Mean curvature flow and quasilocal mass for two-surfaces in Hamiltonian General Relativity

A family of quasilocal mass definitions that includes as special cases the Hawking mass and the Brown-York ``rest mass'' energy is derived for spacelike 2-surfaces in spacetime. The definitions involve an integral of powers of the norm of the spacetime mean curvature vector of the 2-surface, whose properties are connected with apparent horizons. In particular, for any spacelike 2-surface, the direction of mean curvature is orthogonal (dual in the normal space) to a unique normal direction in which the 2-surface has vanishing expansion in spacetime. The quasilocal mass definitions are obtained by an analysis of boundary terms arising in the gravitational ADM Hamiltonian on hypersurfaces with a spacelike 2-surface boundary, using a geometric time-flow chosen proportional to the dualized mean curvature vector field at the boundary surface. A similar analysis is made choosing a geometric rotational flow given in terms of the twist covector of the dual pair of mean curvature vector fields, which leads to a family of quasilocal angular momentum definitions involving the squared norm of the twist. The large sphere limit of these definitions is shown to yield the ADM mass and angular momentum in asymptotically flat spacetimes, while at apparent horizons a quasilocal version of the Gibbons-Penrose inequality is derived. Finally, some results concerning positivity are proved for the quasilocal masses, motivated by consideration of spacelike mean curvature flow of 2-surfaces in spacetime.Comment: Revised version, includes an analysis of null flows with applications to mass and angular momentum for apparent horizon

Limit curve theorems in Lorentzian geometry

The subject of limit curve theorems in Lorentzian geometry is reviewed. A general limit curve theorem is formulated which includes the case of converging curves with endpoints and the case in which the limit points assigned since the beginning are one, two or at most denumerable. Some applications are considered. It is proved that in chronological spacetimes, strong causality is either everywhere verified or everywhere violated on maximizing lightlike segments with open domain. As a consequence, if in a chronological spacetime two distinct lightlike lines intersect each other then strong causality holds at their points. Finally, it is proved that two distinct components of the chronology violating set have disjoint closures or there is a lightlike line passing through each point of the intersection of the corresponding boundaries.Comment: 25 pages, 1 figure. v2: Misprints fixed, matches published versio

Causes of Prolonged Waiting Time in Public Health Facilities among Health Care Seekers in Calabar Municipal Council of Cross River State, Nigeria

The purpose of this study was to investigate the causes of prolonged waiting time in public health care facilities among health care seekers in Calabar Municipal Council of Cross River State, Nigeria. To carry out this investigation, two hypotheses were formulated to guide the study. Survey research design was adopted for this study. A sample of one hundred and eighteen (118) respondents was selected. The selection was done through cluster sampling technique. The questionnaire was the main instrument used for data collection. It was constructed by the researchers with assistance of some measurement experts that gave it face and content validity. The Chi-square (X2) inferential statistics set at 0.05 was used to test the hypothesis. The result shows that there is significant contribution of poor record keeping and inadequate health personnel to the prolonged waiting time in public health care facilities among health care seekers. Based on these findings, some recommendations and suggestions for further studies were made. Keywords: Prolong waiting time; Public health facilities, Health care seekers. Poor record keeping; inadequate health personnel

Magnification relations for Kerr lensing and testing Cosmic Censorship

A Kerr black hole with mass parameter m and angular momentum parameter a acting as a gravitational lens gives rise to two images in the weak field limit. We study the corresponding magnification relations, namely the signed and absolute magnification sums and the centroid up to post-Newtonian order. We show that there are post-Newtonian corrections to the total absolute magnification and centroid proportional to a/m, which is in contrast to the spherically symmetric case where such corrections vanish. Hence we also propose a new set of lensing observables for the two images involving these corrections, which should allow measuring a/m with gravitational lensing. In fact, the resolution capabilities needed to observe this for the Galactic black hole should in principle be accessible to current and near-future instrumentation. Since a/m >1 indicates a naked singularity, a most interesting application would be a test of the Cosmic Censorship conjecture. The technique used to derive the image properties is based on the degeneracy of the Kerr lens and a suitably displaced Schwarzschild lens at post-Newtonian order. A simple physical explanation for this degeneracy is also given.Comment: 13 pages, version 2: references added, minor changes. To appear in Phys. Rev.

The Geometry of Warped Product Singularities

In this article the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.Comment: 14 page

Spinorial Characterizations of Surfaces into 3-dimensional pseudo-Riemannian Space Forms

We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in $\mathbb{R}^{2,1}$ to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well as for spacelike and timelike immersions of surfaces of signature (0,2), hence achieving a complete spinorial description for this class of pseudo-Riemannian immersions.Comment: 9 page

Painleve-Gullstrand Coordinates for the Kerr Solution

We construct a coordinate system for the Kerr solution, based on the zero angular momentum observers dropped from infinity, which generalizes the Painleve-Gullstrand coordinate system for the Schwarzschild solution. The Kerr metric can then be interpreted as describing space flowing on a (curved) Riemannian 3-manifold. The stationary limit arises as the set of points on this manifold where the speed of the flow equals the speed of light, and the horizons as the set of points where the radial speed equals the speed of light. A deeper analysis of what is meant by the flow of space reveals that the acceleration of free-falling objects is generally not in the direction of this flow. Finally, we compare the new coordinate system with the closely related Doran coordinate system.Comment: 6 pages; v2: new section, matches final published version; v3: sign error in the expression of the function delta correcte

A Morse-theoretical analysis of gravitational lensing by a Kerr-Newman black hole

Consider, in the domain of outer communication of a Kerr-Newman black hole, a point (observation event) and a timelike curve (worldline of light source). Assume that the worldline of the source (i) has no past end-point, (ii) does not intersect the caustic of the past light-cone of the observation event, and (iii) goes neither to the horizon nor to infinity in the past. We prove that then for infinitely many positive integers k there is a past-pointing lightlike geodesic of (Morse) index k from the observation event to the worldline of the source, hence an observer at the observation event sees infinitely many images of the source. Moreover, we demonstrate that all lightlike geodesics from an event to a timelike curve in the domain of outer communication are confined to a certain spherical shell. Our characterization of this spherical shell shows that in the Kerr-Newman spacetime the occurrence of infinitely many images is intimately related to the occurrence of centrifugal-plus-Coriolis force reversal.Comment: 14 pages, 2 figures; REVTEX; submitted to J. Math. Phy

Staffordshire Bull Terriers in the UK: their disorder predispositions and protections

Abstract: Background: The Staffordshire Bull Terrier is a popular dog breed in the UK but there is limited reliable evidence on disorder predispositions and protections within the breed. Using anonymised veterinary clinical data from the VetCompass™ Programme, this study aimed to identify common disorders with predisposition and protection in the Staffordshire Bull Terrier. The study hypothesised that Staffordshire Bull Terriers would have higher odds of aggression compared with non-Staffordshire Bull Terriers. Results: The clinical records of a random sample of dogs of all types were reviewed to extract the most definitive diagnoses for all disorders existing during 2016. A combined list from the 30 most common disorders in Staffordshire Bull Terriers and the 30 most common disorders in non-Staffordshire Bull Terriers was generated. Multivariable logistic regression was used to report the odds of each of these disorders in 1304 (5.8%) Staffordshire Bull Terriers compared with 21,029 (94.2%) non-Staffordshire Bull Terriers. After accounting for confounding, Staffordshire Bull Terriers had significantly increased odds of 4/36 (11.1%) disorders compared to non-Staffordshire Bull Terriers with highest odds for seizure disorder (OR 2.06; 95% CI 1.24 to 3.40; p = 0.005). Conversely, Staffordshire Bull Terriers had reduced odds of 5/36 (13.9%) disorders, with lowest odds for patellar luxation (OR 0.15; 95% CI 0.04 to 0.61; p = 0.008). There was no significant difference in the odds of aggression between Staffordshire Bull Terriers compared with non-Staffordshire Bull Terriers (OR 1.09; 95% CI 0.75 to 1.58; p = 0.644). Conclusions: This study provides a reliable evidence base of breed-specific disorder predispositions and protections that can be used by breeders to optimise breeding decisions. The findings can assist prospective owners of Staffordshire Bull Terriers to make informed decisions when acquiring a dog. From the relative number of predispositions to protections identified, there is no evidence that Staffordshire Bull Terriers have higher overall health problems than non-Staffordshire Bull Terriers

Endoscopic submucosal dissection of rectal lesion recurrence at the anastomosis site: when the staples lead the way

info:eu-repo/semantics/publishedVersio