162 research outputs found

    A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric

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    A key result in the proof of black hole uniqueness in 4-dimensions is that a stationary black hole that is ``rotating''--i.e., is such that the stationary Killing field is not everywhere normal to the horizon--must be axisymmetric. The proof of this result in 4-dimensions relies on the fact that the orbits of the stationary Killing field on the horizon have the property that they must return to the same null geodesic generator of the horizon after a certain period, PP. This latter property follows, in turn, from the fact that the cross-sections of the horizon are two-dimensional spheres. However, in spacetimes of dimension greater than 4, it is no longer true that the orbits of the stationary Killing field on the horizon must return to the same null geodesic generator. In this paper, we prove that, nevertheless, a higher dimensional stationary black hole that is rotating must be axisymmetric. No assumptions are made concerning the topology of the horizon cross-sections other than that they are compact. However, we assume that the horizon is non-degenerate and, as in the 4-dimensional proof, that the spacetime is analytic.Comment: 24 pages, no figures, v2: footnotes and references added, v3: numerous minor revision

    The long and the short of it: Mechanisms of synchronous and compensatory dynamics across temporal scales

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    Synchronous dynamics (fluctuations that occur in unison) are universal phenomena with widespread implications for ecological stability. Synchronous dynamics can amplify the destabilizing effect of environmental variability on ecosystem functions such as productivity, whereas the inverse, compensatory dynamics, can stabilize function. Here we combine simulation and empirical analyses to elucidate mechanisms that underlie patterns of synchronous versus compensatory dynamics. In both simulated and empirical communities, we show that synchronous and compensatory dynamics are not mutually exclusive but instead can vary by timescale. Our simulations identify multiple mechanisms that can generate timescale-specific patterns, including different environmental drivers, diverse life histories, dispersal, and non-stationary dynamics. We find that traditional metrics for quantifying synchronous dynamics are often biased toward long-term drivers and may miss the importance of short-term drivers. Our findings indicate key mechanisms to consider when assessing synchronous versus compensatory dynamics and our approach provides a pathway for disentangling these dynamics in natural systems

    On the `Stationary Implies Axisymmetric' Theorem for Extremal Black Holes in Higher Dimensions

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    All known stationary black hole solutions in higher dimensions possess additional rotational symmetries in addition to the stationary Killing field. Also, for all known stationary solutions, the event horizon is a Killing horizon, and the surface gravity is constant. In the case of non-degenerate horizons (non-extremal black holes), a general theorem was previously established [gr-qc/0605106] proving that these statements are in fact generally true under the assumption that the spacetime is analytic, and that the metric satisfies Einstein's equation. Here, we extend the analysis to the case of degenerate (extremal) black holes. It is shown that the theorem still holds true if the vector of angular velocities of the horizon satisfies a certain "diophantine condition," which holds except for a set of measure zero.Comment: 30pp, Latex, no figure

    Bracing adolescent idiopathic scoliosis (BASIS) study – night-time versus full-time bracing in adolescent idiopathic scoliosis: study protocol for a multicentre, randomized controlled trial

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    Aims Scoliosis is a lateral curvature of the spine with associated rotation, often causing distress due to appearance. For some curves, there is good evidence to support the use of a spinal brace, worn for 20 to 24 hours a day to minimize the curve, making it as straight as possible during growth, preventing progression. Compliance can be poor due to appearance and comfort. A night-time brace, worn for eight to 12 hours, can achieve higher levels of curve correction while patients are supine, and could be preferable for patients, but evidence of efficacy is limited. This is the protocol for a randomized controlled trial of ‘full-time bracing’ versus ‘night-time bracing’ in adolescent idiopathic scoliosis (AIS). Methods UK paediatric spine clinics will recruit 780 participants aged ten to 15 years-old with AIS, Risser stage 0, 1, or 2, and curve size (Cobb angle) 20° to 40° with apex at or below T7. Patients are randomly allocated 1:1, to either full-time or night-time bracing. A qualitative sub-study will explore communication and experiences of families in terms of bracing and research. Patient and Public Involvement & Engagement informed study design and will assist with aspects of trial delivery and dissemination. Discussion The primary outcome is ‘treatment failure’ (Cobb angle progression to 50° or more before skeletal maturity); skeletal maturity is at Risser stage 4 in females and 5 in males, or ‘treatment success’ (Cobb angle less than 50° at skeletal maturity). The comparison is on a non-inferiority basis (non-inferiority margin 11%). Participants are followed up every six months while in brace, and at one and two years after skeletal maturity. Secondary outcomes include the Scoliosis Research Society 22 questionnaire and measures of quality of life, psychological effects of bracing, adherence, anxiety and depression, sleep, satisfaction, and educational attainment. All data will be collected through the British Spine Registry
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