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The perturbation equations

Some Interesting Topics on QNM QNM in time-dependent Black hole backgrounds QNM of Black Strings QNM of colliding Black Holes. The perturbation equations. The perturbation is described by Incoming wave transmitted reflected wave wave.

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The perturbation equations

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  1. Some Interesting Topics on QNMQNM in time-dependent Black hole backgroundsQNM of Black StringsQNM of colliding Black Holes

  2. The perturbation equations • The perturbation is described by Incoming wave transmitted reflected wave wave

  3. Tail phenomenon of a time-dependent case • Hod PRD66,024001(2002) V(x,t) is a time-dependent effective curvatue potential which determines the scattering of the wave by background geometry

  4. QNM in time-dependent background • Vaidya metric • In this coordinate, the scalar perturbation equation is Where x=r+2m ln(r/2m-1) […]=ln(r/2m -1)-1/(1-2m/r)

  5. the charged Vaidya solution the Klein-Gordon equation Solution of Is dependent on initial perturbation? How to simplify the wave equation ?

  6. For the charged Vaidya black hole, horizons r± can be inferred from the null hypersurface condition

  7. (1) the genericalized tortoise coordinate transformation the wave equation

  8. the following variable transformation the wave equation When Q0 invalidate

  9. (2) the genericalized tortoise coordinate transformation the wave equation

  10. q - - 0 0.483 0.481 0.0965 0.0962 0.7 0.532 0.530 0.0985 0.0981 0.999 0.626 0.624 0.0889 0.0886 Limit to RN black hole For the slowest damped QNMs numerical result

  11. linear model event horizon

  12. q=0,l=2, evaluated at r=5, initial perturbation located at r=5

  13. M , the oscillation period becomes longer q=0,l=2, r=5

  14. M , The decay of the oscillation becomes slower q=0,l=2, r=5

  15. The slope of the curve is equal to the are nearly equal for different q

  16. q=0,l=2

  17. QNM in Black Strings

  18. the branes are at y = 0, d. Metric perturbations satisfy Here m is the effective mass on the visible brane of the Kaluza-Klein (KK) mode of the 5D graviton.

  19. Then the boundary conditions in RS gauge are For this zero-mode, the metric perturbations reduce to those of a 4D Schwarzschild metric, as expected.. For m not 0, the boundary conditions lead to a discrete tower of KK mass eigenvalues,

  20. Radial master equations. We generalize the standard 4D analysis to find radial master equations for a reduced set of variables, for all classes of perturbations. The total gravity wave signal at the observer (x = x_obs) is a superposition of the waveforms ψ(τ) associated with the mass eigenvalues m_n. WE present signals associated with the four lowest masses for a marginally stable black string.

  21. Colliding Black Holes

  22. Can QNM tell us EOS • Strange star • Neutron star Stars: fluid making up star carry oscillations, Perturbations exist in metric and matter quantities over all space of star

  23. Thanks!!

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