Non-extremal black hole solutions from the c-map

We construct new static, spherically symmetric non-extremal black hole solutions of four-dimensional ${\cal N}=2$ supergravity, using a systematic technique based on dimensional reduction over time (the c-map) and the real formulation of special geometry. For a certain class of models we actually obtain the general solution to the full second order equations of motion, whilst for other classes of models, such as those obtainable by dimensional reduction from five dimensions, heterotic tree-level models, and type-II Calabi-Yau compactifications in the large volume limit a partial set of solutions are found. When considering specifically non-extremal black hole solutions we find that regularity conditions reduce the number of integration constants by one half. Such solutions satisfy a unique set of first order equations, which we identify. Several models are investigated in detail, including examples of non-homogeneous spaces such as the quantum deformed $STU$ model. Though we focus on static, spherically symmetric solutions of ungauged supergravity, the method is adaptable to other types of solutions and to gauged supergravity.Comment: 57 pages. Minor changes to the introduction, typos corrected and references added. Accepted for publication in JHE

Tom Vaughan to Mr. Silver 4 May 1959

Professional correspondenc

Essays on Firm Strategies and Market Outcomes

In the first chapter of my dissertation, Aleksandr Yankelevich and I examine the effects of price matching guarantees on duopoly markets. We find that a commitment to price-match raises prices by altering consumer search behavior in three ways. First, price-matching diminishes firms’ incentives to lower prices to attract consumers who have no search costs. Second, for consumers with positive search costs, price-matching lowers the marginal benefit of search, inducing them to accept higher prices. Finally, price-matching can lead to asymmetric equilibria where one firm runs fewer sales and both firms tend to offer smaller discounts than in a symmetric equilibrium. These price increases grow with the proportion of consumers who invoke price-matching guarantees and also in the level of equilibrium asymmetry. The second chapter studies the effect of the complexity of consumers’ preferences over a product on that product’s market structure. I relate complexity of preferences to the number of dimensions of a Lancasterian characteristic space. Using a novel higher dimensional Hotelling model, I find that a fixed number of firms are likely to be better off competing over products with more complex preferences. Although firms face more intense competition in higher dimensional markets, the greater product differentiation afforded to them allows them to charge higher prices and earn higher profits. This result provides a clear theoretical foundation for the observation that goods associated with more complex preferences typically display a greater variety of products sold. Additionally, I show that the behavior of more than two firms competing in more than one dimension differs wildly from that of firms typically studied in models of spatial competition. The final chapter will examine firms\u27 motives for implementing grandfather clauses that allow certain consumers to continue to access a service at a favorable, but no longer available price. Grandfather clauses permit firms to price discriminate between early adopters and new consumers in exchange for forfeiting the right to optimally set prices for early adopters. They may be used to thwart competition following a structural change, to respond to cost shocks, or to retain customers who consume another good from a multiproduct firm. We analyze under what conditions firms might choose to offer grandfather clauses and what effects they have on welfare

Wittgensteinian descriptivism and concepts of self-renunciation

Part I presents a systematic presentation of what is termed 'the Wittgensteinian position', broken down into eight theses, each of which is thought of as intrinsic to self-renouncing faith. Part II consists of three case-studies examining the conception of self-renouncing faith found in the works of Francois Mauriac, Georges Bernanos, and Patrick White. Distinct divergencies from many of the Wittgensteinian theses are unearthed. Part III traces the roots of each of the Wittgensteinian theses to their sitz im leben in a strain of neo-Romanticism centred on securing independence of the world. Connections are made to Tolstoy, Emerson, Rilke, Trakl and Von Hofmannsthal. Part IV argues that each case study in Part II runs counter to the Wittgensteinian position in one of three ways: (1) not having some theses which are proposed by the Wittgensteinian position to be intrinsic to self-renouncing faith; (2) deeming some theses which are proposed by the Wittgensteinian position to be intrinsic to self-renouncing faith as either (2.1) not inherently selfrenouncing or (2.2) actually incompatible with the understanding of selfrenunciation exemplified in the case-study; (3) having a different logical structure to its model of self-renouncing belief from that of the Wittgensteinian position. Points (1), (2) and (3), and particularly points (2.1) and (2.2), suggest that self-renouncing faith is not the unitary phenomenon assumed by the Wittgensteinian position. The casestudies represent three distinct models of self-renouncing faith. These models have no place for the self-concern that characterises the Weltbild of self-concern with which the Wittgensteinian position is impregnated. There follows a broad discussion of the implications of the above findings for the Wittgensteinian position, including Wittgenstein's status as a religious thinker, the way a descriptivist methodology should be understood, the blanket exclusion of the metaphysical from religious belief and the over-simple portrayal of religious belief as a conceptual orientation to the world

Lidar measurements of thermal structure

Rayleigh backscatter observations at 532 nm and 355 nm of relative atmospheric density above Aberystwyth on a total of 93 nights between Dec. 1982 and Feb. 1985 were used to derive the height variation of temperature in the upper stratosphere and mesosphere. Preliminary results for height up to about 25 km were also obtained from observations of Raman backscattering from nitrogen molecules. Comparisons were carried out for stratospheric heights with satellite borne measurements; good agreement was found between equivalent black body temperatures derived from the lidar observations and those obtained from nadir measurements in three channels of the stratosphere sounder units on NOAA satellites; the lidar based atmospheric temperatures have shown general agreement with but a greater degree of structure than the limb sounding measurements obtained using the SAMS experiment on the NOAA-7 satellite. In summer, stratospheric and mesospheric temperatures showed a smooth height variation similar to that of the CIRA model atmosphere. In contrast, the winter data showed a great variability with height, and marked temperature changes both from night to night and within a given night

Testing the validity of the “value of a prevented fatality” (VPF) used to assess UK safety measures

AbstractThe “value of a prevented fatality” (VPF), the maximum amount that it is notionally reasonable to pay for a safety measure that will reduce by one the expected number of preventable premature deaths in a large population, is published by the UK Department for Transport (DfT). The figure, updated for changes in GDP per head, is used by the DfT, the Health and Safety Executive and other UK regulatory bodies as well as very widely in the process, nuclear and other industries as the standard by which to judge how much to spend to reduce harm to humans. The paper tests the validity of the 1999 study on which the VPF is based and finds that that study fails numerous tests of its validity. It is concluded that there is no evidential base for the VPF that has been used for many years in the UK and is still in standard use today. Given the difficulties evident in the interpretation of survey results, an urgent re-appraisal is needed of alternative statistical methodologies that can allow robust regulatory and industry safety decision making and, vitally, give adequate protection to the UK public and to those working in the UK's transport, process, nuclear and other industries