动态黑洞背景的QNM研究
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v Vaidya metric v 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
(2) the genericalized tortoise coordinate transformation the wave equation
Limit to RN black hole For the slowest damped QNMs
numerical result
q
-
-
0
0.483 0.481 0.0965 0.0962
(1) the genericalized tortoise coordinate transformation the wave equation
the following variable transformation
the wave equation
Q 1
When Q0
invalidate
are nearly equal for different q
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.
the Klein-Gordon equation
Solution of
Is dependent on initial perturbation?
How to simplify the wave equation ?
For the charged Vaidya black hole, horizons r± can be inferred from the nulwk.baidu.com hypersurface condition
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,
The perturbation equations
v The perturbation is described by
transmitted wave
Incoming wave reflected wave
Tail phenomenon of a timedependent case
v Hod PRD66,024001(2002)
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.
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
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.
0.7
0.532 0.530 0.0985 0.0981
0.999 0.626 0.624 0.0889 0.0886
linear model event horizon
q=0,l=2, evaluated at r=5, initial perturbation located at r=5
M , the oscillation period becomes longer
q=0,l=2, r=5
M , The decay of the oscillation becomes slower
q=0,l=2, r=5
The slope of the curve is equal to the
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!!
Where x=r+2m ln(r/2m-1) […]=ln(r/2m -1)-1/(1-2m/r)
the charged Vaidya solution
(2) the genericalized tortoise coordinate transformation the wave equation
Limit to RN black hole For the slowest damped QNMs
numerical result
q
-
-
0
0.483 0.481 0.0965 0.0962
(1) the genericalized tortoise coordinate transformation the wave equation
the following variable transformation
the wave equation
Q 1
When Q0
invalidate
are nearly equal for different q
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.
the Klein-Gordon equation
Solution of
Is dependent on initial perturbation?
How to simplify the wave equation ?
For the charged Vaidya black hole, horizons r± can be inferred from the nulwk.baidu.com hypersurface condition
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,
The perturbation equations
v The perturbation is described by
transmitted wave
Incoming wave reflected wave
Tail phenomenon of a timedependent case
v Hod PRD66,024001(2002)
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.
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
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.
0.7
0.532 0.530 0.0985 0.0981
0.999 0.626 0.624 0.0889 0.0886
linear model event horizon
q=0,l=2, evaluated at r=5, initial perturbation located at r=5
M , the oscillation period becomes longer
q=0,l=2, r=5
M , The decay of the oscillation becomes slower
q=0,l=2, r=5
The slope of the curve is equal to the
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!!