347 research outputs found
A Rigorous Treatment of Energy Extraction from a Rotating Black Hole
The Cauchy problem is considered for the scalar wave equation in the Kerr
geometry. We prove that by choosing a suitable wave packet as initial data, one
can extract energy from the black hole, thereby putting supperradiance, the
wave analogue of the Penrose process, into a rigorous mathematical framework.
We quantify the maximal energy gain. We also compute the infinitesimal change
of mass and angular momentum of the black hole, in agreement with
Christodoulou's result for the Penrose process. The main mathematical tool is
our previously derived integral representation of the wave propagator.Comment: 19 pages, LaTeX, proof of Propositions 2.3 and 3.1 given in more
detai
On matching conditions for cosmological perturbations
We derive the matching conditions for cosmological perturbations in a
Friedmann Universe where the equation of state undergoes a sharp jump, for
instance as a result of a phase transition. The physics of the transition which
is needed to follow the fate of the perturbations is clarified. We dissipate
misleading statements made recently in the literature concerning the
predictions of the primordial fluctuations from inflation and confirm standard
results. Applications to string cosmology are considered.Comment: 20 pages, latex (revtex), no figure
ASYMPTOTIC BEHAVIOR OF COMPLEX SCALAR FIELDS IN A FRIEDMAN-LEMAITRE UNIVERSE
We study the coupled Einstein-Klein-Gordon equations for a complex scalar
field with and without a quartic self-interaction in a curvatureless
Friedman-Lema\^{\i}\-tre Universe. The equations can be written as a set of
four coupled first order non-linear differential equations, for which we
establish the phase portrait for the time evolution of the scalar field. To
that purpose we find the singular points of the differential equations lying in
the finite region and at infinity of the phase space and study the
corresponding asymptotic behavior of the solutions. This knowledge is of
relevance, since it provides the initial conditions which are needed to solve
numerically the differential equations. For some singular points lying at
infinity we recover the expected emergence of an inflationary stage.Comment: uuencoded, compressed tarfile containing a 15 pages Latex file and 2
postscipt figures. Accepted for publication on Phys. Rev.
Conservation Laws and Cosmological Perturbations in Curved Universes
When working in synchronous gauges, pseudo-tensor conservation laws are often
used to set the initial conditions for cosmological scalar perturbations, when
those are generated by topological defects which suddenly appear in an up to
then perfectly homogeneous and isotropic universe. However those conservation
laws are restricted to spatially flat (K=0) Friedmann-Lema\^\i tre spacetimes.
In this paper, we first show that in fact they implement a matching condition
between the pre- and post- transition eras and, in doing so, we are able to
generalize them and set the initial conditions for all . Finally, in the
long wavelength limit, we encode them into a vector conservation law having a
well-defined geometrical meaning.Comment: 15 pages, no figure, to appear in Phys. Rev.
New features of flat (4+1)-dimensional cosmological model with a perfect fluid in Gauss-Bonnet gravity
We investigated a flat multidimensional cosmological model in Gauss-Bonnet
gravity in presence of a matter in form of perfect fluid. We found analytically
new stationary regimes (these results are valid for arbitrary number of spatial
dimensions) and studied their stability by means of numerical recipes in
4+1-dimensional case. In the vicinity of the stationary regime we discovered
numerically another non-singular regime which appears to be periodical.
Finally, we demonstrated that the presence of matter in form of a perfect fluid
lifts some constraints on the dynamics of the 4+1-dimensional model which have
been found earlier.Comment: 14 pages, 5 figures, 1 table; v2 minor corrections, conclusions
unchange
Brane versus shell cosmologies in Einstein and Einstein-Gauss-Bonnet theories
We first illustrate on a simple example how, in existing brane cosmological
models, the connection of a 'bulk' region to its mirror image creates matter on
the 'brane'. Next, we present a cosmological model with no symmetry which
is a spherical symmetric 'shell' separating two metrically different
5-dimensional anti-de Sitter regions. We find that our model becomes
Friedmannian at late times, like present brane models, but that its early time
behaviour is very different: the scale factor grows from a non-zero value at
the big bang singularity. We then show how the Israel matching conditions
across the membrane (that is either a brane or a shell) have to be modified if
more general equations than Einstein's, including a Gauss-Bonnet correction,
hold in the bulk, as is likely to be the case in a low energy limit of string
theory. We find that the membrane can then no longer be treated in the thin
wall approximation. However its microphysics may, in some instances, be simply
hidden in a renormalization of Einstein's constant, in which cases Einstein and
Gauss-Bonnet membranes are identical.Comment: 15 pages, submitted to Phys. Rev.
Normal modes for metric fluctuations in a class of higher-dimensional backgrounds
We discuss a gauge invariant approach to the theory of cosmological
perturbations in a higher-dimensonal background. We find the normal modes which
diagonalize the perturbed action, for a scalar field minimally coupled to
gravity, in a higher-dimensional manifold M of the Bianchi-type I, under the
assumption that the translations along an isotropic spatial subsection of M are
isometries of the full, perturbed background. We show that, in the absence of
scalar field potential, the canonical variables for scalar and tensor metric
perturbations satisfy exactly the same evolution equation, and we discuss the
possible dependence of the spectrum on the number of internal dimensions.Comment: 19 pages, LATEX, an explicit example is added to discuss the possible
dependence of the perturbation spectrum on the number of internal dimensions.
To apper in Class. Quantum Gra
Aspects of Scalar Field Dynamics in Gauss-Bonnet Brane Worlds
The Einstein-Gauss-Bonnet equations projected from the bulk to brane lead to
a complicated Friedmann equation which simplifies to in the
asymptotic regimes. The Randall-Sundrum (RS) scenario corresponds to
whereas & give rise to high energy Gauss-Bonnet (GB) regime and
the standard GR respectively. Amazingly, while evolving from RS regime to high
energy GB limit, one passes through a GR like region which has important
implications for brane world inflation. For tachyon GB inflation with
potentials investigated in this paper, the scalar to
tensor ratio of perturbations is maximum around the RS region and is
generally suppressed in the high energy regime for the positive values of .
The ratio is very low for at all energy scales relative to GB inflation
with ordinary scalar field. The models based upon tachyon inflation with
polynomial type of potentials with generic positive values of turn out to
be in the observational contour bound at all energy scales varying
from GR to high energy GB limit. The spectral index improves for the
lower values of and approaches its scale invariant limit for in the
high energy GB regime. The ratio also remains small for large negative
values of , however, difference arises for models close to scale invariance
limit. In this case, the tensor to scale ratio is large in the GB regime
whereas it is suppressed in the intermediate region between RS and GB. Within
the frame work of patch cosmologies governed by , the behavior
of ordinary scalar field near cosmological singularity and the nature of
scaling solutions are distinguished for the values of .Comment: 15 pages, 10 eps figures; appendix on various scales in GB brane
world included and references updated; final version to appear in PR
Quantum properties of the Dirac field on BTZ black hole backgrounds
We consider a Dirac field on a -dimensional uncharged BTZ black hole
background. We first find out the Dirac Hamiltonian, and study its
self-adjointness properties. We find that, in analogy to the Kerr-Newman-AdS
Dirac Hamiltonian in dimensions, essential self-adjointness on
of the reduced (radial) Hamiltonian is implemented
only if a suitable relation between the mass of the Dirac field and the
cosmological radius holds true. The very presence of a boundary-like
behaviour of is at the root of this problem. Also, we determine in a
complete way qualitative spectral properties for the non-extremal case, for
which we can infer the absence of quantum bound states for the Dirac field.
Next, we investigate the possibility of a quantum loss of angular momentum for
the -dimensional uncharged BTZ black hole. Unlike the corresponding
stationary four-dimensional solutions, the formal treatment of the level
crossing mechanism is much simpler. We find that, even in the extremal case, no
level crossing takes place. Therefore, no quantum loss of angular momentum via
particle pair production is allowed.Comment: 19 pages; IOP styl
Nature of singularities in anisotropic string cosmology
We study nature of singularities in anisotropic string-inspired cosmological
models in the presence of a Gauss-Bonnet term. We analyze two string gravity
models-- dilaton-driven and modulus-driven cases-- in the Bianchi type-I
background without an axion field. In both scenarios singularities can be
classified in two ways- the determinant singularity where the main determinant
of the system vanishes and the ordinary singularity where at least one of the
anisotropic expansion rates of the Universe diverges. In the dilaton case,
either of these singularities inevitably appears during the evolution of the
system. In the modulus case, nonsingular cosmological solutions exist both in
asymptotic past and future with determinant and D=2, respectively.
In both scenarios nonsingular trajectories in either future or past typically
meet the determinant singularity in past/future when the solutions are
singular, apart from the exceptional case where the sign of the time-derivative
of dilaton is negative. This implies that the determinant singularity may play
a crucial role to lead to singular solutions in an anisotropic background.Comment: 21 pages, 8 figure
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