15 research outputs found
Numerical analysis of quasinormal modes in nearly extremal Schwarzschild-de Sitter spacetimes
We calculate high-order quasinormal modes with large imaginary frequencies
for electromagnetic and gravitational perturbations in nearly extremal
Schwarzschild-de Sitter spacetimes. Our results show that for low-order
quasinormal modes, the analytical approximation formula in the extremal limit
derived by Cardoso and Lemos is a quite good approximation for the quasinormal
frequencies as long as the model parameter is small enough, where
and are the black hole horizon radius and the surface gravity,
respectively. For high-order quasinormal modes, to which corresponds
quasinormal frequencies with large imaginary parts, on the other hand, this
formula becomes inaccurate even for small values of . We also find
that the real parts of the quasinormal frequencies have oscillating behaviors
in the limit of highly damped modes, which are similar to those observed in the
case of a Reissner-Nordstr{\" o}m black hole. The amplitude of oscillating
as a function of approaches a non-zero
constant value for gravitational perturbations and zero for electromagnetic
perturbations in the limit of highly damped modes, where denotes the
quasinormal frequency. This means that for gravitational perturbations, the
real part of quasinormal modes of the nearly extremal Schwarzschild-de Sitter
spacetime appears not to approach any constant value in the limit of highly
damped modes. On the other hand, for electromagnetic perturbations, the real
part of frequency seems to go to zero in the limit.Comment: 9 pages, 7 figures, to appear in Physical Review
Late-Time Tails of Wave Propagation in Higher Dimensional Spacetimes
We study the late-time tails appearing in the propagation of massless fields
(scalar, electromagnetic and gravitational) in the vicinities of a
D-dimensional Schwarzschild black hole. We find that at late times the fields
always exhibit a power-law falloff, but the power-law is highly sensitive to
the dimensionality of the spacetime. Accordingly, for odd D>3 we find that the
field behaves as t^[-(2l+D-2)] at late times, where l is the angular index
determining the angular dependence of the field. This behavior is entirely due
to D being odd, it does not depend on the presence of a black hole in the
spacetime. Indeed this tails is already present in the flat space Green's
function. On the other hand, for even D>4 the field decays as t^[-(2l+3D-8)],
and this time there is no contribution from the flat background. This power-law
is entirely due to the presence of the black hole. The D=4 case is special and
exhibits, as is well known, the t^[-(2l+3)] behavior. In the extra dimensional
scenario for our Universe, our results are strictly correct if the extra
dimensions are infinite, but also give a good description of the late time
behaviour of any field if the large extra dimensions are large enough.Comment: 6 pages, 3 figures, RevTeX4. Version to appear in Rapid
Communications of Physical Review
Highly Damped Quasinormal Modes of Kerr Black Holes: A Complete Numerical Investigation
We compute for the first time very highly damped quasinormal modes of the
(rotating) Kerr black hole. Our numerical technique is based on a decoupling of
the radial and angular equations, performed using a large-frequency expansion
for the angular separation constant_{s}A_{l m}. This allows us to go much
further in overtone number than ever before. We find that the real part of the
quasinormal frequencies approaches a non-zero constant value which does not
depend on the spin s of the perturbing field and on the angular index l:
\omega_R=m\varpi(a). We numerically compute \varpi(a). Leading-order
corrections to the asymptotic frequency are likely to be of order 1/\omega_I.
The imaginary part grows without bound, the spacing between consecutive modes
being a monotonic function of a.Comment: 5 pages, 3 figure
Field propagation in de Sitter black holes
We present an exhaustive analysis of scalar, electromagnetic and
gravitational perturbations in the background of Schwarzchild-de Sitter and
Reissner-Nordstrom-de Sitter spacetimes. The field propagation is considered by
means of a semi-analytical (WKB) approach and two numerical schemes: the
characteristic and general initial value integrations. The results are compared
near the extreme cosmological constant regime, where analytical results are
presented. A unifying picture is established for the dynamics of different spin
fields.Comment: 15 pages, 16 figures, published versio
Quasinormal modes of Schwarzschild black holes in four and higher dimensions
We make a thorough investigation of the asymptotic quasinormal modes of the
four and five-dimensional Schwarzschild black hole for scalar, electromagnetic
and gravitational perturbations. Our numerical results give full support to all
the analytical predictions by Motl and Neitzke, for the leading term. We also
compute the first order corrections analytically, by extending to higher
dimensions, previous work of Musiri and Siopsis, and find excellent agreement
with the numerical results. For generic spacetime dimension number D the
first-order corrections go as . This means that
there is a more rapid convergence to the asymptotic value for the five
dimensional case than for the four dimensional case, as we also show
numerically.Comment: 12 pages, 5 figures, RevTeX4. v2. Typos corrected, references adde
Dirty black holes: Quasinormal modes
In this paper, we investigate the asymptotic nature of the quasinormal modes
for "dirty" black holes -- generic static and spherically symmetric spacetimes
for which a central black hole is surrounded by arbitrary "matter" fields. We
demonstrate that, to the leading asymptotic order, the [imaginary] spacing
between modes is precisely equal to the surface gravity, independent of the
specifics of the black hole system.
Our analytical method is based on locating the complex poles in the first
Born approximation for the scattering amplitude. We first verify that our
formalism agrees, asymptotically, with previous studies on the Schwarzschild
black hole. The analysis is then generalized to more exotic black hole
geometries. We also extend considerations to spacetimes with two horizons and
briefly discuss the degenerate-horizon scenario.Comment: 15 pages; uses iopart.cls setstack.sty; V2: one additional reference
added, no physics changes; V3: two extra references, minor changes in
response to referee comment
Dirty black holes: Quasinormal modes for "squeezed" horizons
We consider the quasinormal modes for a class of black hole spacetimes that,
informally speaking, contain a closely ``squeezed'' pair of horizons. (This
scenario, where the relevant observer is presumed to be ``trapped'' between the
horizons, is operationally distinct from near-extremal black holes with an
external observer.) It is shown, by analytical means, that the spacing of the
quasinormal frequencies equals the surface gravity at the squeezed horizons.
Moreover, we can calculate the real part of these frequencies provided that the
horizons are sufficiently close together (but not necessarily degenerate or
even ``nearly degenerate''). The novelty of our analysis (which extends a
model-specific treatment by Cardoso and Lemos) is that we consider ``dirty''
black holes; that is, the observable portion of the (static and spherically
symmetric) spacetime is allowed to contain an arbitrary distribution of matter.Comment: 15 pages, uses iopart.cls and setstack.sty V2: Two references added.
Also, the appendix now relates our computation of the Regge-Wheeler potential
for gravity in a generic "dirty" black hole to the results of Karlovini
[gr-qc/0111066
Comparison of area spectra in loop quantum gravity
We compare two area spectra proposed in loop quantum gravity in different
approaches to compute the entropy of the Schwarzschild black hole. We describe
the black hole in general microcanonical and canonical area ensembles for these
spectra. We show that in the canonical ensemble, the results for all
statistical quantities for any spectrum can be reproduced by a heuristic
picture of Bekenstein up to second order. For one of these spectra - the
equally-spaced spectrum - in light of a proposed connection of the black hole
area spectrum to the quasinormal mode spectrum and following hep-th/0304135, we
present explicit calculations to argue that this spectrum is completely
consistent with this connection. This follows without requiring a change in the
gauge group of the spin degrees of freedom in this formalism from SU(2) to
SO(3). We also show that independent of the area spectrum, the degeneracy of
the area observable is bounded by , where is measured in
Planck units and is a constant of order unity.Comment: 8 pages, Revtex 4, version to appear in Classical and Quantum Gravit
Dynamical Boson Stars
The idea of stable, localized bundles of energy has strong appeal as a model
for particles. In the 1950s John Wheeler envisioned such bundles as smooth
configurations of electromagnetic energy that he called {\em geons}, but none
were found. Instead, particle-like solutions were found in the late 1960s with
the addition of a scalar field, and these were given the name {\em boson
stars}. Since then, boson stars find use in a wide variety of models as sources
of dark matter, as black hole mimickers, in simple models of binary systems,
and as a tool in finding black holes in higher dimensions with only a single
killing vector. We discuss important varieties of boson stars, their dynamic
properties, and some of their uses, concentrating on recent efforts.Comment: 79 pages, 25 figures, invited review for Living Reviews in
Relativity; major revision in 201