5,565 research outputs found
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.
Incorporating DNA Sequencing into Current Prenatal Screening Practice for Down's Syndrome
PMCID: PMC3604109This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
Skyrme Black Holes in the Isolated Horizons Formalism
We study static, spherically symmetric, Skyrme black holes in the context of
the assumption that they can be viewed as bound states between ordinary bare
black holes and solitons. This assumption and results stemming from the
isolated horizons formalism lead to several conjectures about the static black
hole solutions. These conjectures are tested against the Skyrme black hole
solutions. It is shown that, while there is in general good agreement with the
conjectures, a crucial aspect seems to violate one of the conjectures.Comment: Full journal version, 6 pages, 5 figure
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.+
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
Lagrangian perfect fluids and black hole mechanics
The first law of black hole mechanics (in the form derived by Wald), is
expressed in terms of integrals over surfaces, at the horizon and spatial
infinity, of a stationary, axisymmetric black hole, in a diffeomorphism
invariant Lagrangian theory of gravity. The original statement of the first law
given by Bardeen, Carter and Hawking for an Einstein-perfect fluid system
contained, in addition, volume integrals of the fluid fields, over a spacelike
slice stretching between these two surfaces. When applied to the
Einstein-perfect fluid system, however, Wald's methods yield restricted
results. The reason is that the fluid fields in the Lagrangian of a gravitating
perfect fluid are typically nonstationary. We therefore first derive a first
law-like relation for an arbitrary Lagrangian metric theory of gravity coupled
to arbitrary Lagrangian matter fields, requiring only that the metric field be
stationary. This relation includes a volume integral of matter fields over a
spacelike slice between the black hole horizon and spatial infinity, and
reduces to the first law originally derived by Bardeen, Carter and Hawking when
the theory is general relativity coupled to a perfect fluid. We also consider a
specific Lagrangian formulation for an isentropic perfect fluid given by
Carter, and directly apply Wald's analysis. The resulting first law contains
only surface integrals at the black hole horizon and spatial infinity, but this
relation is much more restrictive in its allowed fluid configurations and
perturbations than that given by Bardeen, Carter and Hawking. In the Appendix,
we use the symplectic structure of the Einstein-perfect fluid system to derive
a conserved current for perturbations of this system: this current reduces to
one derived ab initio for this system by Chandrasekhar and Ferrari.Comment: 26 pages LaTeX-2
Note on counterterms in asymptotically flat spacetimes
We consider in more detail the covariant counterterm proposed by Mann and
Marolf in asymptotically flat spacetimes. With an eye to specific practical
computations using this counterterm, we present explicit expressions in general
dimensions that can be used in the so-called `cylindrical cut-off' to
compute the action and the associated conserved quantities for an
asymptotically flat spacetime. As applications, we show how to compute the
action and the conserved quantities for the NUT-charged spacetime and for the
Kerr black hole in four dimensions.Comment: 13 pages, v. 2 added reference
Exact Hairy Black Holes and their Modification to the Universal Law of Gravitation
In this paper two things are done. First, it is pointed out the existence of
exact asymptotically flat, spherically symmetric black holes when a self
interacting, minimally coupled scalar field is the source of the energy
momentum of the Einstein equations in four dimensions. The scalar field
potential is the recently found to be compatible with the hairy generalization
of the Plebanski-Demianski solution of general relativity. This paper describes
the spherically symmetric solutions that smoothly connect the Schwarzschild
black hole with its hairy counterpart. The geometry and scalar field are
everywhere regular except at the usual Schwarzschild like singularity inside
the black hole. The scalar field energy momentum tensor satisfies the null
energy condition in the static region of the spacetime. The first law holds
when the parameters of the scalar field potential are fixed under
thermodynamical variation. Secondly, it is shown that an extra, dimensionless
parameter, present in the hairy solution, allows to modify the gravitational
field of a spherically symmetric black hole in a remarkable way. When the
dimensionless parameter is increased, the scalar field generates a flat
gravitational potential, that however asymptotically matches the Schwarzschild
gravitational field. Finally, it is shown that a positive cosmological constant
can render the scalar field potential convex if the parameters are within a
specific rank.Comment: Two new references, 10 pages, 2 figure
Upper limits of particle emission from high-energy collision and reaction near a maximally rotating Kerr black hole
The center-of-mass energy of two particles colliding near the horizon of a
maximally rotating black hole can be arbitrarily high if the angular momentum
of either of the incident particles is fine-tuned, which we call a critical
particle. We study particle emission from such high-energy collision and
reaction in the equatorial plane fully analytically. We show that the
unconditional upper limit of the energy of the emitted particle is given by
218.6% of that of the injected critical particle, irrespective of the details
of the reaction and this upper limit can be realized for massless particle
emission. The upper limit of the energy extraction efficiency for this emission
as a collisional Penrose process is given by 146.6%, which can be realized in
the collision of two massive particles with optimized mass ratio. Moreover, we
analyze perfectly elastic collision, Compton scattering, and pair annihilation
and show that net positive energy extraction is really possible for these three
reactions. The Compton scattering is most efficient among them and the
efficiency can reach 137.2%. On the other hand, our result is qualitatively
consistent with the earlier claim that the mass and energy of the emitted
particle are at most of order the total energy of the injected particles and
hence we can observe neither super-heavy nor super-energetic particles.Comment: 22 pages, 3 figures, typos corrected, reference updated, accepted for
publication in Physical Review D, typos correcte
Towards a wave--extraction method for numerical relativity: III. Analytical examples for the Beetle--Burko radiation scalar
Beetle and Burko recently introduced a background--independent scalar
curvature invariant for general relativity that carries information only about
the gravitational radiation in generic spacetimes, in cases where such
radiation is incontrovertibly defined. In this paper we adopt a formalism that
only uses spatial data as they are used in numerical relativity and compute the
Beetle--Burko radiation scalar for a number of analytical examples,
specifically linearized Einstein--Rosen cylindrical waves, linearized
quadrupole waves, the Kerr spacetime, Bowen--York initial data, and the Kasner
spacetime. These examples illustrate how the Beetle--Burko radiation scalar can
be used to examine the gravitational wave content of numerically generated
spacetimes, and how it may provide a useful diagnostic for initial data sets.Comment: 23 pages, 4 figures; We changed the convention used, corrected typos,
and expanded the discussio
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