3,670 research outputs found
On the exact evaluation of spin networks
We introduce a fully coherent spin network amplitude whose expansion
generates all SU(2) spin networks associated with a given graph. We then give
an explicit evaluation of this amplitude for an arbitrary graph. We show how
this coherent amplitude can be obtained from the specialization of a generating
functional obtained by the contraction of parametrized intertwiners a la
Schwinger. We finally give the explicit evaluation of this generating
functional for arbitrary graphs
Spacetime structure of static solutions in Gauss-Bonnet gravity: charged case
We have studied spacetime structures of static solutions in the
-dimensional Einstein-Gauss-Bonnet-Maxwell- system. Especially we
focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet
coefficient is non-negative and in
order to define the relevant vacuum state. Solutions have the
-dimensional Euclidean sub-manifold whose curvature is , or -1.
In Gauss-Bonnet gravity, solutions are classified into plus and minus branches.
In the plus branch all solutions have the same asymptotic structure as those in
general relativity with a negative cosmological constant. The charge affects a
central region of the spacetime. A branch singularity appears at the finite
radius for any mass parameter. There the Kretschmann invariant
behaves as , which is much milder than divergent behavior of
the central singularity in general relativity . Some charged
black hole solutions have no inner horizon in Gauss-Bonnet gravity. Although
there is a maximum mass for black hole solutions in the plus branch for
in the neutral case, no such maximum exists in the charged case. The solutions
in the plus branch with and have an "inner" black hole, and
inner and the "outer" black hole horizons. Considering the evolution of black
holes, we briefly discuss a classical discontinuous transition from one black
hole spacetime to another.Comment: 20 pages, 10 figure
Spin-Raising Operators and Spin-3/2 Potentials in Quantum Cosmology
Local boundary conditions involving field strengths and the normal to the
boundary, originally studied in anti-de Sitter space-time, have been recently
considered in one-loop quantum cosmology. This paper derives the conditions
under which spin-raising operators preserve these local boundary conditions on
a 3-sphere for fields of spin 0,1/2,1,3/2 and 2. Moreover, the two-component
spinor analysis of the four potentials of the totally symmetric and independent
field strengths for spin 3/2 is applied to the case of a 3-sphere boundary. It
is shown that such boundary conditions can only be imposed in a flat Euclidean
background, for which the gauge freedom in the choice of the potentials
remains.Comment: 13 pages, plain-tex, recently appearing in Classical and Quantum
Gravity, volume 11, April 1994, pages 897-903. Apologies for the delay in
circulating the file, due to technical problems now fixe
The Seeds of Cosmic structure as a door to New Physics
There is something missing in our understanding of the origin of the seeds of
Cosmic Structuture.
The fact that the fluctuation spectrum can be extracted from the inflationary
scenario through an analysis that involves quantum field theory in curved
space-time, and that it coincides with the observational data has lead to a
certain complacency in the community, which prevents the critical analysis of
the obscure spots in the derivation. The point is that the inhomogeneity and
anisotropy of our universe seem to emerge from an exactly homogeneous and
isotropic initial state through processes that do not break those symmetries.
This article gives a brief recount of the problems faced by the arguments based
on established physics, which comprise the point of view held by a large
majority of researchers in the field.
The conclusion is that we need some new physics to be able to fully address
the problem. The article then exposes one avenue that has been used to address
the central issue and elaborates on the degree to which, the new approach makes
different predictions from the standard analyses.
The approach is inspired on Penrose's proposals that Quantum Gravity might
lead to a real, dynamical collapse of the wave function, a process that we
argue has the properties needed to extract us from the theoretical impasse
described above.Comment: Prepared for the proceedings of the conference NEBXII " Recent
Developments in Gravity", Napfio Grece June 2006. LateX, 15 page
Comment on "Absence of trapped surfaces and singularities in cylindrical collapse"
Recently, the gravitational collapse of an infinite cylindrical thin shell of
matter in an otherwise empty spacetime with two hypersurface orthogonal Killing
vectors was studied by Gon\c{c}alves [Phys. Rev. {\bf D65}, 084045 (2002).]. By
using three "alternative" criteria for trapped surfaces, the author claimed to
have shown that {\em they can never form either outside or on the shell,
regardingless of the matter content for the shell, except at asymptotical
future null infinite}.
Following Penrose's original idea, we first define trapped surfaces in
cylindrical spacetimes in terms of the expansions of null directions orthogonal
to the surfaces, and then show that the first criterion used by Gon\c{c}alves
is incorrect. We also show that his analysis of non-existence of trapped
surfaces in vacuum is incomplete. To confirm our claim, we present an example
that is a solution to the vacuum Einstein field equations and satisfies all the
regular conditions imposed by Gon\c{c}alves. After extending the solution to
the whole spacetime, we show explicitly that trapped surfaces exist in the
extended region.Comment: latex, 2 figures, the last version to appear in Phys. Rev.
Minimal data at a given point of space for solutions to certain geometric systems
We consider a geometrical system of equations for a three dimensional
Riemannian manifold. This system of equations has been constructed as to
include several physically interesting systems of equations, such as the
stationary Einstein vacuum field equations or harmonic maps coupled to gravity
in three dimensions. We give a characterization of its solutions in a
neighbourhood of a given point through sequences of symmetric trace free
tensors (referred to as `null data'). We show that the null data determine a
formal expansion of the solution and we obtain necessary and sufficient growth
estimates on the null data for the formal expansion to be absolutely convergent
in a neighbourhood of the given point. This provides a complete
characterization of all the solutions to the given system of equations around
that point.Comment: 26 pages, no figure
Degeneracy measures for the algebraic classification of numerical spacetimes
We study the issue of algebraic classification of the Weyl curvature tensor,
with a particular focus on numerical relativity simulations. The spacetimes of
interest in this context, binary black hole mergers, and the ringdowns that
follow them, present subtleties in that they are generically, strictly
speaking, Type I, but in many regions approximately, in some sense, Type D. To
provide meaning to any claims of "approximate" Petrov class, one must define a
measure of degeneracy on the space of null rays at a point. We will investigate
such a measure, used recently to argue that certain binary black hole merger
simulations ring down to the Kerr geometry, after hanging up for some time in
Petrov Type II. In particular, we argue that this hangup in Petrov Type II is
an artefact of the particular measure being used, and that a geometrically
better-motivated measure shows a black hole merger produced by our group
settling directly to Petrov Type D.Comment: 14 pages, 7 figures. Version 2 adds two references
Decoherence of Macroscopic Closed Systems within Newtonian Quantum Gravity
A theory recently proposed by the author aims to explain decoherence and the
thermodynamical behaviour of closed systems within a conservative, unitary,
framework for quantum gravity by assuming that the operators tied to the
gravitational degrees of freedom are unobservable and equating physical entropy
with matter-gravity entanglement entropy. Here we obtain preliminary results on
the extent of decoherence this theory predicts. We treat first a static state
which, if one were to ignore quantum gravitational effects, would be a quantum
superposition of two spatially displaced states of a single classically well
describable ball of uniform mass density in empty space. Estimating the quantum
gravitational effects on this system within a simple Newtonian approximation,
we obtain formulae which predict e.g. that as long as the mass of the ball is
considerably larger than the Planck mass, such a would-be-coherent static
superposition will actually be decohered whenever the separation of the centres
of mass of the two ball-states excedes a small fraction (which decreases as the
mass of the ball increases) of the ball radius. We then obtain a formula for
the quantum gravitational correction to the would-be-pure density matrix of a
non-relativistic many-body Schroedinger wave function and argue that this
formula predicts decoherence between configurations which differ (at least) in
the "relocation" of a cluster of particles of Planck mass. We estimate the
entropy of some simple model closed systems, finding a tendency for it to
increase with "matter-clumping" suggestive of a link with existing
phenomenological discussions of cosmological entropy increase.Comment: 11 pages, plain TeX, no figures. Accepted for publication as a
"Letter to the Editor" in "Classical and Quantum Gravity
Spherical gravitational collapse in N-dimensions
We investigate here spherically symmetric gravitational collapse in a
spacetime with an arbitrary number of dimensions and with a general {\it type
I} matter field, which is a broad class that includes most of the physically
reasonable matter forms. We show that given the initial data for matter in
terms of the initial density and pressure profiles at an initial surface
from which the collapse evolves, there exist rest of the initial data
functions and classes of solutions of Einstein equations which we construct
here, such that the spacetime evolution goes to a final state which is either a
black hole or a naked singularity, depending on the nature of initial data and
evolutions chosen, and subject to validity of the weak energy condition. The
results are discussed and analyzed in the light of the cosmic censorship
hypothesis in black hole physics. The formalism here combines the earlier
results on gravitational collapse in four dimensions in a unified treatment.
Also the earlier work is generalized to higher dimensional spacetimes to allow
a study of the effect of number of dimensions on the possible final outcome of
the collapse in terms of either a black hole or naked singularity. No
restriction is adopted on the number of dimensions, and other limiting
assumptions such as self-similarity of spacetime are avoided, in order to keep
the treatment general. Our methodology allows to consider to an extent the
genericity and stability aspects related to the occurrence of naked
singularities in gravitational collapse.Comment: Revtex4, The replaced version matches the published on
The Positivity of Energy for Asymptotically Anti-de Sitter Spacetimes
We use the formulation of asymptotically anti-de Sitter boundary conditions
given by Ashtekar and Magnon to obtain a coordinate expression for the general
asymptotically AdeS metric in a neighbourhood of infinity. From this, we are
able to compute the time delay of null curves propagating near infinity. If the
gravitational mass is negative, so will be the time delay (relative to null
geodesics at infinity) for certain null geodesics in the spacetime. Following
closely an argument given by Penrose, Sorkin, and Woolgar, who treated the
asymptotically flat case, we are then able to argue that a negative time delay
is inconsistent with non-negative matter-energies in spacetimes having good
causal properties. We thereby obtain a new positive mass theorem for these
spacetimes. The theorem may be applied even when the matter flux near the
boundary-at-infinity falls off so slowly that the mass changes, provided the
theorem is applied in a time-averaged sense. The theorem also applies in
certain spacetimes having local matter-energy that is sometimes negative, as
can be the case in semi-classical gravity.Comment: (Plain TeX - figures not included
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