4,034 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
First Law of Black Rings Thermodynamics in Higher Dimensional Dilaton Gravity with p + 1 Strength Forms
We derive the first law of black rings thermodynamics in n-dimensional
Einstein dilaton gravity with additional (p+1)-form field strength being the
simplest generalization of five-dimensional theory containing a stationary
black ring solution with dipole charge. It was done by means of choosing any
cross section of the event horizon to the future of the bifurcation surface.Comment: 6 pages, to be published in Phys.Rev.D1
New thought experiment to test the generalized second law of thermodynamics
We propose an extension of the original thought experiment proposed by
Geroch, which sparked much of the actual debate and interest on black hole
thermodynamics, and show that the generalized second law of thermodynamics is
in compliance with it.Comment: 4 pages (revtex), 3 figure
On Cosmological Implication of the Trace Anomaly
We establish a connection between the trace anomaly and a thermal radiation
in the context of the standard cosmology. This is done by solving the covariant
conservation equation of the stress tensor associated with a conformally
invariant quantum scalar field. The solution corresponds to a thermal radiation
with a temperature which is given in terms of a cut-off time excluding the
spacetime regions very close to the initial singularity. We discuss the
interrelation between this result and the result obtained in a two-dimensional
schwarzschild spacetime.Comment: 8 pages, no figure
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.
On the fate of black string instabilities: An Observation
Gregory and Laflamme (hep-th/9301052) have argued that an instability causes
the Schwarzschild black string to break up into disjoint black holes. On the
other hand, Horowitz and Maeda (arXiv:hep-th/0105111) derived bounds on the
rate at which the smallest sphere can pinch off, showing that, if it happens at
all, such a pinch-off can occur only at infinite affine parameter along the
horizon. An interesting point is that, if a singularity forms, such an infinite
affine parameter may correspond to a finite advanced time -- which is in fact a
more appropriate notion of time at infinity. We argue below that pinch-off at a
finite advanced time is in fact a natural expectation under the bounds derived
by Horowitz and Maeda.Comment: 4 pages, RevTex, 1 figure, references adde
An axisymmetric generalized harmonic evolution code
We describe the first axisymmetric numerical code based on the generalized
harmonic formulation of the Einstein equations which is regular at the axis. We
test the code by investigating gravitational collapse of distributions of
complex scalar field in a Kaluza-Klein spacetime. One of the key issues of the
harmonic formulation is the choice of the gauge source functions, and we
conclude that a damped wave gauge is remarkably robust in this case. Our
preliminary study indicates that evolution of regular initial data leads to
formation both of black holes with spherical and cylindrical horizon
topologies. Intriguingly, we find evidence that near threshold for black hole
formation the number of outcomes proliferates. Specifically, the collapsing
matter splits into individual pulses, two of which travel in the opposite
directions along the compact dimension and one which is ejected radially from
the axis. Depending on the initial conditions, a curvature singularity develops
inside the pulses.Comment: 21 page, 18 figures. v2: minor corrections, added references, new
Fig. 9; journal version
A general variational principle for spherically symmetric perturbations in diffeomorphism covariant theories
We present a general method for the analysis of the stability of static,
spherically symmetric solutions to spherically symmetric perturbations in an
arbitrary diffeomorphism covariant Lagrangian field theory. Our method involves
fixing the gauge and solving the linearized gravitational field equations to
eliminate the metric perturbation variable in terms of the matter variables. In
a wide class of cases--which include f(R) gravity, the Einstein-aether theory
of Jacobson and Mattingly, and Bekenstein's TeVeS theory--the remaining
perturbation equations for the matter fields are second order in time. We show
how the symplectic current arising from the original Lagrangian gives rise to a
symmetric bilinear form on the variables of the reduced theory. If this
bilinear form is positive definite, it provides an inner product that puts the
equations of motion of the reduced theory into a self-adjoint form. A
variational principle can then be written down immediately, from which
stability can be tested readily. We illustrate our method in the case of
Einstein's equation with perfect fluid matter, thereby re-deriving, in a
systematic manner, Chandrasekhar's variational principle for radial
oscillations of spherically symmetric stars. In a subsequent paper, we will
apply our analysis to f(R) gravity, the Einstein-aether theory, and
Bekenstein's TeVeS theory.Comment: 13 pages; submitted to Phys. Rev. D. v2: changed formatting, added
conclusion, corrected sign convention
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
First Law of Black Saturn Thermodynamics
The physical version and equilibrium state version of the first law of
thermodynamics for a black object consisting of n-dimensional charged
stationary axisymmetric black hole surrounded by black rings, the so-called
black Saturn was derived. The general setting for our derivation is
n-dimensional dilaton gravity with p + 1 strength form fields.Comment: 9 pages, RevTex, to be published in Phys.Rev.D1
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