1. Spin and Quadrupole corrections to IMRIs
Asia Pacific Center for Theoretical Physics
Jiang Long (龙江)
Dec 28, 2018, Shandong

2. Contents
Introduction and motivation Gravitational waves Conclusion

3. Introduction and motivation
Breakthrough from theoretical physics: holography
Development from experimental physics: discovery of gravitational waves
Question: overlap region?
Near horizon region of near extreme Kerr black hole: constraints from conformal symmetry
Merger of binary black hole

4. Recent development of gravitational waves (Picture from LIGO)

5. Recent development of gravitational waves (Picture from LIGO)

6. Binary black hole Binary system: key to gravitational wave observation
Newton gravity: exactly sovable
Einstein gravity: no general analytic solution be found

7. Extreme mass ratio inspirals (EMRIs) and Intermediate mass ratio inspirals(IMRIs)

8. EMRIs around high spin Kerr black hole

9. Three steps to fall into high spin Kerr BH
Question: Orbits and Gravitational waves ?
Focus on the final stage of the merger
Conformal symmetry dominates the process
Analytic results
J.Bardeen, W.Press,S.Teakolsky, 1972

10. Assumptions

11. Spin supplementary condition(SSC)

12. Quadrupole model Up to quadruple correction
Up to linear term of Riemann tensor and quadratic term of spin
The gravito-electric and gravito-magnetic tidal force is higher order

13. Orbits

14. Gravitational waves
Leading order: solve linear Teukolsky equation in Newman-Penrose formalism
Gravitational waveform (circular orbits)
Frequency: expanded in terms of spin
Leading order: determined by orbital angular momentum
Subsubleading order: corrected by spin, vanishes for BHs.

15. Gravitational waves
Polynomial decay+ exponential decay

16. Conclusion