2,530 research outputs found
Does backreaction enforce the averaged null energy condition in semiclassical gravity?
The expected stress-energy tensor of quantum fields generically
violates the local positive energy conditions of general relativity. However,
may satisfy some nonlocal conditions such as the averaged null energy
condition (ANEC), which would rule out traversable wormholes. Although ANEC
holds in Minkowski spacetime, it can be violated in curved spacetimes if one is
allowed to choose the spacetime and quantum state arbitrarily, without
imposition of the semiclassical Einstein equation G_{ab} = 8 \pi . In
this paper we investigate whether ANEC holds for solutions to this equation, by
studying a free, massless scalar field with arbitrary curvature coupling in
perturbation theory to second order about the flat spacetime/vacuum solution.
We "reduce the order" of the perturbation equations to eliminate spurious
solutions, and consider the limit in which the lengthscales determined by the
incoming state are much larger than the Planck length. We also need to assume
that incoming classical gravitational radiation does not dominate the first
order metric perturbation. We find that although the ANEC integral can be
negative, if we average the ANEC integral transverse to the geodesic with a
suitable Planck scale smearing function, then a strictly positive result is
obtained in all cases except for the flat spacetime/vacuum solution. This
result suggests --- in agreement with conclusions drawn by Ford and Roman from
entirely independent arguments --- that if traversable wormholes do exist as
solutions to the semiclassical equations, they cannot be macroscopic but must
be ``Planck scale''. A large portion of our paper is devoted to the analysis of
general issues concerning the nature of the semiclassical Einstein equation and
of prescriptions for extracting physically relevant solutions.Comment: 54 pages, 3 figures, uses revtex macros and epsf.tex, to appear in
Phys Rev D. A new appendix has been added showing consistency of our results
with recent results of Visser [gr-qc/9604008]. Some corrections were made to
Appendix A, and several other minor changes to the body of the paper also
were mad
A Survey on Soft Subspace Clustering
Subspace clustering (SC) is a promising clustering technology to identify
clusters based on their associations with subspaces in high dimensional spaces.
SC can be classified into hard subspace clustering (HSC) and soft subspace
clustering (SSC). While HSC algorithms have been extensively studied and well
accepted by the scientific community, SSC algorithms are relatively new but
gaining more attention in recent years due to better adaptability. In the
paper, a comprehensive survey on existing SSC algorithms and the recent
development are presented. The SSC algorithms are classified systematically
into three main categories, namely, conventional SSC (CSSC), independent SSC
(ISSC) and extended SSC (XSSC). The characteristics of these algorithms are
highlighted and the potential future development of SSC is also discussed.Comment: This paper has been published in Information Sciences Journal in 201
Quantum Fluctuations and the Unruh Effect in Strongly-Coupled Conformal Field Theories
Through the AdS/CFT correspondence, we study a uniformly accelerated quark in
the vacuum of strongly-coupled conformal field theories in various dimensions,
and determine the resulting stochastic fluctuations of the quark trajectory.
From the perspective of an inertial observer, these are quantum fluctuations
induced by the gluonic radiation emitted by the accelerated quark. From the
point of view of the quark itself, they originate from the thermal medium
predicted by the Unruh effect. We scrutinize the relation between these two
descriptions in the gravity side of the correspondence, and show in particular
that upon transforming the conformal field theory from Rindler space to the
open Einstein universe, the acceleration horizon disappears from the boundary
theory but is preserved in the bulk. This transformation allows us to directly
connect our calculation of radiation-induced fluctuations in vacuum with the
analysis by de Boer et al. of the Brownian motion of a quark that is on average
static within a thermal medium. Combining this same bulk transformation with
previous results of Emparan, we are also able to compute the stress-energy
tensor of the Unruh thermal medium.Comment: 1+31 pages; v2: reference adde
The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity - I: Dynamical Synchronization and Generalized Inertial Effects
This is the first of a couple of papers in which, by exploiting the
capabilities of the Hamiltonian approach to general relativity, we get a number
of technical achievements that are instrumental both for a disclosure of
\emph{new} results concerning specific issues, and for new insights about
\emph{old} foundational problems of the theory. The first paper includes: 1) a
critical analysis of the various concepts of symmetry related to the
Einstein-Hilbert Lagrangian viewpoint on the one hand, and to the Hamiltonian
viewpoint, on the other. This analysis leads, in particular, to a
re-interpretation of {\it active} diffeomorphisms as {\it passive and
metric-dependent} dynamical symmetries of Einstein's equations, a
re-interpretation which enables to disclose the (nearly unknown) connection of
a subgroup of them to Hamiltonian gauge transformations {\it on-shell}; 2) a
re-visitation of the canonical reduction of the ADM formulation of general
relativity, with particular emphasis on the geometro-dynamical effects of the
gauge-fixing procedure, which amounts to the definition of a \emph{global
(non-inertial) space-time laboratory}. This analysis discloses the peculiar
\emph{dynamical nature} that the traditional definition of distant simultaneity
and clock-synchronization assume in general relativity, as well as the {\it
gauge relatedness} of the "conventions" which generalize the classical
Einstein's convention.Comment: 45 pages, Revtex4, some refinements adde
Cosmological perturbations in Massive Gravity and the Higuchi bound
In de Sitter spacetime there exists an absolute minimum for the mass of a
spin-2 field set by the Higuchi bound m^2 \geq 2H^2. We generalize this bound
to arbitrary spatially flat FRW geometries in the context of the recently
proposed ghost-free models of Massive Gravity with an FRW reference metric, by
performing a Hamiltonian analysis for cosmological perturbations. We find that
the bound generically indicates that spatially flat FRW solutions in FRW
massive gravity, which exhibit a Vainshtein mechanism in the background as
required by consistency with observations, imply that the helicity zero mode is
a ghost. In contradistinction to previous works, the tension between the
Higuchi bound and the Vainshtein mechanism is equally strong regardless of the
equation of state for matter.Comment: 24 pages, typos and conventions correcte
Some Aspects of the AdS/CFT Correspondence
This is a very brief review of some aspects of the AdS/CFT correspondence
with an emphasis on the role of the topology of the boundary and the meaning of
the sum over bulk geometries. To appear in the proceedings of the 73rd Meeting
between Physicists and Mathematicians ``(A)dS/CFT correspondence,'' Strasbourg,
September 11-13, 2003.Comment: LaTeX, 32 pages, 1 figure. To appear in the proceedings of the 73rd
Meeting between Physicists and Mathematicians ``(A)dS/CFT correspondence,''
Strasbourg, September 11-13, 2003. v3: minor changes and references adde
Fields of accelerated sources: Born in de Sitter
This paper deals thoroughly with the scalar and electromagnetic fields of
uniformly accelerated charges in de Sitter spacetime. It gives details and
makes various extensions of our Physical Review Letter from 2002. The basic
properties of the classical Born solutions representing two uniformly
accelerated charges in flat spacetime are first summarized. The worldlines of
uniformly accelerated particles in de Sitter universe are defined and described
in a number of coordinate frames, some of them being of cosmological
significance, the other are tied naturally to the particles. The scalar and
electromagnetic fields due to the accelerated charges are constructed by using
conformal relations between Minkowski and de Sitter space. The properties of
the generalized `cosmological' Born solutions are analyzed and elucidated in
various coordinate systems. In particular, a limiting procedure is demonstrated
which brings the cosmological Born fields in de Sitter space back to the
classical Born solutions in Minkowski space. In an extensive Appendix, which
can be used independently of the main text, nine families of coordinate systems
in de Sitter spacetime are described analytically and illustrated graphically
in a number of conformal diagrams.Comment: 37 pages, 23 figures, reformatted version of the paper published in
JMP; low-resolution figures due to arXiv size restrictions; for the version
with high-resolution figures see http://utf.mff.cuni.cz/~krtous/papers
From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
This article reviews some aspects in the current relationship between
mathematical and numerical General Relativity. Focus is placed on the
description of isolated systems, with a particular emphasis on recent
developments in the study of black holes. Ideas concerning asymptotic flatness,
the initial value problem, the constraint equations, evolution formalisms,
geometric inequalities and quasi-local black hole horizons are discussed on the
light of the interaction between numerical and mathematical relativists.Comment: Topical review commissioned by Classical and Quantum Gravity.
Discussion inspired by the workshop "From Geometry to Numerics" (Paris, 20-24
November, 2006), part of the "General Relativity Trimester" at the Institut
Henri Poincare (Fall 2006). Comments and references added. Typos corrected.
Submitted to Classical and Quantum Gravit
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