58 research outputs found
Cosmological spacetimes not covered by a constant mean curvature slicing
We show that there exist maximal globally hyperbolic solutions of the
Einstein-dust equations which admit a constant mean curvature Cauchy surface,
but are not covered by a constant mean curvature foliation.Comment: 11 page
On completeness of orbits of Killing vector fields
A Theorem is proved which reduces the problem of completeness of orbits of
Killing vector fields in maximal globally hyperbolic, say vacuum, space--times
to some properties of the orbits near the Cauchy surface. In particular it is
shown that all Killing orbits are complete in maximal developements of
asymptotically flat Cauchy data, or of Cauchy data prescribed on a compact
manifold. This result gives a significant strengthening of the uniqueness
theorems for black holes.Comment: 16 pages, Latex, preprint NSF-ITP-93-4
Topology of the Future Chronological Boundary: Universality for Spacelike Boundaries
A method is presented for imputing a topology for any chronological set,
i.e., a set with a chronology relation, such as a spacetime or a spacetime with
some sort of boundary. This topology is shown to have several good properties,
such as replicating the manifold topology for a spacetime and replicating the
expected topology for some simple examples of spacetime-with-boundary; it also
allows for a complete categorical characterization, in topological categories,
of the Future Causal Boundary construction of Geroch, Kronheimer, and Penrose,
showing that construction to have a universal property for future-completing
chronological sets with spacelike boundaries. Rigidity results are given for
any reasonable future completion of a spacetime, in terms of the GKP boundary:
In the imputed topology, any such boundary must be homeomorphic to the GKP
boundary (if all points have indecomposable pasts) or to a topological quotient
of a closely related boundary (if boundaries are spacelike). A large class of
warped-product-type spacetimes with spacelike boundaries is examined,
calculating the GKP and other possible boundaries, and showing that the imputed
topology gives expected results; included among these are the Schwarzschild
singularity and those Robertson-Walker singularities which are spacelike.Comment: 56 pages, AMS-TeX; 1 page of figure captions (TeX); 22 figures, EPS
format; to be published in Quantum Class. Grav.; principal reason for
replacement is to have the figures included (also, introduction is expanded
slightly, and one example is simplified
Causal Relationship: a new tool for the causal characterization of Lorentzian manifolds
We define and study a new kind of relation between two diffeomorphic
Lorentzian manifolds called {\em causal relation}, which is any diffeomorphism
characterized by mapping every causal vector of the first manifold onto a
causal vector of the second. We perform a thorough study of the mathematical
properties of causal relations and prove in particular that two given
Lorentzian manifolds (say and ) may be causally related only in one
direction (say from to , but not from to ). This leads us to the
concept of causally equivalent (or {\em isocausal} in short) Lorentzian
manifolds as those mutually causally related. This concept is more general and
of a more basic nature than the conformal relationship, because we prove the
remarkable result that a conformal relation \f is characterized by the fact
of being a causal relation of the {\em particular} kind in which both \f and
\f^{-1} are causal relations. For isocausal Lorentzian manifolds there are
one-to-one correspondences, which sometimes are non-trivial, between several
classes of their respective future (and past) objects. A more important feature
of isocausal Lorentzian manifolds is that they satisfy the same causality
constraints. This indicates that the causal equivalence provides a possible
characterization of the {\it basic causal structure}, in the sense of mutual
causal compatibility, for Lorentzian manifolds. Thus, we introduce a partial
order for the equivalence classes of isocausal Lorentzian manifolds providing a
classification of spacetimes in terms of their causal properties, and a
classification of all the causal structures that a given fixed manifold can
have. A full abstract inside the paper.Comment: 47 pages, 10 figures. Version to appear in Classical and Quantum
Gravit
The Causal Boundary of spacetimes revisited
We present a new development of the causal boundary of spacetimes, originally
introduced by Geroch, Kronheimer and Penrose. Given a strongly causal spacetime
(or, more generally, a chronological set), we reconsider the GKP ideas to
construct a family of completions with a chronology and topology extending the
original ones. Many of these completions present undesirable features, like
those appeared in previous approaches by other authors. However, we show that
all these deficiencies are due to the attachment of an ``excessively big''
boundary. In fact, a notion of ``completion with minimal boundary'' is then
introduced in our family such that, when we restrict to these minimal
completions, which always exist, all previous objections disappear. The optimal
character of our construction is illustrated by a number of satisfactory
properties and examples.Comment: 37 pages, 10 figures; Definition 6.1 slightly modified; multiple
minor changes; one figure added and another replace
On the Singularity Structure and Stability of Plane Waves
We describe various aspects of plane wave backgrounds. In particular, we make
explicit a simple criterion for singularity by establishing a relation between
Brinkmann metric entries and diffeomorphism-invariant curvature information. We
also address the stability of plane wave backgrounds by analyzing the
fluctuations of generic scalar modes. We focus our attention on cases where
after fixing the light-cone gauge the resulting world sheet fields appear to
have negative "mass terms". We nevertheless argue that these backgrounds may be
stable.Comment: 21 pages, 1 figur
Geo-environmental mapping using physiographic analysis: constraints on the evaluation of land instability and groundwater pollution hazards in the Metropolitan District of Campinas, Brazil
Geo-environmental terrain assessments and territorial zoning are useful tools for the formulation and implementation of environmental management instruments (including policy-making, planning, and enforcement of statutory regulations). They usually involve a set of procedures and techniques for delimitation, characterisation and classification of terrain units. However, terrain assessments and zoning exercises are often costly and time-consuming, particularly when encompassing large areas, which in many cases prevent local agencies in developing countries from properly benefiting from such assessments. In the present paper, a low-cost technique based on the analysis of texture of satellite imagery was used for delimitation of terrain units. The delimited units were further analysed in two test areas situated in Southeast Brazil to provide estimates of land instability and the vulnerability of groundwater to pollution hazards. The implementation incorporated procedures for inferring the influences and potential implications of tectonic fractures and other discontinuities on ground behaviour and local groundwater flow. Terrain attributes such as degree of fracturing, bedrock lithology and weathered materials were explored as indicators of ground properties. The paper also discusses constraints on- and limitations of- the approaches taken
Dynamical locality and covariance: What makes a physical theory the same in all spacetimes?
The question of what it means for a theory to describe the same physics on
all spacetimes (SPASs) is discussed. As there may be many answers to this
question, we isolate a necessary condition, the SPASs property, that should be
satisfied by any reasonable notion of SPASs. This requires that if two theories
conform to a common notion of SPASs, with one a subtheory of the other, and are
isomorphic in some particular spacetime, then they should be isomorphic in all
globally hyperbolic spacetimes (of given dimension). The SPASs property is
formulated in a functorial setting broad enough to describe general physical
theories describing processes in spacetime, subject to very minimal
assumptions. By explicit constructions, the full class of locally covariant
theories is shown not to satisfy the SPASs property, establishing that there is
no notion of SPASs encompassing all such theories. It is also shown that all
locally covariant theories obeying the time-slice property possess two local
substructures, one kinematical (obtained directly from the functorial
structure) and the other dynamical (obtained from a natural form of dynamics,
termed relative Cauchy evolution). The covariance properties of relative Cauchy
evolution and the kinematic and dynamical substructures are analyzed in detail.
Calling local covariant theories dynamically local if their kinematical and
dynamical local substructures coincide, it is shown that the class of
dynamically local theories fulfills the SPASs property. As an application in
quantum field theory, we give a model independent proof of the impossibility of
making a covariant choice of preferred state in all spacetimes, for theories
obeying dynamical locality together with typical assumptions.Comment: 60 pages, LaTeX. Version to appear in Annales Henri Poincar
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