1. Y.K.Lau Institute of Appl. Maths, CAS

2. Bondi Sachs Formulation of the Kerr Metric Gravitational Wave Physics of a Kerr Black Hole

3. Joint work with Shan Bai, Zhoujian Cao, Xuefei Gong, Xiaoning Wu IAM, AMSS Yuguang Shi Peking University

4. Numerical Relativity Numerical Simulation Using Large Scale Computation Compute Gravitational Waveform Data Mining Of Experimental Database Relativistic Two body Einstein field equations

5. Angular momentum carries away gravitational radiation Rotating star Gravitational radiation emitted

6. Wavefront Tracking

7. Distortion of wavefront by angular momentum of the source ?

8. Constant time slice Wavefront Two sphere as snapshot of wave front

9. Describes the distortion of the two sphere Eigenvectors Two states of polarization of GW

10. Why Angular Momentum is Tough?

11. Dilemma In need of a pragmatic description at the level of application Lack of good theoretic foundation

12. Kerr Metric of a Prototype of Rotating Source

13. Motivations for Studying Kerr Waveform generated by Rotating Star Extreme Mass Ratio Inspiral Problem (LISA Template) Stability of Black Hole ………..

14. Kerr black hole in Boyer- Lindquist coordinate Dragging effect of star’s angular momentum

15. Construction of Wavefronts Solution of Eikonal Equation

16. Eikonal Equation

17. Asymptotic Solution as r tends to infinity

18. Moving frame adapted to the null hypersurface

23. Conserved Quantity for Gravitational Radiation Field Maxwell Theory: Total Charge Conserved General Relativity: Mass, Momentum, Angular Momentum are not conserved!

24. Newman Penrose Constants Newman-Penrose Constants Absolutely Conserved at Null Infinity

25. NP const defined NP constant---independent on the wavefront that intersects infinity # of NP constants=10

26. NP constants constructed from the multipole expansion of the ingoing radiation field

27. # of NP constants=10 Definition of NP constants reads: u -- time measured at null infinity

28. Newman Penrose Constants …..Another problem is to understand the significance (either mathematical or physical) of a certain curious set of ten exactly conserved asymptotically defined quantities ….. Roger Penrose “Unsolved Problems in General Relativity” in “Seminars in Differential Geometry” edited by S.T.Yau, Princeton Univ. Press, 1982

29. Mathematical Physical Constraint of NP constants to initial data? What role will the NP constants play in the evolution of field eqs? Are there deeper physical meaning for these absolute conserved quantities?

30. NP constant of Kerr spacetime NP constants of Kerr spacetime all vanish!

31. Evolution of Binary Stars No hair theorem means Kerr end state NP constant vanishes for generic initial data set ?

32. NP constants for binary system (Dain and Kroon) What happens from binary to Kerr? Possible ways out of this dilemma?

33. Journey to the Promised Land Numerical Simulation of the angular momentum of gravitational waves generated by tidal distortion of Kerr Understand better the Newman Penrose Constant in Binary Black Hole Spacetime