5,918 research outputs found
Brane Universe: Global Geometry
The global geometries of bulk vacuum space-times in the brane-universe models
are investigated and classified in terms of geometrical invariants. The
corresponding Carter-Penrose diagrams and embedding diagrams are constructed.
It is shown that for a given energy-momentum induced on the brane there can be
different types of global geometries depending on the signs of a bulk
cosmological term and surface energy density of the brane (the sign of the
latter does not influence the internal cosmological evolution). It is shown
that in the Randall-Sundrum scenario it is possible to have an asymmetric
hierarchy splitting even with a -symmetric matching of "our" brane to the
bulk.Comment: 23 pages, 34 figures, Talk given at the "Invisible Universe
International Conference ", Paris, June 29 -July 3, 200
Fibers and global geometry of functions
Since the seminal work of Ambrosetti and Prodi, the study of global folds was
enriched by geometric concepts and extensions accomodating new examples. We
present the advantages of considering fibers, a construction dating to Berger
and Podolak's view of the original theorem. A description of folds in terms of
properties of fibers gives new perspective to the usual hypotheses in the
subject. The text is intended as a guide, outlining arguments and stating
results which will be detailed elsewhere
Global geometry of two-dimensional charged black holes
The semiclassical geometry of charged black holes is studied in the context
of a two-dimensional dilaton gravity model where effects due to pair-creation
of charged particles can be included in a systematic way. The classical
mass-inflation instability of the Cauchy horizon is amplified and we find that
gravitational collapse of charged matter results in a spacelike singularity
that precludes any extension of the spacetime geometry. At the classical level,
a static solution describing an eternal black hole has timelike singularities
and multiple asymptotic regions. The corresponding semiclassical solution, on
the other hand, has a spacelike singularity and a Penrose diagram like that of
an electrically neutral black hole. Extremal black holes are destabilized by
pair-creation of charged particles. There is a maximally charged solution for a
given black hole mass but the corresponding geometry is not extremal. Our
numerical data exhibits critical behavior at the threshold for black hole
formation.Comment: REVTeX, 13 pages, 12 figures; Reference adde
Sets of unique continuation for heat equation
We study nodal lines of solutions to the heat equations. We are interested in
the global geometry of nodal sets, in the whole domain of definition of the
solution. The local structure of nodal sets is a well understander subject,
while the global geometry of nodal lines is much less clear. We give a detailed
analysis of a simple component of a nodal set of a solution of the heat
equation
The global geometry of the moduli space of curves
This is a survey written for the Proceedings of the AMS Summer Institute in
Algebraic Geometry held in Seattle in 2005. Topics discussed in the survey
include the ample and the effective cone of the moduli space of curves, Kodaira
dimension, Slope Conjecture, log canonical models etc.Comment: 23 pages. Minor revisions. To appear in the Proceedings of the AMS
Summer Research Institute in Algebraic Geometry-Seattle 200
Global geometry of the 2+1 rotating black hole
The generic rotating BTZ black hole, obtained by identifications in AdS3
space through a discrete subgroup of its isometry group, is investigated within
a Lie theoretical context. This space is found to admit a foliation by
two-dimensional leaves, orbits of a two-parameter subgroup of SL(2,R) and
invariant under the BTZ identification subgroup. A global expression for the
metric is derived, allowing a better understanding of the causal structure of
the black hole.Comment: 9 pages, 1 figur
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