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

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

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)

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

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

the wave equation (1) the genericalized tortoise coordinate transformation

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

the wave equation (2) the genericalized tortoise coordinate transformation

Limit to RN black hole For the slowest damped QNMs q numerical result

linear model event horizon

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

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

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

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

q=0,l=2

QNM in Black Strings

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.

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,

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.

Colliding Black Holes

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

Thanks!!