The study of rotating non-Kerr black hole

Songbai Chen

Hunan Normal University

Chongqing, 2012. 5

2012年两岸粒子物理与宇宙学研讨会

Outline

1. Introduction

2. Rotating non-Kerr black hole

3. Thin disk around a rotating non-Kerr black hole

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

5. Summary

1. Introduction

1 No-Hair Theorem

Parameters of BH : M, a, Q

General Relativity (GR)

Kerr metric: stationary, axisymmetric, asymptotically flat vacuum spacetime

an event horizon but no closed timelike curves outside of the horizon

a definite proof for is still lacking !

It predicts that all astrophysical black holes are Kerr black holes

Possible approaches: Gravitational-wave

Electromagnetic spectrum

Test to no hair theorem

The existence of black holes

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 !

Suggestion

Several models with parametric deviations from the Kerr metric

(1) 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).

Problem:

(5) Sopuerta & Yunes: a slowly rotating black hole violating parity

Phys. Rev. D 80, 064006 (2009).

(6) Vigeland et al: parametric deviations from the Kerr metric by possessing four integrals of the motion

Phys. Rev. D 83, 104027 (2011)……

outside of the event horizonSingularities or closed timelike loops

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.

For moderately spinning black holes

2. Rotating non-Kerr black hole

T. Johannsen and D. Psaltis

The metric of the rotating non-Kerr black hole

Phys. Rev. D83 124015 (2011)

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

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

3. Thin disk around a rotating non-Kerr black hole

Songbai Chen, Jiliang Jing ， Phys. Lett. B 711, 81-87 (2012)

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

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

SO

Lens

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

Thank you!