256 research outputs found
Asymptotic quasinormal modes of Reissner-Nordstr\"om and Kerr black holes
According to a recent proposal, the so-called Barbero-Immirzi parameter of
Loop Quantum Gravity can be fixed, using Bohr's correspondence principle, from
a knowledge of highly-damped black hole oscillation frequencies. Such
frequencies are rather difficult to compute, even for Schwarzschild black
holes. However, it is now quite likely that they may provide a fundamental link
between classical general relativity and quantum theories of gravity. Here we
carry out the first numerical computation of very highly damped quasinormal
modes (QNM's) for charged and rotating black holes. In the Reissner-Nordstr\"om
case QNM frequencies and damping times show an oscillatory behaviour as a
function of charge. The oscillations become faster as the mode order increases.
At fixed mode order, QNM's describe spirals in the complex plane as the charge
is increased, tending towards a well defined limit as the hole becomes
extremal. Kerr QNM's have a similar oscillatory behaviour when the angular
index . For the real part of Kerr QNM frequencies tends to
, being the angular velocity of the black hole horizon, while
the asymptotic spacing of the imaginary parts is given by .Comment: 13 pages, 7 figures. Added result on the asymptotic spacing of the
imaginary part, minor typos correcte
One-Loop Supergravity Corrections to the Black Hole Entropy and Residual Supersymmetry
We study the one-loop corrections to the effective on-shell action of N=2
supergravity in the background of the Reissner-Nordstrom black hole. In the
extreme case the contributions from graviton, gravitino and photon to the
one-loop corrections to the entropy are shown to cancel. This gives the first
explicit example of the supersymmetric non-renormalization theorem for the
on-shell action (entropy) for BPS configurations which admit Killing spinors.
We display the residual supersymmetry of the perturbations of a general
supersymmetric theory in a bosonic BPS background.Comment: 13 Pages, LaTe
A detailed study of quasinormal frequencies of the Kerr black hole
We compute the quasinormal frequencies of the Kerr black hole using a
continued fraction method. The continued fraction method first proposed by
Leaver is still the only known method stable and accurate for the numerical
determination of the Kerr quasinormal frequencies. We numerically obtain not
only the slowly but also the rapidly damped quasinormal frequencies and analyze
the peculiar behavior of these frequencies at the Kerr limit. We also calculate
the algebraically special frequency first identified by Chandrasekhar and
confirm that it coincide with the quasinormal frequency only at the
Schwarzschild limit.Comment: REVTEX, 15 pages, 7 eps figure
On scattering off the extreme Reissner-Nordstr\"om black hole in N=2 supergravity
The scattering amplitudes for the perturbed fields of the N=2 supergravity
about the extreme Reissner-Nordstr\"om black hole is examined. Owing to the
fact that the extreme hole is a BPS state of the theory and preserves an
unbroken global supersymmetry(N=1), the scattering amplitudes of the component
fields should be related to each other. In this paper, we derive the formula of
the transformation of the scattering amplitudes.Comment: 9 pages, revtex, no figures, a few typing errors correcte
Gravitational quasinormal radiation of higher-dimensional black holes
We find the gravitational resonance (quasinormal) modes of the higher
dimensional Schwarzschild and Reissner-Nordstrem black holes. The effect on the
quasinormal behavior due to the presence of the term is investigated.
The QN spectrum is totally different for different signs of . In more
than four dimensions there excited three types of gravitational modes: scalar,
vector, and tensor. They produce three different quasinormal spectra, thus the
isospectrality between scalar and vector perturbations, which takes place for
D=4 Schwarzschild and Schwarzschild-de-Sitter black holes, is broken in higher
dimensions. That is the scalar-type gravitational perturbations, connected with
deformations of the black hole horizon, which damp most slowly and therefore
dominate during late time of the black hole ringing.Comment: 13 pages, 2 figures, several references are adde
Kerr black hole quasinormal frequencies
Black-hole quasinormal modes (QNM) have been the subject of much recent
attention, with the hope that these oscillation frequencies may shed some light
on the elusive theory of quantum gravity. We compare numerical results for the
QNM spectrum of the (rotating) Kerr black hole with an {\it exact} formula
Re, which is based on Bohr's correspondence
principle. We find a close agreement between the two. Possible implications of
this result to the area spectrum of quantum black holes are discussed.Comment: 3 pages, 2 figure
Highly damped quasinormal modes of Kerr black holes
Motivated by recent suggestions that highly damped black hole quasinormal
modes (QNM's) may provide a link between classical general relativity and
quantum gravity, we present an extensive computation of highly damped QNM's of
Kerr black holes. We do not limit our attention to gravitational modes, thus
filling some gaps in the existing literature. The frequency of gravitational
modes with l=m=2 tends to \omega_R=2 \Omega, \Omega being the angular velocity
of the black hole horizon. If Hod's conjecture is valid, this asymptotic
behaviour is related to reversible black hole transformations. Other highly
damped modes with m>0 that we computed do not show a similar behaviour. The
real part of modes with l=2 and m<0 seems to asymptotically approach a constant
value \omega_R\simeq -m\varpi, \varpi\simeq 0.12 being (almost) independent of
a. For any perturbing field, trajectories in the complex plane of QNM's with
m=0 show a spiralling behaviour, similar to the one observed for
Reissner-Nordstrom (RN) black holes. Finally, for any perturbing field, the
asymptotic separation in the imaginary part of consecutive modes with m>0 is
given by 2\pi T_H (T_H being the black hole temperature). We conjecture that
for all values of l and m>0 there is an infinity of modes tending to the
critical frequency for superradiance (\omega_R=m) in the extremal limit.
Finally, we study in some detail modes branching off the so--called
``algebraically special frequency'' of Schwarzschild black holes. For the first
time we find numerically that QNM multiplets emerge from the algebraically
special Schwarzschild modes, confirming a recent speculation.Comment: 19 pages, 11 figures. Minor typos corrected. Updated references to
take into account some recent development
The scalar perturbation of the higher-dimensional rotating black holes
The massless scalar field in the higher-dimensional Kerr black hole (Myers-
Perry solution with a single rotation axis) has been investigated. It has been
shown that the field equation is separable in arbitrary dimensions. The
quasi-normal modes of the scalar field have been searched in five dimensions
using the continued fraction method. The numerical result shows the evidence
for the stability of the scalar perturbation of the five-dimensional Kerr black
holes. The time scale of the resonant oscillation in the rapidly rotating black
hole, in which case the horizon radius becomes small, is characterized by
(black hole mass)^{1/2}(Planck mass)^{-3/2} rather than the light-crossing time
of the horizon.Comment: 16 pages, 7 figures, revised versio
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