on the galactic center and beyond. New Astronomy Reviews.53(11-12):301-306. DOI: 10.1103/PhysRev.164.1776.
- [82]J.-P. MacQuart, N. Kanekar, D. A. Frail, S. M. Ransom. et al.(2010). A high-frequency search for pulsars within the central parsec of Sgr A*. Astrophysical Journal.715(2):939-946. DOI: 10.1103/PhysRev.164.1776.
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