18 research outputs found
Cosmic censorship of smooth structures
It is observed that on many 4-manifolds there is a unique smooth structure
underlying a globally hyperbolic Lorentz metric. For instance, every
contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric
is diffeomorphic to the standard . Similarly, a smooth 4-manifold
homeomorphic to the product of a closed oriented 3-manifold and and
admitting a globally hyperbolic Lorentz metric is in fact diffeomorphic to
. Thus one may speak of a censorship imposed by the global
hyperbolicty assumption on the possible smooth structures on
-dimensional spacetimes.Comment: 5 pages; V.2 - title changed, minor edits, references adde
A MODEST review
We present an account of the state of the art in the fields explored by the
research community invested in 'Modeling and Observing DEnse STellar systems'.
For this purpose, we take as a basis the activities of the MODEST-17
conference, which was held at Charles University, Prague, in September 2017.
Reviewed topics include recent advances in fundamental stellar dynamics,
numerical methods for the solution of the gravitational N-body problem,
formation and evolution of young and old star clusters and galactic nuclei,
their elusive stellar populations, planetary systems, and exotic compact
objects, with timely attention to black holes of different classes of mass and
their role as sources of gravitational waves.
Such a breadth of topics reflects the growing role played by collisional
stellar dynamics in numerous areas of modern astrophysics. Indeed, in the next
decade, many revolutionary instruments will enable the derivation of positions
and velocities of individual stars in the Milky Way and its satellites and will
detect signals from a range of astrophysical sources in different portions of
the electromagnetic and gravitational spectrum, with an unprecedented
sensitivity. On the one hand, this wealth of data will allow us to address a
number of long-standing open questions in star cluster studies; on the other
hand, many unexpected properties of these systems will come to light,
stimulating further progress of our understanding of their formation and
evolution.Comment: 42 pages; accepted for publication in 'Computational Astrophysics and
Cosmology'. We are much grateful to the organisers of the MODEST-17
conference (Charles University, Prague, September 2017). We acknowledge the
input provided by all MODEST-17 participants, and, more generally, by the
members of the MODEST communit
Fibred knots and disks with clasps.
It is known that every closed, orientable 3-manifold contains a fi-bered knot—a simple closed curve whose complement is a surface bundle over S1. For K such a fibered knot in a rational homology 3-sphere M it is shown that for any compact submanifold X of M containing K as a null-homologous subset, each component of ∂X is compressible in M−K. If K is a doubled knot (bounds a disk with one clasp) then it follows that K is a double of the trivial knot. More generally, it follows that the genus of X (minimum number of one-handles) is less than the genus of M