6,775 research outputs found
Piecewise Conserved Quantities
We review the treatment of conservation laws in spacetimes that are glued
together in various ways, thus adding a boundary term to the usual conservation
laws. Several examples of such spacetimes will be described, including the
joining of Schwarzschild spacetimes of different masses, and the possibility of
joining regions of different signatures. The opportunity will also be taken to
explore some of the less obvious properties of Lorentzian vector calculus.Comment: To appear in Gravity and the Quantum, Springer 2017
(http://www.springer.com/in/book/9783319516998
Tensor Distributions in the Presence of Degenerate Metrics
Tensor distributions and their derivatives are described without assuming the
presence of a metric. This provides a natural framework for discussing tensor
distributions on manifolds with degenerate metrics, including in particular
metrics which change signature.Comment: REVTeX, 19 pages; submitted to IJMP
Interpolating Between Topologies: Casimir Energies
A set of models is considered which, in a certain sense, interpolates between
1+1 free quantum field theories on topologically distinct backgrounds. The
intermediate models may be termed free quantum field theories, though they are
certainly not local. Their ground state energies are computed and shown to be
finite. The possible relevance to changing spacetime topologies is discussed.Comment: 7 pages Revtex, Note and reference adde
Note on Signature Change and Colombeau Theory
Recent work alludes to various `controversies' associated with signature
change in general relativity. As we have argued previously, these are in fact
disagreements about the (often unstated) assumptions underlying various
possible approaches. The choice between approaches remains open.Comment: REVTex, 3 pages; to appear in GR
Covariant Derivatives on Null Submanifolds
The degenerate nature of the metric on null hypersurfaces makes it difficult
to define a covariant derivative on null submanifolds. Recent approaches using
decomposition to define a covariant derivative on null hypersurfaces are
investigated, with examples demonstrating the limitations of the methods.
Motivated by Geroch's work on asymptotically flat spacetimes, conformal
transformations are used to construct a covariant derivative on null
hypersurfaces, and a condition on the Ricci tensor is given to determine when
this construction can be used. Several examples are given, including the
construction of a covariant derivative operator for the class of spherically
symmetric hypersurfaces.Comment: 13 pages, no figure
Revisiting Guerry's data: Introducing spatial constraints in multivariate analysis
Standard multivariate analysis methods aim to identify and summarize the main
structures in large data sets containing the description of a number of
observations by several variables. In many cases, spatial information is also
available for each observation, so that a map can be associated to the
multivariate data set. Two main objectives are relevant in the analysis of
spatial multivariate data: summarizing covariation structures and identifying
spatial patterns. In practice, achieving both goals simultaneously is a
statistical challenge, and a range of methods have been developed that offer
trade-offs between these two objectives. In an applied context, this
methodological question has been and remains a major issue in community
ecology, where species assemblages (i.e., covariation between species
abundances) are often driven by spatial processes (and thus exhibit spatial
patterns). In this paper we review a variety of methods developed in community
ecology to investigate multivariate spatial patterns. We present different ways
of incorporating spatial constraints in multivariate analysis and illustrate
these different approaches using the famous data set on moral statistics in
France published by Andr\'{e}-Michel Guerry in 1833. We discuss and compare the
properties of these different approaches both from a practical and theoretical
viewpoint.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS356 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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