220 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
Superconductivity in Na_xCoO_2yH_2O by charge fluctuation
A new mechanism for superconductivity in the newly discovered Co-based oxide
is proposed by using charge fluctuation. A single-band extended Hubbard model
on the triangular lattice is studied within random phase approximation.
-wave triplet superconductivity is stabilized in the vicinity of
charge-density-wave instability, which is in sharp contrast with the
square-lattice case. The physical origin of the realization of the -wave
triplet state as well as the relevance to experiments are discussed
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
Superconductivity in the Three-Fold Charge-Ordered Metal of the Triangular-Lattice Extended Hubbard Model
The quarter-filling extended Hubbard model on the triangular lattice is
studied to explore pairing instability in the three-fold charge-ordered (CO)
metal. We derive a second-order strong-coupling effective Hamiltonian of doped
carriers into the three-fold CO insulator at electron density of , and
then study the - and -wave superconductivities down to by
using the BCS mean-field approximation. It is found that the triplet -wave
pairing is more stable than the -wave one. We also point out that this
coexisting state of the charge ordering and superconductivity is possible to
have critical temperature .Comment: 4 pages, 7 figure
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
Invariant varieties of periodic points for some higher dimensional integrable maps
By studying various rational integrable maps on with
invariants, we show that periodic points form an invariant variety of dimension
for each period, in contrast to the case of nonintegrable maps in which
they are isolated. We prove the theorem: {\it `If there is an invariant variety
of periodic points of some period, there is no set of isolated periodic points
of other period in the map.'}Comment: 24 page
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
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