572 research outputs found
Theorems on existence and global dynamics for the Einstein equations
This article is a guide to theorems on existence and global dynamics of
solutions of the Einstein equations. It draws attention to open questions in
the field. The local-in-time Cauchy problem, which is relatively well
understood, is surveyed. Global results for solutions with various types of
symmetry are discussed. A selection of results from Newtonian theory and
special relativity that offer useful comparisons is presented. Treatments of
global results in the case of small data and results on constructing spacetimes
with prescribed singularity structure or late-time asymptotics are given. A
conjectural picture of the asymptotic behaviour of general cosmological
solutions of the Einstein equations is built up. Some miscellaneous topics
connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living
Rev. Rel. 5 (2002)
The entropy of black holes: a primer
After recalling the definition of black holes, and reviewing their energetics
and their classical thermodynamics, one expounds the conjecture of Bekenstein,
attributing an entropy to black holes, and the calculation by Hawking of the
semi-classical radiation spectrum of a black hole, involving a thermal
(Planckian) factor. One then discusses the attempts to interpret the black-hole
entropy as the logarithm of the number of quantum micro-states of a macroscopic
black hole, with particular emphasis on results obtained within string theory.
After mentioning the (technically cleaner, but conceptually more intricate)
case of supersymmetric (BPS) black holes and the corresponding counting of the
degeneracy of Dirichlet-brane systems, one discusses in some detail the
``correspondence'' between massive string states and non-supersymmetric
Schwarzschild black holes.Comment: 51 pages, 4 figures, talk given at the "Poincare seminar" (Paris, 6
December 2003), to appear in Poincare Seminar 2003 (Birkhauser
Brane-world black holes and the scale of gravity
A particle in four dimensions should behave like a classical black hole if
the horizon radius is larger than the Compton wavelength or, equivalently, if
its degeneracy (measured by entropy in units of the Planck scale) is large. For
spherically symmetric black holes in 4 + d dimensions, both arguments again
lead to a mass threshold MC and degeneracy scale Mdeg of the order of the
fundamental scale of gravity MG. In the brane-world, deviations from the
Schwarzschild metric induced by bulk effects alter the horizon radius and
effective four-dimensional Euclidean action in such a way that MC \simeq Mdeg
might be either larger or smaller than MG. This opens up the possibility that
black holes exist with a mass smaller than MG and might be produced at the LHC
even if M>10 TeV, whereas effects due to bulk graviton exchanges remain
undetectable because suppressed by inverse powers of MG. Conversely, even if
black holes are not found at the LHC, it is still possible that MC>MG and MG
\simeq 1TeV.Comment: 4 pages, no figur
Theorems on existence and global dynamics for the Einstein equations
This article is a guide to theorems on existence and global dynamics of
solutions of the Einstein equations. It draws attention to open questions in
the field. The local in time Cauchy problem, which is relatively well
understood, is surveyed. Global results for solutions with various types of
symmetry are discussed. A selection of results from Newtonian theory and
special relativity which offer useful comparisons is presented. Treatments of
global results in the case of small data and results on constructing spacetimes
with prescribed singularity structure are given. A conjectural picture of the
asymptotic behaviour of general cosmological solutions of the Einstein
equations is built up. Some miscellaneous topics connected with the main theme
are collected in a separate section.Comment: 54 pages, submitted to Living Reviews in Relativit
The EROS2 search for microlensing events towards the spiral arms: the complete seven season results
The EROS-2 project has been designed to search for microlensing events
towards any dense stellar field. The densest parts of the Galactic spiral arms
have been monitored to maximize the microlensing signal expected from the stars
of the Galactic disk and bulge. 12.9 million stars have been monitored during 7
seasons towards 4 directions in the Galactic plane, away from the Galactic
center. A total of 27 microlensing event candidates have been found. Estimates
of the optical depths from the 22 best events are provided. A first order
interpretation shows that simple Galactic models with a standard disk and an
elongated bulge are in agreement with our observations. We find that the
average microlensing optical depth towards the complete EROS-cataloged stars of
the spiral arms is , a number that is
stable when the selection criteria are moderately varied. As the EROS catalog
is almost complete up to , the optical depth estimated for the
sub-sample of bright target stars with () is easier to interpret. The set of microlensing events
that we have observed is consistent with a simple Galactic model. A more
precise interpretation would require either a better knowledge of the distance
distribution of the target stars, or a simulation based on a Galactic model.
For this purpose, we define and discuss the concept of optical depth for a
given catalog or for a limiting magnitude.Comment: 22 pages submitted to Astronomy & Astrophysic
Dynamics of Disks and Warps
This chapter reviews theoretical work on the stellar dynamics of galaxy
disks. All the known collective global instabilities are identified, and their
mechanisms described in terms of local wave mechanics. A detailed discussion of
warps and other bending waves is also given. The structure of bars in galaxies,
and their effect on galaxy evolution, is now reasonably well understood, but
there is still no convincing explanation for their origin and frequency. Spiral
patterns have long presented a special challenge, and ideas and recent
developments are reviewed. Other topics include scattering of disk stars and
the survival of thin disks.Comment: Chapter accepted to appear in Planets, Stars and Stellar Systems, vol
5, ed G. Gilmore. 32 pages, 17 figures. Includes minor corrections made in
proofs. Uses emulateapj.st
Sequential formation and resolution of multiple rosettes drive embryo remodelling after implantation
The morphogenetic remodelling of embryo architecture after implantation culminates in pro-amniotic cavity formation. Despite its key importance, how this transformation occurs remains unknown. Here, we apply high-resolution imaging of embryos developing in vivo and in vitro, spatial RNA sequencing and 3D trophoblast stem cell models to determine the sequence and mechanisms of these remodelling events. We show that cavitation of the embryonic tissue is followed by folding of extra-embryonic tissue to mediate the formation of a second extra-embryonic cavity. Concomitantly, at the boundary between embryonic and extra-embryonic tissues, a hybrid 3D rosette forms. Resolution of this rosette enables the embryonic cavity to invade the extra-embryonic tissue. Subsequently, β1-integrin signalling mediates the formation of multiple extra-embryonic 3D rosettes. Podocalyxin exocytosis leads to their polarized resolution, permitting the extension of embryonic and extra-embryonic cavities and their fusion into a unified pro-amniotic cavity. These morphogenetic transformations of embryogenesis reveal a previously unappreciated mechanism for lumen expansion and fusionThe M.Z.G lab is supported by grants from the European Research Council (669198) and the Welcome Trust (098287/Z/12/Z) and the EU Horizon 2020 Marie Sklodowska-Curie actions (ImageInLife,721537). C.K is supported by BBSRC Doctoral training studentship
The Einstein-Vlasov System/Kinetic Theory
The main purpose of this article is to provide a guide to theorems on global
properties of solutions to the Einstein--Vlasov system. This system couples
Einstein's equations to a kinetic matter model. Kinetic theory has been an
important field of research during several decades in which the main focus has
been on non-relativistic and special relativistic physics, i.e., to model the
dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In
1990, Rendall and Rein initiated a mathematical study of the Einstein--Vlasov
system. Since then many theorems on global properties of solutions to this
system have been established.Comment: Published version http://www.livingreviews.org/lrr-2011-
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