Magnification relations in gravitational lensing via multidimensional residue integrals

We investigate the so-called magnification relations of gravitational lensing models. We show that multidimensional residue integrals provide a simple explanation for the existence of these relations, and an effective method of computation. We illustrate the method with several examples, thereby deriving new magnification relations for galaxy lens models and microlensing (point mass lensing).Comment: 16 pages, uses revtex4, submitted to Journal of Mathematical Physic

The distribution of microlensed light curve derivatives: the relationship between stellar proper motions and transverse velocity

We present a method for computing the probability distribution of microlensed light curve derivatives both in the case of a static lens with a transverse velocity, and in the case of microlensing that is produced through stellar proper motions. The distributions are closely related in form, and can be considered equivalent after appropriate scaling of the input transverse velocity. The comparison of the distributions in this manner provides a consistent way to consider the relative contribution to microlensing (both large and small fluctuations) of the two classes of motion, a problem that is otherwise an extremely expensive computational exercise. We find that the relative contribution of stellar proper motions to the microlensing rate is independent of the mass function assumed for the microlenses, but is a function of optical depth and shear. We find that stellar proper motions produce a higher overall microlensing rate than a transverse velocity of the same magnitude. This effect becomes more pronounced at higher optical depth. With the introduction of shear, the relative rates of microlensing become dependent on the direction of the transverse velocity. This may have important consequences in the case of quadruply lensed quasars such as Q2237+0305, where the alignment of the shear vector with the source trajectory varies between images.Comment: 12 pages, including 9 figures. Submitted to M.N.R.A.S. Revised version includes a short section on the applicability of the metho

Exotic Statistics for Ordinary Particles in Quantum Gravity

Objects exhibiting statistics other than the familiar Bose and Fermi ones are natural in theories with topologically nontrivial objects including geons, strings, and black holes. It is argued here from several viewpoints that the statistics of ordinary particles with which we are already familiar are likely to be modified due to quantum gravity effects. In particular, such modifications are argued to be present in loop quantum gravity and in any theory which represents spacetime in a fundamentally piecewise-linear fashion. The appearance of unusual statistics may be a generic feature (such as the deformed position-momentum uncertainty relations and the appearance of a fundamental length scale) which are to be expected in any theory of quantum gravity, and which could be testable.Comment: Awarded an honourable mention in the 2008 Gravity Research Foundation Essay Competitio

The Post-Newtonian Limit of f(R)-gravity in the Harmonic Gauge

A general analytic procedure is developed for the post-Newtonian limit of $f(R)$-gravity with metric approach in the Jordan frame by using the harmonic gauge condition. In a pure perturbative framework and by using the Green function method a general scheme of solutions up to $(v/c)^4$ order is shown. Considering the Taylor expansion of a generic function $f$ it is possible to parameterize the solutions by derivatives of $f$. At Newtonian order, $(v/c)^2$, all more important topics about the Gauss and Birkhoff theorem are discussed. The corrections to "standard" gravitational potential ($tt$-component of metric tensor) generated by an extended uniform mass ball-like source are calculated up to $(v/c)^4$ order. The corrections, Yukawa and oscillating-like, are found inside and outside the mass distribution. At last when the limit $f\rightarrow R$ is considered the $f(R)$-gravity converges in General Relativity at level of Lagrangian, field equations and their solutions.Comment: 16 pages, 10 figure

My Clinging Ivy : My Ivy Green

https://digitalcommons.library.umaine.edu/mmb-vp/2168/thumbnail.jp

Topological Censorship

All three-manifolds are known to occur as Cauchy surfaces of asymptotically flat vacuum spacetimes and of spacetimes with positive-energy sources. We prove here the conjecture that general relativity does not allow an observer to probe the topology of spacetime: any topological structure collapses too quickly to allow light to traverse it. More precisely, in a globally hyperbolic, asymptotically flat spacetime satisfying the null energy condition, every causal curve from \scri^- to {\scri}^+ is homotopic to a topologically trivial curve from \scri^- to {\scri}^+. (If the Poincar\'e conjecture is false, the theorem does not prevent one from probing fake 3-spheres).Comment: 12 pages, REVTEX; 1 postscript figure in a separate uuencoded file. Our earlier version (PRL 71, 1486 (1993)) contained a secondary result, mistakenly attributed to Schoen and Yau, regarding ``passive topological censorship'' of a certain class of topologies. As Gregory Burnett has pointed out (gr-qc/9504012), this secondary result is false. The main topological censorship theorem is unaffected by the erro

A small source in Q2237+0305 ?

Microlensing in Q2237+0305 between 1985 and 1995 (eg. Irwin et al. 1989; Corrigan et al. 1991; Ostensen et al. 1996) has been interpreted in two different ways; as microlensing by stellar mass objects of a continuum source having dimensions significantly smaller than the microlens Einstein radius (ER) (eg. Wambsganss, Paczynski & Schneider 1990; Rauch & Blandford 1991), and as microlensing by very low mass objects of a source as large as 5 ER (Refsdal & Stabell 1993; Haugan 1996). In this paper we present evidence in favour of a small source. Limits on the source size (in units of ER) are obtained from the combination of limits on the number of microlens Einstein radii crossed by the source during the monitoring period with two separate light-curve features. Firstly, recently published monitoring data (Wozniak et al. 2000; OGLE web page) show large variations (~0.8-1.5 magnitudes) between image brightnesses over a period of 700 days or ~15% of the monitoring period. Secondly, the 1988 peak in the image A light-curve had a duration that is a small fraction (<0.02) of the monitoring period. Such rapid microlensing rises and short microlensing peaks only occur for small sources. We find that the observed large-rapid variation limits the source size to be <0.2 ER (95% confidence). The width of the light-curve peak provides a stronger constraint of <0.02 ER (99% confidence). The Einstein radius (projected into the source plane) of the average microlens mass (m) in Q2237+0305 is ER ~ 10^{17}\sqrt{m} cm. The interpretation that stars are responsible for microlensing in Q2237+0305 therefore results in limits on the continuum source size that are consistent with current accretion disc theory.Comment: 8 pages, 3 figures, accepted for publication in M.N.R.A.

Discovery of a New Quadruple Lens HST 1411+5211

Gravitational lensing is an important tool for probing the mass distribution of galaxies. In this letter we report the discovery of a new quadruple lens HST 1411+5211 found in archived WFPC2 images of the galaxy cluster CL140933+5226. If the galaxy is a cluster member then its redshift is $z=0.46$. The images of the source appear unresolved in the WFC implying that the source is a quasar. We have modeled the lens as both a single galaxy and a galaxy plus a cluster. The latter model yields excellent fits to the image positions along with reasonable parameters for the galaxy and cluster making HST 1411+5211 a likely gravitational lens. Determination of the source redshift and confirmation of the lens redshift would allow us to put strong constraints on the mass distribution of the lensing galaxy.Comment: 11 pages including 1 postscript figure, aastex. Accepted to the ApJL. Also available from: http://www.astro.lsa.umich.edu:80/users/philf/www/papers/list.htm

Workers Compensation-Reported Injuries Among Security and Law Enforcement Personnel in the Private Versus Public Sectors

Background: Private and Public security and law enforcement (SLE) sectors perform multiple overlapping job duties. Methods: Workers’ compensation (WC) SLE first reports of injury (FROI) data (2005–2015) were analyzed to describe injuries, identify differences in awarded WC benefits, and compare the probability of a FROI resulting in awarded benefits between Public and Private SLE. A Pearson’s chi-square test was utilized and reverse selection logistic regression was performed to estimate the odds ratio that a FROI would result in an awarded benefit for Private vs. Public SLE, while adjusting for relevant covariates. Results: Private SLE had higher FROI percentages for younger and for older workers, fall injuries, and back injuries, compared to Public SLE. The adjusted odds that a FROI resulted in an awarded benefit was 1.4 times higher for Private SLE compared to Public SLE; (95% confidence interval [CI] = 1.09,1.69). Middle-aged SLE employee adjusted odds of awarded benefits was 3.3 times (95% CI [1.96, 5.39]) higher compared to younger employees. Adjusted odds of awarded benefits was 3.8 times (95% CI [1.34, 10.61]) higher for gunshots and 1.7 times (95% CI [1.22, 2.39]) higher for fractures/dislocations compared to other nature of injuries. Motor vehicle injury, fall/slip, and strain related FROIs had elevated adjusted odds of awarded benefits compared to other injury causes. Conclusions: Results highlight the importance of injury prevention education and worker safety training for Private and Public SLE sector workers on fall prevention (especially in Private SLE) and strain prevention (especially in Public SLE), as well as motor vehicle safety

The Influence of Central Black Holes on Gravitational Lenses

Recent observations indicate that many if not all galaxies host massive central black holes. In this paper we explore the influence of black holes on the lensing properties. We model the lens as an isothermal ellipsoid with a finite core radius plus a central black hole. We show that the presence of the black hole substantially changes the critical curves and caustics. If the black hole mass is above a critical value, then it will completely suppress the central images for all source positions. Realistic central black holes likely have masses below this critical value. Even in such sub-critical cases, the black hole can suppress the central image when the source is inside a zone of influence, which depends on the core radius and black hole mass. In the sub-critical cases, an additional image may be created by the black hole in some regions, which for some radio lenses may be detectable with high-resolution and large dynamic-range VLBI maps. The presence of central black holes should also be taken into account when one constrains the core radius from the lack of central images in gravitational lenses.Comment: 7 pages, 3 figures; submitted to MNRA