The study of rotating non-Kerr black hole

1. 2012年两岸粒子物理与宇宙学研讨会 The study of rotating non-Kerr black hole Songbai Chen Hunan Normal University Chongqing, 2012. 5

2. Outline • Introduction • Rotating non-Kerr black hole • Thin disk around a rotating non-Kerr black hole • Strong gravitational lensing by rotating non-Kerr black hole • Summary

3. 1. Introduction 1 No-Hair Theorem General Relativity (GR) Parameters of BH : M, a, Q Kerr metric: stationary, axisymmetric, asymptotically flat vacuum spacetime an event horizon but no closed timelike curves outside of the horizon

4. It predicts that all astrophysical black holes are Kerr black holes Test to no hair theorem The existence of black holes a definite proof for is still lacking ! Possible approaches: Gravitational-wave Electromagnetic spectrum

5. Suggestion Free parameters: measure potential deviations from the Kerr metric (1) no deviation the compact object is indeed a Kerr black hole. (2) a deviation is measured to be nonzero a) GR: the object cannot be a black hole b) The object is known to possess an event horizon, The no-hair theorem would be falsified !

6. Several models with parametric deviations from the Kerr metric • Ryan et al: compact objects with a general expansion in • Geroch-Hansen multipoles • Phys. Rev. D 52, 5707 (1995); Phys. Rev. D 56, 1845 (1997) (2) Collins et al: Kerr-like metrics with perturbations in the form of Weyl sector bumps Phys. Rev. D 69, 124022 (2004), Phys. Rev. D 81, 024030 (2010). (3) Glampedakis et al: Kerr-like metric deviating from the Kerr metric by an independent quadrupole moment. Class. Quantum Grav. 23, 4167 (2006). (4) Gair : metric with the quadrupole as well as higher order moments. Phys. Rev. D 77, 024035 (2008).

7. (5) Sopuerta & Yunes: a slowly rotating black hole violating parity Phys. Rev. D 80, 064006 (2009). • Vigeland et al: parametric deviations from the Kerr metric • by possessing four integrals of the motion Phys. Rev. D 83, 104027 (2011) …… Problem: Singularities or closed timelike loops outside of the event horizon For moderately spinning black holes an artificial cutoff: motion of particle far away the region with singularity or CTC For rapidly spinning black holes, the artificial cutoff is no longer possible since R_isco becomes comparable to R_H.

8. 2. Rotating non-Kerr black hole T. Johannsen and D. Psaltis Phys. Rev. D83 124015 (2011) The metric of the rotating non-Kerr black hole

11. C.Bambi, L. Modesto, Phys. Lett. B 706:13-18 (2011)

12. Changqing Liu, Songbai Chen, Jiliang Jing, accepted by APJ

15. 3.Thin disk around a rotating non-Kerr black hole Songbai Chen, Jiliang Jing， Phys. Lett. B 711, 81-87 (2012)

20. D.N. Page, K.S. Thorne, Astrophys. J. 191 (1974) 499. K.S. Thorne, Astrophys. J. 191 (1974) 507

26. 4. Strong gravitational lensing by rotating non-Kerr black hole

27. O S Lens

39. 5.Summary 1. Properties of the rotating non-Kerr black hole 2. Thin accrete disk around the rotating non-Kerr black hole 3. Gravitational lensing by the rotating non-Kerr black hole

40. Thank you!