2,914 research outputs found
The Jang equation reduction of the spacetime positive energy theorem in dimensions less than eight
We extend the Jang equation proof of the positive energy theorem due to R.
Schoen and S.-T. Yau from dimension to dimensions . This
requires us to address several technical difficulties that are not present when
. The regularity and decay assumptions for the initial data sets to which
our argument applies are weaker than those of R. Schoen and S.-T. Yau. In
recent joint work with L.-H. Huang, D. Lee, and R. Schoen we have given a
different proof of the full positive mass theorem in dimensions .
We pointed out that this theorem can alternatively be derived from our density
argument and the positive energy theorem of the present paper.Comment: All comments welcome! Final version to appear in Comm. Math. Phy
A generalization of Hawking's black hole topology theorem to higher dimensions
Hawking's theorem on the topology of black holes asserts that cross sections
of the event horizon in 4-dimensional asymptotically flat stationary black hole
spacetimes obeying the dominant energy condition are topologically 2-spheres.
This conclusion extends to outer apparent horizons in spacetimes that are not
necessarily stationary. In this paper we obtain a natural generalization of
Hawking's results to higher dimensions by showing that cross sections of the
event horizon (in the stationary case) and outer apparent horizons (in the
general case) are of positive Yamabe type, i.e., admit metrics of positive
scalar curvature. This implies many well-known restrictions on the topology,
and is consistent with recent examples of five dimensional stationary black
hole spacetimes with horizon topology . The proof is inspired
by previous work of Schoen and Yau on the existence of solutions to the Jang
equation (but does not make direct use of that equation).Comment: 8 pages, latex2e, references updated, minor corrections, to appear in
Communications in Mathematical Physic
Existence, Regularity, and Properties of Generalized Apparent Horizons
We prove a conjecture of Tom Ilmanen's and Hubert Bray's regarding the
existence of the outermost generalized apparent horizon in an initial data set
and that it is outer area minimizing.Comment: 16 pages, thoroughly revised, no major changes, to appear in Comm.
Math. Phy
Gluing Initial Data Sets for General Relativity
We establish an optimal gluing construction for general relativistic initial
data sets. The construction is optimal in two distinct ways. First, it applies
to generic initial data sets and the required (generically satisfied)
hypotheses are geometrically and physically natural. Secondly, the construction
is completely local in the sense that the initial data is left unaltered on the
complement of arbitrarily small neighborhoods of the points about which the
gluing takes place. Using this construction we establish the existence of
cosmological, maximal globally hyperbolic, vacuum space-times with no constant
mean curvature spacelike Cauchy surfaces.Comment: Final published version - PRL, 4 page
Maintaining Health Insurance During a Recession: Likely COBRA Eligibility
Assesses laid-off workers' eligibility and financial ability to extend employer-sponsored insurance through COBRA. Recommends extending COBRA and providing premium assistance, as well as expanding Medicaid and State Children's Health Insurance Programs
Depletion potentials near geometrically structured substrates
Using the recently developed so-called White Bear version of Rosenfeld's
Fundamental Measure Theory we calculate the depletion potentials between a
hard-sphere colloidal particle in a solvent of small hard spheres and simple
models of geometrically structured substrates: a right-angled wedge or edge. In
the wedge geometry, there is a strong attraction beyond the corresponding one
near a planar wall that significantly influences the structure of colloidal
suspensions in wedges. In accordance with an experimental study, for the edge
geometry we find a free energy barrier of the order of several which
repels a big colloidal particle from the edge.Comment: 7 pages, 7 figure
Rite of Passage? Why Young Adults Become Uninsured and How New Policies Can Help
Assesses the scope of the health insurance problem facing young adults, its causes and implications, and offers policy changes that could help them stay insured as they make the transition to independent living
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