5,296 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
The Poisson bracket on free null initial data for gravity
Free initial data for general relativity on a pair of intersecting null
hypersurfaces are well known, but the lack of a Poisson bracket and concerns
about caustics have stymied the development of a constraint free canonical
theory. Here it is pointed out how caustics and generator crossings can be
neatly avoided and a Poisson bracket on free data is given. On sufficiently
regular functions of the solution spacetime geometry this bracket matches the
Poisson bracket defined on such functions by the Hilbert action via Peierls'
prescription. The symplectic form is also given in terms of free data.Comment: 4 pages,1 figure. Some changes to text to improve clarity of
presentation, this is the final published versio
On leading order gravitational backreactions in de Sitter spacetime
Backreactions are considered in a de Sitter spacetime whose cosmological
constant is generated by the potential of scalar field. The leading order
gravitational effect of nonlinear matter fluctuations is analyzed and it is
found that the initial value problem for the perturbed Einstein equations
possesses linearization instabilities. We show that these linearization
instabilities can be avoided by assuming strict de Sitter invariance of the
quantum states of the linearized fluctuations. We furthermore show that quantum
anomalies do not block the invariance requirement. This invariance constraint
applies to the entire spectrum of states, from the vacuum to the excited states
(should they exist), and is in that sense much stronger than the usual Poincare
invariance requirement of the Minkowski vacuum alone. Thus to leading order in
their effect on the gravitational field, the quantum states of the matter and
metric fluctuations must be de Sitter invariant.Comment: 12 pages, no figures, typos corrected and some clarifying comments
added, version accepted by Phys. Rev.
New Proof of the Generalized Second Law
The generalized second law of black hole thermodynamics was proved by Frolov
and Page for a quasi-stationary eternal black hole. However, realistic black
holes arise from a gravitational collapse, and in this case their proof does
not hold. In this paper we prove the generalized second law for a
quasi-stationary black hole which arises from a gravitational collapse.Comment: 13 pages, Late
Spinning Black Holes as Particle Accelerators
It has recently been pointed out that particles falling freely from rest at
infinity outside a Kerr black hole can in principle collide with arbitrarily
high center of mass energy in the limiting case of maximal black hole spin.
Here we aim to elucidate the mechanism for this fascinating result, and to
point out its practical limitations, which imply that ultra-energetic
collisions cannot occur near black holes in nature.Comment: 3 pages; v2: references added, minor modifications to match version
published in PR
General static spherically symmetric solutions in Horava gravity
We derive general static spherically symmetric solutions in the Horava theory
of gravity with nonzero shift field. These represent "hedgehog" versions of
black holes with radial "hair" arising from the shift field. For the case of
the standard de Witt kinetic term (lambda =1) there is an infinity of solutions
that exhibit a deformed version of reparametrization invariance away from the
general relativistic limit. Special solutions also arise in the anisotropic
conformal point lambda = 1/3.Comment: References adde
Newtonian and Relativistic Cosmologies
Cosmological N-body simulations are now being performed using Newtonian
gravity on scales larger than the Hubble radius. It is well known that a
uniformly expanding, homogeneous ball of dust in Newtonian gravity satisfies
the same equations as arise in relativistic FLRW cosmology, and it also is
known that a correspondence between Newtonian and relativistic dust cosmologies
continues to hold in linearized perturbation theory in the marginally
bound/spatially flat case. Nevertheless, it is far from obvious that Newtonian
gravity can provide a good global description of an inhomogeneous cosmology
when there is significant nonlinear dynamical behavior at small scales. We
investigate this issue in the light of a perturbative framework that we have
recently developed, which allows for such nonlinearity at small scales. We
propose a relatively straightforward "dictionary"---which is exact at the
linearized level---that maps Newtonian dust cosmologies into general
relativistic dust cosmologies, and we use our "ordering scheme" to determine
the degree to which the resulting metric and matter distribution solve
Einstein's equation. We find that Einstein's equation fails to hold at "order
1" at small scales and at "order " at large scales. We then find the
additional corrections to the metric and matter distribution needed to satisfy
Einstein's equation to these orders. While these corrections are of some
interest in their own right, our main purpose in calculating them is that their
smallness should provide a criterion for the validity of the original
dictionary (as well as simplified versions of this dictionary). We expect that,
in realistic Newtonian cosmologies, these additional corrections will be very
small; if so, this should provide strong justification for the use of Newtonian
simulations to describe relativistic cosmologies, even on scales larger than
the Hubble radius.Comment: 35 pages; minor change
Over-spinning a black hole with a test body
It has long been known that a maximally spinning black hole can not be
over-spun by tossing in a test body. Here we show that if instead the black
hole starts out with below maximal spin, then indeed over-spinning can be
achieved when adding either orbital or spin angular momentum. We find that
requirements on the size and internal structure of the test body can be met as
well. Our analysis neglects radiative and self-force effects,which may prevent
the over-spinning.Comment: 4 pages; v2: reference added, incorporates the missed case of an
oblate test body, which appears with the published version only as an
erratum, other minor edits (with respect to v1
Global Extensions of Spacetimes Describing Asymptotic Final States of Black Holes
We consider a globally hyperbolic, stationary spacetime containing a black
hole but no white hole. We assume, further, that the event horizon, \tn, of
the black hole is a Killing horizon with compact cross-sections. We prove that
if surface gravity is non-zero constant throughout the horizon one can {\it
globally} extend such a spacetime so that the image of is a proper
subset of a regular bifurcate Killing horizon in the enlarged spacetime. The
necessary and sufficient conditions are given for the extendibility of matter
fields to the enlarged spacetime. These conditions are automatically satisfied
if the spacetime is static (and, hence ``"-reflection symmetric) or
stationary-axisymmetric with ``" reflection isometry and the matter
fields respect the reflection isometry. In addition, we prove that a necessary
and sufficient condition for the constancy of the surface gravity on a Killing
horizon is that the exterior derivative of the twist of the horizon Killing
field vanish on the horizon. As a corollary of this, we recover a result of
Carter that constancy of surface gravity holds for any black hole which is
static or stationary- axisymmetric with the ``" reflection isometry. No
use of Einstein's equation is made in obtaining any of the above results. Taken
together, these results support the view that any spacetime representing the
asymptotic final state of a black hole formed by gravitational collapse may be
assumed to possess a bifurcate Killing horizon or a Killing horizon with
vanishing surface gravity.Comment: 20 pages, plain te
Glassy states and microphase separation in cross-linked homopolymer blends
The physical properties of blends of distinct homopolymers, cross-linked
beyond the gelation point, are addressed via a Landau approach involving a pair
of coupled order-parameter fields: one describing vulcanisation, the other
describing local phase separation. Thermal concentration fluctuations, present
at the time of cross-linking, are frozen in by cross-linking, and the structure
of the resulting glassy fluctuations is analysed at the Gaussian level in
various regimes, determined by the relative values of certain physical
length-scales. The enhancement, due to gelation, of the stability of the blend
with respect to demixing is also analysed. Beyond the corresponding stability
limit, gelation prevents complete demixing, replacing it by microphase
separation, which occurs up to a length-scale set by the rigidity of the
network, as a simple variational scheme reveals.Comment: 7 pages, 6 figure
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