1. Some Interesting Topics on QNM QNM in time-dependent Black hole backgrounds QNM of Black Strings QNM 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 How to simplify the wave equation ? Solution of Is dependent on initial perturbation?

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

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

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

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

10. Limit to RN black hole For the slowest damped QNMs q-- 00.4830.4810.09650.0962 0.70.5320.5300.09850.0981 0.9990.6260.6240.08890.0886 numerical result

11. linear model event horizon

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

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

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

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

18. q=0,l=2

20. QNM in Black Strings

21. 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.

22. 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,

23. 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.

25. Colliding Black Holes

26. 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

27. Thanks!!