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

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 $C^0$ 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 $\times$ time. This result is related to Yau's Lorentzian splitting conjecture.Comment: 3 pages, uses revtex.sty, to appear in Physical Review

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 (``$i^0$-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 $i^0$-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

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

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

Angular Momentum Transfer in the Binary X-ray Pulsar GX 1+4

We describe three presentations relating to the X-ray pulsar GX 1+4 at a workshop on magnetic fields and accretion at the Astrophysical Theory Centre, Australian National University on 1998, November 12-13. Optical and X-ray spectroscopy indicate that GX 1+4 is seen through a cloud of gravitationaly bound matter. We discuss an unstable negative feedback mechanism (originally proposed by Kotani et al, 1999), based on X-ray heating of this matter which controls the accretion rate when the source is in a low X-ray luminosity state. A deep minimum lasting ~6 hours occurred during observations with the RXTE satellite over 1996, July 19-21. The shape of the X-ray pulses changed remarkably from before to after the minimum. These changes may be related to the transition from neutron star spin-down to spin-up which occurred at about the same time. Smoothed particle hydrodynamic simulations of the effect of adding matter with opposite angular momentum to an existing disc, show that it is possible for a number of concentric rings with alternating senses of rotation to co-exist in a disc. This could provide an explanation for the step-like changes in Pdot which are observed in GX 1+4. Changes at the inner boundary of the disc occur at the same timescale as that imposed at the outer boundary. Reversals of material torque on the neutron star occur at a minimum in L_X.Comment: 10 pages, 5 figures; accepted for publication by PAS

Non-Existence of Black Holes in Certain Λ<0\Lambda<0 Spacetimes

Assuming certain asymptotic conditions, we prove a general theorem on the non-existence of static regular (i.e., nondegenerate) black holes in spacetimes with a negative cosmological constant, given that the fundamental group of space is infinite. We use this to rule out the existence of regular negative mass AdS black holes with Ricci flat scri. For any mass, we also rule out a class of conformally compactifiable static black holes whose conformal infinity has positive scalar curvature and infinite fundamental group, subject to our asymptotic conditions. In a limited, but important, special case our result adds new support to the AdS/CFT inspired positive mass conjecture of Horowitz and Myers.Comment: 17 pages, Latex. Typos corrected, minor changes to the text. Accepted for publication in Classical and Quantum Gravit