5,518 research outputs found
On the Gannon-Lee Singularity Theorem in Higher Dimensions
The Gannon-Lee singularity theorems give well-known restrictions on the
spatial topology of singularity-free (i.e., nonspacelike geodesically
complete), globally hyperbolic spacetimes. In this paper, we revisit these
classic results in the light of recent developments, especially the failure in
higher dimensions of a celebrated theorem by Hawking on the topology of black
hole horizons. The global hyperbolicity requirement is weakened, and we expand
the scope of the main results to allow for the richer variety of spatial
topologies which are likely to occur in higher-dimensional spacetimes.Comment: 13 pages, no figures, to appear in Class. Quantum Gra
The Cosmic Censor Forbids Naked Topology
For any asymptotically flat spacetime with a suitable causal structure
obeying (a weak form of) Penrose's cosmic censorship conjecture and satisfying
conditions guaranteeing focusing of complete null geodesics, we prove that
active topological censorship holds. We do not assume global hyperbolicity, and
therefore make no use of Cauchy surfaces and their topology. Instead, we
replace this with two underlying assumptions concerning the causal structure:
that no compact set can signal to arbitrarily small neighbourhoods of spatial
infinity (``-avoidance''), and that no future incomplete null geodesic is
visible from future null infinity. We show that these and the focusing
condition together imply that the domain of outer communications is simply
connected. Furthermore, we prove lemmas which have as a consequence that if a
future incomplete null geodesic were visible from infinity, then given our
-avoidance assumption, it would also be visible from points of spacetime
that can communicate with infinity, and so would signify a true naked
singularity.Comment: To appear in CQG, this improved version contains minor revisions to
incorporate referee's suggestions. Two revised references. Plain TeX, 12
page
A Strong Maximum Principle for Weak Solutions of Quasi-Linear Elliptic Equations with Applications to Lorentzian and Riemannian Geometry
The strong maximum principle is proved to hold for weak (in the sense of
support functions) sub- and super-solutions to a class of quasi-linear elliptic
equations that includes the mean curvature equation for spacelike
hypersurfaces in a Lorentzian manifold. As one application a Lorentzian warped
product splitting theorem is given.Comment: 37 pages, 1 figure, ams-latex using eepi
Rigid Singularity Theorem in Globally Hyperbolic Spacetimes
We show the rigid singularity theorem, that is, a globally hyperbolic
spacetime satisfying the strong energy condition and containing past trapped
sets, either is timelike geodesically incomplete or splits isometrically as
space time. This result is related to Yau's Lorentzian splitting
conjecture.Comment: 3 pages, uses revtex.sty, to appear in Physical Review
A simple proof of the recent generalisations of Hawking's black hole topology theorem
A key result in four dimensional black hole physics, since the early 1970s,
is Hawking's topology theorem asserting that the cross-sections of an "apparent
horizon", separating the black hole region from the rest of the spacetime, are
topologically two-spheres. Later, during the 1990s, by applying a variant of
Hawking's argument, Gibbons and Woolgar could also show the existence of a
genus dependent lower bound for the entropy of topological black holes with
negative cosmological constant. Recently Hawking's black hole topology theorem,
along with the results of Gibbons and Woolgar, has been generalised to the case
of black holes in higher dimensions. Our aim here is to give a simple
self-contained proof of these generalisations which also makes their range of
applicability transparent.Comment: 12 pages, 1 figur
Soliton Solutions to the Einstein Equations in Five Dimensions
We present a new class of solutions in odd dimensions to Einstein's equations
containing either a positive or negative cosmological constant. These solutions
resemble the even-dimensional Eguchi-Hanson--(anti)-de Sitter ((A)dS) metrics,
with the added feature of having Lorentzian signatures. They provide an
affirmative answer to the open question as to whether or not there exist
solutions with negative cosmological constant that asymptotically approach
AdS, but have less energy than AdS. We present
evidence that these solutions are the lowest-energy states within their
asymptotic class.Comment: 9 pages, Latex; Final version that appeared in Phys. Rev. Lett; title
changed by journal from original title "Eguchi-Hanson Solitons
Increasing security of supply by the use of a local power controller during large system disturbances
This paper describes intelligent ways in which distributed generation and local loads can be controlled during large system disturbances, using Local Power Controllers. When distributed generation is available, and a system disturbance is detected early enough, the generation can be dispatched, and its output power can be matched as closely as possible to local microgrid demand levels. Priority-based load shedding can be implemented to aid this process. In this state, the local microgrid supports the wider network by relieving the wider network of the micro-grid load. Should grid performance degrade further, the local microgrid can separate itself from the network and maintain power to the most important local loads, re-synchronising to the grid only after more normal performance is regained. Such an intelligent system would be a suitable for hospitals, data centres, or any other industrial facility where there are critical loads. The paper demonstrates the actions of such Local Power Controllers using laboratory experiments at the 10kVA scale
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