Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables

In this paper, we discuss hidden symmetries in rotating black hole spacetimes. We start with an extended introduction which mainly summarizes results on hidden symmetries in four dimensions and introduces Killing and Killing-Yano tensors, objects responsible for hidden symmetries. We also demonstrate how starting with a principal CKY tensor (that is a closed non-degenerate conformal Killing-Yano 2-form) in 4D flat spacetime one can "generate" 4D Kerr-NUT-(A)dS solution and its hidden symmetries. After this we consider higher-dimensional Kerr-NUT-(A)dS metrics and demonstrate that they possess a principal CKY tensor which allows one to generate the whole tower of Killing-Yano and Killing tensors. These symmetries imply complete integrability of geodesic equations and complete separation of variables for the Hamilton-Jacobi, Klein-Gordon, and Dirac equations in the general Kerr-NUT-(A)dS metrics.Comment: 33 pages, no figures, updated references and corrected typo

The material soul: Strategies for naturalising the soul in an early modern epicurean context

We usually portray the early modern period as one characterised by the ‘birth of subjectivity’ with Luther and Descartes as two alternate representatives of this radical break with the past, each ushering in the new era in which ‘I’ am the locus of judgements about the world. A sub-narrative called ‘the mind-body problem’ recounts how Cartesian dualism, responding to the new promise of a mechanistic science of nature, “split off” the world of the soul/mind/self from the world of extended, physical substance—a split which has preoccupied the philosophy of mind up until the present day. We would like to call attention to a different constellation of texts—neither a robust ‘tradition’ nor an isolated ‘episode’, somewhere in between—which have in common their indebtedness to, and promotion of an embodied, Epicurean approach to the soul. These texts follow the evocative hint given in Lucretius’ De rerum natura that ‘the soul is to the body as scent is to incense’ (in an anonymous early modern French version). They neither assert the autonomy of the soul, nor the dualism of body and soul, nor again a sheer physicalism in which ‘intentional’ properties are reduced to the basic properties of matter. Rather, to borrow the title of one of these treatises (L’Âme Matérielle), they seek to articulate the concept of a material soul. We reconstruct the intellectual development of a corporeal, mortal and ultimately material soul, in between medicine, natural philosophy and metaphysics, including discussions of Malebranche and Willis, but focusing primarily on texts including the 1675 Discours anatomiques by the Epicurean physician Guillaume Lamy; the anonymous manuscript from circa 1725 entitled L’Âme Matérielle, which is essentially a compendium of texts from the later seventeenth century (Malebranche, Bayle) along with excerpts from Lucretius; and materialist writings such Julien Offray de La Mettrie’s L’Homme-Machine (1748), in order to articulate this concept of a ‘material soul’ with its implications for notions of embodiment, materialism and selfhood

BHPR research: qualitative1. Complex reasoning determines patients' perception of outcome following foot surgery in rheumatoid arhtritis

Background: Foot surgery is common in patients with RA but research into surgical outcomes is limited and conceptually flawed as current outcome measures lack face validity: to date no one has asked patients what is important to them. This study aimed to determine which factors are important to patients when evaluating the success of foot surgery in RA Methods: Semi structured interviews of RA patients who had undergone foot surgery were conducted and transcribed verbatim. Thematic analysis of interviews was conducted to explore issues that were important to patients. Results: 11 RA patients (9 ♂, mean age 59, dis dur = 22yrs, mean of 3 yrs post op) with mixed experiences of foot surgery were interviewed. Patients interpreted outcome in respect to a multitude of factors, frequently positive change in one aspect contrasted with negative opinions about another. Overall, four major themes emerged. Function: Functional ability & participation in valued activities were very important to patients. Walking ability was a key concern but patients interpreted levels of activity in light of other aspects of their disease, reflecting on change in functional ability more than overall level. Positive feelings of improved mobility were often moderated by negative self perception ("I mean, I still walk like a waddling duck”). Appearance: Appearance was important to almost all patients but perhaps the most complex theme of all. Physical appearance, foot shape, and footwear were closely interlinked, yet patients saw these as distinct separate concepts. Patients need to legitimize these feelings was clear and they frequently entered into a defensive repertoire ("it's not cosmetic surgery; it's something that's more important than that, you know?”). Clinician opinion: Surgeons' post operative evaluation of the procedure was very influential. The impact of this appraisal continued to affect patients' lasting impression irrespective of how the outcome compared to their initial goals ("when he'd done it ... he said that hasn't worked as good as he'd wanted to ... but the pain has gone”). Pain: Whilst pain was important to almost all patients, it appeared to be less important than the other themes. Pain was predominately raised when it influenced other themes, such as function; many still felt the need to legitimize their foot pain in order for health professionals to take it seriously ("in the end I went to my GP because it had happened a few times and I went to an orthopaedic surgeon who was quite dismissive of it, it was like what are you complaining about”). Conclusions: Patients interpret the outcome of foot surgery using a multitude of interrelated factors, particularly functional ability, appearance and surgeons' appraisal of the procedure. While pain was often noted, this appeared less important than other factors in the overall outcome of the surgery. Future research into foot surgery should incorporate the complexity of how patients determine their outcome Disclosure statement: All authors have declared no conflicts of interes

Gardens of happiness: Sir William Temple, temperance and China

This is the author accepted manuscript. The final version is available from Taylor & Francis via the DOI in this recordSir William Temple, an English statesman and humanist, wrote “Upon the Gardens of Epicurus” in 1685, taking a neo-epicurean approach to happiness and temperance. In accord with Pierre Gassendi’s epicureanism, “happiness” is characterised as freedom from disturbance and pain in mind and body, whereas “temperance” means following nature (Providence and one’s physiopsychological constitution). For Temple, cultivating fruit trees in his garden was analogous to the threefold cultivation of temperance as a virtue in the humoral body (as food), the mind (as freedom from the passions), and the bodyeconomic (as circulating goods) in order to attain happiness. A regimen that was supposed to cure the malaise of Restoration amidst a crisis of unbridled passions, this threefold cultivation of temperance underlines Temple’s reception of China and Confucianism wherein happiness and temperance are highlighted. Thus Temple’s “gardens of happiness” represent not only a reinterpretation of classical ideas, but also his dialogue with China.European CommissionLeverhulme Trus

Baconianism

The philosophy of Francis Bacon was interpreted in various ways in the seventeenth century. In England, his utopian project and natural history became the basis for the pro- jects of religious pacification, pedagogical ref- ormation, and scientific cooperation of Hartlib, Comenius and Charleton. In the hands of Eve- lyn, Wilkins, and Wren, moreover, Bacon’s ideal of cooperative science engendered the birth of the Royal Society, and his natural history guided the experimental activities of Boyle and Hooke. In France and the Nether- lands, attention was paid to Bacon’s natural history especially within the circle of friends of Descartes. In the second half of the seven- teenth century, though Bacon’s historical approach was gradually supplanted by mechanical-mathematical science in Europe, Baconianism still served as a source of argu- ments in the Dutch Cartesian context, as to his theory of error and as a source of criticisms to Aristotelianism