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

Y.K.Lau Institute of Appl. Maths, CAS. Bondi Sachs Formulation of the Kerr Metric. Gravitational Wave Physics of a Kerr Black Hole. Joint work with Shan Bai, Zhoujian Cao, Xuefei Gong, Xiaoning Wu IAM, AMSS Yuguang Shi Peking University. Numerical Relativity. Relativistic Two body.

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

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  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 WuIAM, AMSSYuguang ShiPeking University

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

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

  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 Two states of polarization of GW Eigenvectors

  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 toinfinity

  18. Moving frame adapted to the null hypersurface

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

  20. Newman Penrose ConstantsNewman-Penrose Constants Absolutely Conserved at Null Infinity

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

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

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

  24. 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

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

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

  27. No hair theorem means Kerr end stateNP constant vanishes for generic initial data set ? Evolution of Binary Stars

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

  29. 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

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