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

Contents Introduction and motivation Gravitational waves Conclusion

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

Recent development of gravitational waves (Picture from LIGO)

Recent development of gravitational waves (Picture from LIGO)

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

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

EMRIs around high spin Kerr black hole  

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

Assumptions  

Spin supplementary condition(SSC)  

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

Orbits  

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.

Gravitational waves Polynomial decay+ exponential decay

Conclusion