Gauge and motion in perturbation theory

Through second order in perturbative general relativity, a small compact object in an external vacuum spacetime obeys a generalized equivalence principle: although it is accelerated with respect to the external background geometry, it is in free fall with respect to a certain \emph{effective} vacuum geometry. However, this single principle takes very different mathematical forms, with very different behaviors, depending on how one treats perturbed motion. Furthermore, any description of perturbed motion can be altered by a gauge transformation. In this paper, I clarify the relationship between two treatments of perturbed motion and the gauge freedom in each. I first show explicitly how one common treatment, called the Gralla-Wald approximation, can be derived from a second, called the self-consistent approximation. I next present a general treatment of smooth gauge transformations in both approximations, in which I emphasise that the approximations' governing equations can be formulated in an invariant manner. All of these analyses are carried through second perturbative order, but the methods are general enough to go to any order. Furthermore, the tools I develop, and many of the results, should have broad applicability to any description of perturbed motion, including osculating-geodesic and two-timescale descriptions.Comment: 26 pages, 3 figures. Minor corrections. Equations (120) and (126) are more general than in PRD versio

Challenges and Changes in Community-Based Lending for Homeownership

Many community based organizations have been providing mortgage loans in low-to-moderate income and minority communities on a small scale since the 1970s, In the wake of the housing crisis, they faced special challenges. They approached these with emphasis on flexible underwriting, counseling and education, and a variety of other solutions

"So many people going the other way" : an examination of the moral strategy of language usage in five novels by Janet Frame : a thesis presented in partial fulfilment of the requirements for the degree of Master of Arts in English at Massey University

The title quotation is from Janet Frame's novel, Living in the Maniototo (72). Abbreviations and editions of the five primary sources referred to in the text are as follows: EA The Edge of the Alphabets London: W.H. Allen & Co., 1962. SG Scented Gardens for the Blind. London: The Women's Press Ltd., 1982. SS A State of Siege. London: Sirius, 1989. LM Living in the Maniototo. London: The Women's Press Ltd., 1981. CP The Carpathians. London: Century Hutchinson Ltd., 1988. Some of the ideas developed in the chapter on Living in the Maniototo were first sketched out in a paper on that novel (39.498) written in 1990. I wish to thank my supervisor, Dr William Broughton, for his influence and patient guidance in the preparation of this thesis. Sincere thanks also to my husband, Geoff, and our children Mark and Bronwyn for their enthusiastic support

Lawn Establishment

PDF pages: 1

A practical, covariant puncture for second-order self-force calculations

Accurately modeling an extreme-mass-ratio inspiral requires knowledge of the second-order gravitational self-force on the inspiraling small object. Recently, numerical puncture schemes have been formulated to calculate this force, and their essential analytical ingredients have been derived from first principles. However, the \emph{puncture}, a local representation of the small object's self-field, in each of these schemes has been presented only in a local coordinate system centered on the small object, while a numerical implementation will require the puncture in coordinates covering the entire numerical domain. In this paper we provide an explicit covariant self-field as a local expansion in terms of Synge's world function. The self-field is written in the Lorenz gauge, in an arbitrary vacuum background, and in forms suitable for both self-consistent and Gralla-Wald-type representations of the object's trajectory. We illustrate the local expansion's utility by sketching the procedure of constructing from it a numerically practical puncture in any chosen coordinate system.Comment: 23 pages, 1 figure, final version to be published in Phys Rev

Functional significance of human female orgasm still hypothetical

The official published version can be accessed from the link below - Copyright © Cambridge University Press 2000Human males are more polygamously inclined than females. However, there is substantial within-sex variation in polygamous inclinations and practices. This is acknowledged by Gangestad & Simpson but we pose the question: Is the target article's “strategic pluralism” pluralistic enough? In addition, we argue that the hypothesis that the female orgasm is an adaptation for post-copulatory female choice between rival ejaculates demands more research