71,029 research outputs found
The Generalized Hartle-Hawking Initial State: Quantum Field Theory on Einstein Conifolds
Recent arguments have indicated that the sum over histories formulation of
quantum amplitudes for gravity should include sums over conifolds, a set of
histories with more general topology than that of manifolds. This paper
addresses the consequences of conifold histories in gravitational functional
integrals that also include scalar fields. This study will be carried out
explicitly for the generalized Hartle-Hawking initial state, that is the
Hartle-Hawking initial state generalized to a sum over conifolds. In the
perturbative limit of the semiclassical approximation to the generalized
Hartle-Hawking state, one finds that quantum field theory on Einstein conifolds
is recovered. In particular, the quantum field theory of a scalar field on de
Sitter spacetime with spatial topology is derived from the generalized
Hartle-Hawking initial state in this approximation. This derivation is carried
out for a scalar field of arbitrary mass and scalar curvature coupling.
Additionally, the generalized Hartle-Hawking boundary condition produces a
state that is not identical to but corresponds to the Bunch-Davies vacuum on
de Sitter spacetime. This result cannot be obtained from the original
Hartle-Hawking state formulated as a sum over manifolds as there is no Einstein
manifold with round boundary.Comment: Revtex 3, 31 pages, 4 epsf figure
DESQ: Frequent Sequence Mining with Subsequence Constraints
Frequent sequence mining methods often make use of constraints to control
which subsequences should be mined. A variety of such subsequence constraints
has been studied in the literature, including length, gap, span,
regular-expression, and hierarchy constraints. In this paper, we show that many
subsequence constraints---including and beyond those considered in the
literature---can be unified in a single framework. A unified treatment allows
researchers to study jointly many types of subsequence constraints (instead of
each one individually) and helps to improve usability of pattern mining systems
for practitioners. In more detail, we propose a set of simple and intuitive
"pattern expressions" to describe subsequence constraints and explore
algorithms for efficiently mining frequent subsequences under such general
constraints. Our algorithms translate pattern expressions to compressed finite
state transducers, which we use as computational model, and simulate these
transducers in a way suitable for frequent sequence mining. Our experimental
study on real-world datasets indicates that our algorithms---although more
general---are competitive to existing state-of-the-art algorithms.Comment: Long version of the paper accepted at the IEEE ICDM 2016 conferenc
Stable and Unstable Circular Strings in Inflationary Universes
It was shown by Garriga and Vilenkin that the circular shape of nucleated
cosmic strings, of zero loop-energy in de Sitter space, is stable in the sense
that the ratio of the mean fluctuation amplitude to the loop radius is
constant. This result can be generalized to all expanding strings (of non-zero
loop-energy) in de Sitter space. In other curved spacetimes the situation,
however, may be different.
In this paper we develop a general formalism treating fluctuations around
circular strings embedded in arbitrary spatially flat FRW spacetimes. As
examples we consider Minkowski space, de Sitter space and power law expanding
universes. In the special case of power law inflation we find that in certain
cases the fluctuations grow much slower that the radius of the underlying
unperturbed circular string. The inflation of the universe thus tends to wash
out the fluctuations and to stabilize these strings.Comment: 15 pages Latex, NORDITA 94/14-
Sequences of Bubbles and Holes: New Phases of Kaluza-Klein Black Holes
We construct and analyze a large class of exact five- and six-dimensional
regular and static solutions of the vacuum Einstein equations. These solutions
describe sequences of Kaluza-Klein bubbles and black holes, placed alternately
so that the black holes are held apart by the bubbles. Asymptotically the
solutions are Minkowski-space times a circle, i.e. Kaluza-Klein space, so they
are part of the (\mu,n) phase diagram introduced in hep-th/0309116. In
particular, they occupy a hitherto unexplored region of the phase diagram,
since their relative tension exceeds that of the uniform black string. The
solutions contain bubbles and black holes of various topologies, including
six-dimensional black holes with ring topology S^3 x S^1 and tuboid topology
S^2 x S^1 x S^1. The bubbles support the S^1's of the horizons against
gravitational collapse. We find two maps between solutions, one that relates
five- and six-dimensional solutions, and another that relates solutions in the
same dimension by interchanging bubbles and black holes. To illustrate the
richness of the phase structure and the non-uniqueness in the (\mu,n) phase
diagram, we consider in detail particular examples of the general class of
solutions.Comment: 71 pages, 22 figures, v2: Typos fixed, comment added in sec. 5.
Hawking radiation and thermodynamics of dynamical black holes in phantom dominated universe
The thermodynamic properties of dark energy-dominated universe in the
presence of a black hole are investigated in the general case of a varying
equation-of-state-parameter . We show that all the thermodynamics
quantities are regular at the phantom divide crossing, and particularly the
temperature and the entropy of the dark fluid are always positive definite. We
also study the accretion process of a phantom fluid by black holes and the
conditions required for the validity of the generalized second law of
thermodynamics. As a results we obtain a strictly negative chemical potential
and an equation-of-state parameter Comment: 22 pages,3 figure
Nonholonomic Ricci Flows: II. Evolution Equations and Dynamics
This is the second paper in a series of works devoted to nonholonomic Ricci
flows. By imposing non-integrable (nonholonomic) constraints on the Ricci flows
of Riemannian metrics we can model mutual transforms of generalized
Finsler-Lagrange and Riemann geometries. We verify some assertions made in the
first partner paper and develop a formal scheme in which the geometric
constructions with Ricci flow evolution are elaborated for canonical nonlinear
and linear connection structures. This scheme is applied to a study of
Hamilton's Ricci flows on nonholonomic manifolds and related Einstein spaces
and Ricci solitons. The nonholonomic evolution equations are derived from
Perelman's functionals which are redefined in such a form that can be adapted
to the nonlinear connection structure. Next, the statistical analogy for
nonholonomic Ricci flows is formulated and the corresponding thermodynamical
expressions are found for compact configurations. Finally, we analyze two
physical applications: the nonholonomic Ricci flows associated to evolution
models for solitonic pp-wave solutions of Einstein equations, and compute the
Perelman's entropy for regular Lagrange and analogous gravitational systems.Comment: v2 41 pages, latex2e, 11pt, the variant accepted by J. Math. Phys.
with former section 2 eliminated, a new section 5 with applications in
gravity and geometric mechanics, and modified introduction, conclusion and
new reference
Multi-Trace Operators and the Generalized AdS/CFT Prescription
We show that multi-trace interactions can be consistently incorporated into
an extended AdS/CFT prescription involving the inclusion of generalized
boundary conditions and a modified Legendre transform prescription. We find new
and consistent results by considering a self-contained formulation which
relates the quantization of the bulk theory to the AdS/CFT correspondence and
the perturbation at the boundary by double-trace interactions. We show that
there exist particular double-trace perturbations for which irregular modes are
allowed to propagate as well as the regular ones. We perform a detailed
analysis of many different possible situations, for both minimally and
non-minimally coupled cases. In all situations, we make use of a new constraint
which is found by requiring consistence. In the particular non-minimally
coupled case, the natural extension of the Gibbons-Hawking surface term is
generated.Comment: 27 pages, LaTeX, v.2:minor changes, v.3:comments added, v.4:several
new results, discussions, references and a section of Conclusions added.
Previous results unchanged, v.5: minor changes. Final version to be published
in Phys.Rev.
Curvature perturbations from dimensional decoupling
The scalar modes of the geometry induced by dimensional decoupling are
investigated. In the context of the low energy string effective action,
solutions can be found where the spatial part of the background geometry is the
direct product of two maximally symmetric Euclidean manifolds whose related
scale factors evolve at a dual rate so that the expanding dimensions first
accelerate and then decelerate while the internal dimensions always contract.
After introducing the perturbative treatment of the inhomogeneities, a class of
five-dimensional geometries is discussed in detail. Quasi-normal modes of the
system are derived and the numerical solution for the evolution of the metric
inhomogeneities shows that the fluctuations of the internal dimensions provide
a term that can be interpreted, in analogy with the well-known four-dimensional
situation, as a non-adiabatic pressure density variation. Implications of this
result are discussed with particular attention to string cosmological
scenarios.Comment: 25 pages, 3 figure
Radial asymptotics of Lemaitre-Tolman-Bondi dust models
We examine the radial asymptotic behavior of spherically symmetric
Lemaitre-Tolman-Bondi dust models by looking at their covariant scalars along
radial rays, which are spacelike geodesics parametrized by proper length
, orthogonal to the 4-velocity and to the orbits of SO(3). By introducing
quasi-local scalars defined as integral functions along the rays, we obtain a
complete and covariant representation of the models, leading to an initial
value parametrization in which all scalars can be given by scaling laws
depending on two metric scale factors and two basic initial value functions.
Considering regular "open" LTB models whose space slices allow for a diverging
, we provide the conditions on the radial coordinate so that its
asymptotic limit corresponds to the limit as . The "asymptotic
state" is then defined as this limit, together with asymptotic series expansion
around it, evaluated for all metric functions, covariant scalars (local and
quasi-local) and their fluctuations. By looking at different sets of initial
conditions, we examine and classify the asymptotic states of parabolic,
hyperbolic and open elliptic models admitting a symmetry center. We show that
in the radial direction the models can be asymptotic to any one of the
following spacetimes: FLRW dust cosmologies with zero or negative spatial
curvature, sections of Minkowski flat space (including Milne's space), sections
of the Schwarzschild--Kruskal manifold or self--similar dust solutions.Comment: 44 pages (including a long appendix), 3 figures, IOP LaTeX style.
Typos corrected and an important reference added. Accepted for publication in
General Relativity and Gravitatio
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