1,679 research outputs found
On marginally outer trapped surfaces in stationary and static spacetimes
In this paper we prove that for any spacelike hypersurface containing an
untrapped barrier in a stationary spacetime satisfying the null energy
condition, any marginally outer trapped surface cannot lie in the exterior
region where the stationary Killing vector is timelike. In the static case we
prove that any marginally outer trapped surface cannot penetrate into the
exterior region where the static Killing vector is timelike. In fact, we prove
these result at an initial data level, without even assuming existence of a
spacetime. The proof relies on a powerful theorem by Andersson and Metzger on
existence of an outermost marginally outer trapped surface.Comment: 22 pages, 3 figures; 1 reference added, 1 figure changed, other minor
change
A knowledge-based approach to VLSI-design in an open CAD-environment
A knowledge-based approach is suggested to assist a designer in the increasingly complex task of generating VLSI-chips from abstract, high-level specifications of the system. The complexity of designing VLSI-circuits has reached a level where computer-based assistance has become indispensable. Not all of the design tasks allow for algorithmic solutions. AI technique can be used, in order to support the designer with computer-aided tools for tasks not suited for algorithmic approaches. The approach described in this paper is based upon the underlying characteristics of VLSI design processes in general, comprising all stages of the design. A universal model is presented, accompanied with a recording method for the acquisition of design knowledge - strategic and task-specific - in terms of the design actions involved and their effects on the design itself. This method is illustrated by a simple design example: the implementation of the logical EXOR-component. Finally suggestions are made for obtaining a universally usable architecture of a knowledge-based system for VLSI-design
Singularity-Free Cylindrical Cosmological Model
A cylindrically symmetric perfect fluid spacetime with no curvature
singularity is shown. The equation of state for the perfect fluid is that of a
stiff fluid. The metric is diagonal and non-separable in comoving coordinates
for the fluid. It is proven that the spacetime is geodesically complete and
globally hyperbolic.Comment: LaTeX 2e, 8 page
The Wahlquist-Newman solution
Based on a geometrical property which holds both for the Kerr metric and for
the Wahlquist metric we argue that the Kerr metric is a vacuum subcase of the
Wahlquist perfect-fluid solution. The Kerr-Newman metric is a physically
preferred charged generalization of the Kerr metric. We discuss which geometric
property makes this metric so special and claim that a charged generalization
of the Wahlquist metric satisfying a similar property should exist. This is the
Wahlquist-Newman metric, which we present explicitly in this paper. This family
of metrics has eight essential parameters and contains the Kerr-Newman-de
Sitter and the Wahlquist metrics, as well as the whole Pleba\'nski limit of the
rotating C-metric, as particular cases. We describe the basic geometric
properties of the Wahlquist-Newman metric, including the electromagnetic field
and its sources, the static limit of the family and the extension of the
spacetime across the horizon.Comment: LaTeX, 18 pages, no figures. Accepted for publication in Phys. Rev.
A counter-example to a recent version of the Penrose conjecture
By considering suitable axially symmetric slices on the Kruskal spacetime, we
construct counterexamples to a recent version of the Penrose inequality in
terms of so-called generalized apparent horizons.Comment: 12 pages. Appendix added with technical details. To appear in
Classical and Quantum Gravit
Influence of general convective motions on the exterior of isolated rotating bodies in equilibrium
The problem of describing isolated rotating bodies in equilibrium in General
Relativity has so far been treated under the assumption of the circularity
condition in the interior of the body. For a fluid without energy flux, this
condition implies that the fluid flow moves only along the angular direction,
i.e. there is no convection. Using this simplification, some recent studies
have provided us with uniqueness and existence results for asymptotically flat
vacuum exterior fields given the interior sources. Here, the generalisation of
the problem to include general sources is studied. It is proven that the
convective motions have no direct influence on the exterior field, and hence,
that the aforementioned results on uniqueness and existence of exterior fields
apply equally in the general case.Comment: 8 pages, LaTex, uses iopart style files. To appear in Class. Quatum
Gra
On the dark energy rest frame and the CMB
Dark energy is usually parametrized as a perfect fluid with negative pressure
and a certain equation of state. Besides, it is supposed to interact very
weakly with the rest of the components of the universe and, as a consequence,
there is no reason to expect it to have the same large-scale rest frame as
matter and radiation. Thus, apart from its equation of state and its energy
density one should also consider its velocity as a free parameter
to be determined by observations. This velocity defines a cosmological
preferred frame, so the universe becomes anisotropic and, therefore, the CMB
temperature fluctuations will be affected, modifying mainly the dipole and the
quadrupole.Comment: 4 pages. Contribution to the proceedings of Spanish Relativity
Meeting 2008, Salamanca, Spain, 15-19 September 200
Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants
Recent progress in autoencoder-based sparse identification of nonlinear
dynamics (SINDy) under constraints allows joint discoveries of
governing equations and latent coordinate systems from spatio-temporal data,
including simulated video frames. However, it is challenging for -based
sparse inference to perform correct identification for real data due to the
noisy measurements and often limited sample sizes. To address the data-driven
discovery of physics in the low-data and high-noise regimes, we propose
Bayesian SINDy autoencoders, which incorporate a hierarchical Bayesian
sparsifying prior: Spike-and-slab Gaussian Lasso. Bayesian SINDy autoencoder
enables the joint discovery of governing equations and coordinate systems with
a theoretically guaranteed uncertainty estimate. To resolve the challenging
computational tractability of the Bayesian hierarchical setting, we adapt an
adaptive empirical Bayesian method with Stochatic gradient Langevin dynamics
(SGLD) which gives a computationally tractable way of Bayesian posterior
sampling within our framework. Bayesian SINDy autoencoder achieves better
physics discovery with lower data and fewer training epochs, along with valid
uncertainty quantification suggested by the experimental studies. The Bayesian
SINDy autoencoder can be applied to real video data, with accurate physics
discovery which correctly identifies the governing equation and provides a
close estimate for standard physics constants like gravity , for example, in
videos of a pendulum.Comment: 28 pages, 11 figure
Symmetry-preserving matchings
In the literature, the matchings between spacetimes have been most of the
times implicitly assumed to preserve some of the symmetries of the problem
involved. But no definition for this kind of matching was given until recently.
Loosely speaking, the matching hypersurface is restricted to be tangent to the
orbits of a desired local group of symmetries admitted at both sides of the
matching and thus admitted by the whole matched spacetime. This general
definition is shown to lead to conditions on the properties of the preserved
groups. First, the algebraic type of the preserved group must be kept at both
sides of the matching hypersurface. Secondly, the orthogonal transivity of
two-dimensional conformal (in particular isometry) groups is shown to be
preserved (in a way made precise below) on the matching hypersurface. This
result has in particular direct implications on the studies of axially
symmetric isolated bodies in equilibrium in General Relativity, by making up
the first condition that determines the suitability of convective interiors to
be matched to vacuum exteriors. The definition and most of the results
presented in this paper do not depend on the dimension of the manifolds
involved nor the signature of the metric, and their applicability to other
situations and other higher dimensional theories is manifest.Comment: LaTeX, 19 page
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