Singularity theorems based on trapped submanifolds of arbitrary co-dimension

Standard singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary co-dimension. By using the mean curvature vector to characterize trapped submanifolds, a unification of the several possibilities for the boundary conditions in the traditional theorems and their generalization to arbitrary co-dimension is achieved. The classical convergence conditions must be replaced by a condition on sectional curvatures, or tidal forces, which reduces to the former in the cases of co-dimension 1, 2 or n.Comment: 11 pages, no figures, some corrections

Inertial navigation/calibration/precise time and frequency capabilities

The Aerospace Guidance and Metrology Center was conceived in 1959 to be the US Air Force Inertial Navigation and Metrology Center. This paper will show the mission capabilities of the Inertial Navigation Maintenance Center and the Air Force Measurement and Standards Laboratory. Highlighted will be the precise time and frequency program developed by AGMC to support Air Force precise time and frequency requirements worldwide. A description of the past, present, and future precise time and frequency activities will be presented

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 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

Topological censorship for Kaluza-Klein space-times

The standard topological censorship theorems require asymptotic hypotheses which are too restrictive for several situations of interest. In this paper we prove a version of topological censorship under significantly weaker conditions, compatible e.g. with solutions with Kaluza-Klein asymptotic behavior. In particular we prove simple connectedness of the quotient of the domain of outer communications by the group of symmetries for models which are asymptotically flat, or asymptotically anti-de Sitter, in a Kaluza-Klein sense. This allows one, e.g., to define the twist potentials needed for the reduction of the field equations in uniqueness theorems. Finally, the methods used to prove the above are used to show that weakly trapped compact surfaces cannot be seen from Scri.Comment: minor correction

Uniqueness of de Sitter space

All inextendible null geodesics in four dimensional de Sitter space dS^4 are complete and globally achronal. This achronality is related to the fact that all observer horizons in dS^4 are eternal, i.e. extend from future infinity scri^+ all the way back to past infinity scri^-. We show that the property of having a null line (inextendible achronal null geodesic) that extends from scri^- to scri^+ characterizes dS^4 among all globally hyperbolic and asymptotically de Sitter spacetimes satisfying the vacuum Einstein equations with positive cosmological constant. This result is then further extended to allow for a class of matter models that includes perfect fluids.Comment: 22 pages, 2 figure

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

Thrust and wing loading requirements for short haul aircraft constrained by engine noise and field length

Propulsion system and wing loading requirements are determined for a mechanical flap and an externally blown flap aircraft for various engine noise levels and two engine cycles. Both aircraft are sized to operate from a 914m (3000 ft) runway and perform the same mission. For each aircraft concept, propulsion system sizing is demonstrated for two different engine cycles - one having a fan pressure ratio of 1.5 and a bypass ratio of 9, and the other having a fan pressure ratio of 1.25 and a bypass ratio of 17.8. The results presented include the required thrust-to-weight ratio, wing loading, resulting gross weight, and direct operating costs, as functions of the engine noise level, for each combination of engine cycle and aircraft concept

Artificial neural network prediction of weld distortion rectification using a travelling induction coil

An experimental investigation has been carried out to determine the applicability of an induction heating process with a travelling induction coil for the rectification of angular welding distortion. The results obtained from experimentation have been used to create artificial neural network models with the ability to predict the welding induced distortion and the distortion rectification achieved using a travelling induction coil. The experimental results have shown the ability to reduce the angular distortion for 8 mm and 10 mm thick DH36 steel plate and effectively eliminate the distortion on 6 mm thick plate. Results for 6 mm plate also show the existence of a critical induction coil travel speed at which maximum corrective bending occurs. Artificial neural networks have demonstrated the ability to predict the final distortion of the plate after both welding and induction heating. The models have also been used as a tool to determine the optimum speed to minimise the resulting distortion of steel plate after being subjected to both welding and induction heating processes

A population study of type II bursts in the Rapid Burster

Type II bursts are thought to arise from instabilities in the accretion flow onto a neutron star in an X-ray binary. Despite having been known for almost 40 years, no model can yet satisfactorily account for all their properties. To shed light on the nature of this phenomenon and provide a reference for future theoretical work, we study the entire sample of Rossi X-ray Timing Explorer data of type II bursts from the Rapid Burster (MXB 1730-335). We find that type II bursts are Eddington-limited in flux, that a larger amount of energy goes in the bursts than in the persistent emission, that type II bursts can be as short as 0.130 s, and that the distribution of recurrence times drops abruptly below 15-18 s. We highlight the complicated feedback between type II bursts and the NS surface thermonuclear explosions known as type I bursts, and between type II bursts and the persistent emission. We review a number of models for type II bursts. While no model can reproduce all the observed burst properties and explain the source uniqueness, models involving a gating role for the magnetic field come closest to matching the properties of our sample. The uniqueness of the source may be explained by a special combination of magnetic field strength, stellar spin period and alignment between the magnetic field and the spin axis.Comment: Accepted 2015 February 12. Received 2015 February 10; in original form 2014 December 1