4,328 research outputs found
Trapped surfaces in prolate collapse in the Gibbons-Penrose construction
We investigate existence and properties of trapped surfaces in two models of
collapsing null dust shells within the Gibbons-Penrose construction. In the
first model, the shell is initially a prolate spheroid, and the resulting
singularity forms at the ends first (relative to a natural time slicing by flat
hyperplanes), in analogy with behavior found in certain prolate collapse
examples considered by Shapiro and Teukolsky. We give an explicit example in
which trapped surfaces are present on the shell, but none exist prior to the
last flat slice, thereby explicitly showing that the absence of trapped
surfaces on a particular, natural slicing does not imply an absence of trapped
surfaces in the spacetime. We then examine a model considered by Barrabes,
Israel and Letelier (BIL) of a cylindrical shell of mass M and length L, with
hemispherical endcaps of mass m. We obtain a "phase diagram" for the presence
of trapped surfaces on the shell with respect to essential parameters and . It is found that no trapped surfaces are
present on the shell when or are sufficiently small. (We are
able only to search for trapped surfaces lying on the shell itself.) In the
limit , the existence or nonexistence of trapped surfaces lying
within the shell is seen to be in remarkably good accord with the hoop
conjecture.Comment: 22 pages, 6 figure
Extremal black holes, gravitational entropy and nonstationary metric fields
We show that extremal black holes have zero entropy by pointing out a simple
fact: they are time-independent throughout the spacetime and correspond to a
single classical microstate. We show that non-extremal black holes, including
the Schwarzschild black hole, contain a region hidden behind the event horizon
where all their Killing vectors are spacelike. This region is nonstationary and
the time labels a continuous set of classical microstates, the phase space
, where is a three-metric induced on a
spacelike hypersurface and is its momentum conjugate. We
determine explicitly the phase space in the interior region of the
Schwarzschild black hole. We identify its entropy as a measure of an outside
observer's ignorance of the classical microstates in the interior since the
parameter which labels the states lies anywhere between 0 and 2M. We
provide numerical evidence from recent simulations of gravitational collapse in
isotropic coordinates that the entropy of the Schwarzschild black hole stems
from the region inside and near the event horizon where the metric fields are
nonstationary; the rest of the spacetime, which is static, makes no
contribution. Extremal black holes have an event horizon but in contrast to
non-extremal black holes, their extended spacetimes do not possess a bifurcate
Killing horizon. This is consistent with the fact that extremal black holes are
time-independent and therefore have no distinct time-reverse.Comment: 12 pages, 2 figures. To appear in Class. and Quant. Gravity. Based on
an essay selected for honorable mention in the 2010 gravity research
foundation essay competitio
Maxwell Fields in Spacetimes Admitting Non-Null Killing Vectors
We consider source-free electromagnetic fields in spacetimes possessing a
non-null Killing vector field, . We assume further that the
electromagnetic field tensor, , is invariant under the action of the
isometry group induced by . It is proved that whenever the two
potentials associated with the electromagnetic field are functionally
independent the entire content of Maxwell's equations is equivalent to the
relation \n^aT_{ab}=0. Since this relation is implied by Einstein's equation
we argue that it is enough to solve merely Einstein's equation for these
electrovac spacetimes because the relevant equations of motion will be
satisfied automatically. It is also shown that for the exceptional case of
functionally related potentials \n^aT_{ab}=0 implies along with one of the
relevant equations of motion that the complementary equation concerning the
electromagnetic field is satisfied.Comment: 7 pages,PACS numbers: 04.20.Cv, 04.20.Me, 04.40.+
Stability of BTZ black strings
We study the dynamical stability of the BTZ black string against fermonic and
gravitational perturbations. The BTZ black string is not always stable against
these perturbations. There exist threshold values for related to the
compactification of the extra dimension for fermonic perturbation, scalar part
of the gravitational perturbation and the tensor perturbation, respectively.
Above the threshold values, perturbations are stable; while below these
thresholds, perturbations can be unstable. We find that this non-trivial
stability behavior qualitatively agrees with that predicted by a
thermodynamical argument, showing that the BTZ black string phase is not the
privileged stable phase.Comment: 9 pages, revised version to appear in Phys. Rev.
Regular phantom black holes
For self-gravitating, static, spherically symmetric, minimally coupled scalar
fields with arbitrary potentials and negative kinetic energy (favored by the
cosmological observations), we give a classification of possible regular
solutions to the field equations with flat, de Sitter and AdS asymptotic
behavior. Among the 16 presented classes of regular rsolutions are traversable
wormholes, Kantowski-Sachs (KS) cosmologies beginning and ending with de Sitter
stages, and asymptotically flat black holes (BHs). The Penrose diagram of a
regular BH is Schwarzschild-like, but the singularity at is replaced by a
de Sitter infinity, which gives a hypothetic BH explorer a chance to survive.
Such solutions also lead to the idea that our Universe could be created from a
phantom-dominated collapse in another universe, with KS expansion and
isotropization after crossing the horizon. Explicit examples of regular
solutions are built and discussed. Possible generalizations include -essence
type scalar fields (with a potential) and scalar-tensor theories of gravity.Comment: revtex4, 4 pages, no figure
Time Dependent Cosmologies and Their Duals
We construct a family of solutions in IIB supergravity theory. These are time
dependent or depend on a light-like coordinate and can be thought of as
deformations of AdS_5 x S^5. Several of the solutions have singularities. The
light-like solutions preserve 8 supersymmetries. We argue that these solutions
are dual to the N=4 gauge theory in a 3+1 dimensional spacetime with a metric
and a gauge coupling that is varying with time or the light-like direction
respectively. This identification allows us to map the question of singularity
resolution to the dual gauge theory.Comment: 13 pages REVTeX and AMSLaTeX. v2: corrected typos and made some
clarifications; reference added; v3: more clarifications, references adde
Dirac Quantization of Parametrized Field Theory
Parametrized field theory (PFT) is free field theory on flat spacetime in a
diffeomorphism invariant disguise. It describes field evolution on arbitrary
foliations of the flat spacetime instead of only the usual flat ones, by
treating the `embedding variables' which describe the foliation as dynamical
variables to be varied in the action in addition to the scalar field. A formal
Dirac quantization turns the constraints of PFT into functional Schrodinger
equations which describe evolution of quantum states from an arbitrary Cauchy
slice to an infinitesimally nearby one.This formal Schrodinger picture- based
quantization is unitarily equivalent to the standard Heisenberg picture based
Fock quantization of the free scalar field if scalar field evolution along
arbitrary foliations is unitarily implemented on the Fock space. Torre and
Varadarajan (TV) showed that for generic foliations emanating from a flat
initial slice in spacetimes of dimension greater than 2, evolution is not
unitarily implemented, thus implying an obstruction to Dirac quantization.
We construct a Dirac quantization of PFT,unitarily equivalent to the standard
Fock quantization, using techniques from Loop Quantum Gravity (LQG) which are
powerful enough to super-cede the no- go implications of the TV results. The
key features of our quantization include an LQG type representation for the
embedding variables, embedding dependent Fock spaces for the scalar field, an
anomaly free representation of (a generalization of) the finite transformations
generated by the constraints and group averaging techniques. The difference
between 2 and higher dimensions is that in the latter, only finite gauge
transformations are defined in the quantum theory, not the infinitesimal ones.Comment: 33 page
Nonaxisymmetric instability of rapidly rotating black hole in five dimensions
We present results from numerical solution of Einstein's equation in five
dimensions describing evolution of rapidly rotating black holes. We show, for
the first time, that the rapidly rotating black holes in higher dimensions are
unstable against nonaxisymmetric deformation; for the five-dimensional case,
the critical value of spin parameter for onset of the instability is .Comment: 4 pages, 3 figures, accepted for publication in PRD(R
Truly naked spherically-symmetric and distorted black holes
We demonstrate the existence of spherically-symmetric truly naked black holes
(TNBH) for which the Kretschmann scalar is finite on the horizon but some
curvature components including those responsible for tidal forces as well as
the energy density measured by a free-falling observer are
infinite. We choose a rather generic power-like asymptotics for the metric
functions and analyze possible types of a horizon depending on the behavior of
curvature components in the free-falling frame. It is also shown in a general
case of distorted black holes that and tidal forces are either
both finite or both infinite. The general approach developed in the article
includes previously found examples and, in particular, TNBHs with an infinite
area of a horizon. The fact that the detection of singularity depends on a
frame may be relevant for a more accurate definition of the cosmic censorship
conjecture. TNBHs may be considered as a new example of so-called non-scalar
singularities for which the scalar curvature invariants are finite but some
components of the Riemann tensor may diverge in certain frames.Comment: 18 pages. 2 last sentences on quantum backreaction modified. Typos
corrected. To appear in PR
Black Holes at the IceCube Neutrino Telescope
If the fundamental Planck scale is about a TeV and the cosmic neutrino flux
is at the Waxman-Bahcall level, quantum black holes are created daily in the
Antarctic ice-cap. We re-examine the prospects for observing such black holes
with the IceCube neutrino-detection experiment. To this end, we first revise
the black hole production rate by incorporating the effects of inelasticty,
i.e., the energy radiated in gravitational waves by the multipole moments of
the incoming shock waves. After that we study in detail the process of Hawking
evaporation accounting for the black hole's large momentum in the lab system.
We derive the energy spectrum of the Planckian cloud which is swept forward
with a large, O (10^6), Lorentz factor. (It is noteworthy that the boosted
thermal spectrum is also relevant for the study of near-extremal supersymmetric
black holes, which could be copiously produced at the LHC.) In the
semiclassical regime, we estimate the average energy of the boosted particles
to be less than 20% the energy of the neutrino-progenitor. Armed with such a
constraint, we determine the discovery reach of IceCube by tagging on "soft"
(relative to what one would expect from charged current standard model
processes) muons escaping the electromagnetic shower bubble produced by the
black hole's light descendants. The statistically significant 5-sigma excess
extends up to a quantum gravity scale ~ 1.3 TeV.Comment: Matching version to be published in Phys. Rev.
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