General Relativity simplifies dramatically in the limit that the number of spacetime dimensions D is infinite: it reduces to a theory of non-interacting particles, of finite radius but vanishingly small cross sections, which do not emit nor absorb radiation of any finite frequency. Non-trivial black hole dynamics occurs at length scales that are 1/D times smaller than the horizon radius, and at frequencies D times larger than the inverse of this radius. This separation of scales at large D, which is due to the large gradient of the gravitational potential near the horizon, allows an effective theory of black hole dynamics. We develop to leading order in 1/D this effective description for massless scalar fields and compute analytically the scalar absorption probability. We solve to next-to-next-to-leading order the black brane instability, with very accurate results that improve on previous approximations with other methods. These examples demonstrate that problems that can be formulated in an arbitrary number of dimensions may be tractable in analytic form, and very efficiently so, in the large D expansion.Comment: 50 pages, 2 figures; v3: improved discussion of conceptual point

chocardiography is now recognized as an integral diagnostic tool that enables noninvasive quantification of cardiac chamber size, ventricular mass, and function in the clinical setting. Furthermore, technological advancement in Doppler echocardiography enables quantitative assessment of ventricular diastolic function as well as systolic function. Thus, echocardiography has become an important cardiac imaging technique in a number of clinical trials evaluating the efficacy of drug treatments or new therapeutic strategies.A guideline for quantifying cardiac chamber size and function using echocardiography, and references values for Circulation Journal Vol.72, November 2008 these echocardiographic measurements, were provided by the American Society of Echocardiography in conjunction with the European Association of Echocardiography. 1 Likewise, Doppler echocardiographic criteria for assessing left ventricular (LV) diastolic function were provided by the Canadian Consensus, 2 European 3 and American Medical Association guidelines, 4 and diastolic function parameters were reported to decline gradually with age. 5 However, most of these data are derived from American and European populations and because physical 6,7 and racial 8-10 differences can influence cardiac chamber size and function, it is important to evaluate the echocardiographic parameters in other populations. Reference values based on a large Asian population have not been previously reported, although some investigators have reported these values in a small population. 11 In addition, most studies that have investigated the relationship between age and cardiac chamber size and function have focused on a few parameters and have not assessed all of them in a large population.Accordingly, we designed and conducted a multicenter study, the Japanese Normal Values for Echocardiographic Measurements Project (JAMP) study, to determine the normal values for echocardiographic measurements and evaluate the relationship between these parameters and age in a large, healthy Japanese population. J 2008; 72: 1859 -1866 (Received February 27, 2008 revised manuscript received June 11, 2008; accepted June 26, 2008; released online September 29, 2008) Circ

Abstract:The gravitational field of a black hole is strongly localized near its horizon when the number of dimensions D is very large. In this limit, we can effectively replace the black hole with a surface in a background geometry (e.g. Minkowski or Anti-deSitter space). The Einstein equations determine the effective equations that this 'black hole surface' (or membrane) must satisfy. We obtain them up to next-to-leading order in 1/D for static black holes of the Einstein-(A)dS theory. To leading order, and also to next order in Minkowski backgrounds, the equations of the effective theory are the same as soap-film equations, possibly up to a redshift factor. In particular, the Schwarzschild black hole is recovered as a spherical soap bubble. Less trivially, we find solutions for 'black droplets', i.e. black holes localized at the boundary of AdS, and for non-uniform black strings.

Abstract:The limit of large number of dimensions localizes the gravitational field of a black hole in a well-defined region near the horizon. The perturbative dynamics of the black hole can then be characterized in terms of states in the near-horizon geometry. We investigate this by computing the spectrum of quasinormal modes of the Schwarzschild black hole in the 1/D expansion, which we find splits into two classes. Most modes are non-decoupled modes: non-normalizable states of the near-horizon geometry that straddle between the near-horizon zone and the asymptotic zone. They have frequency of order D/r 0 (with r 0 the horizon radius), and are also present in a large class of other black holes. There also exist a much smaller number of decoupled modes: normalizable states of the near-horizon geometry that are strongly suppressed in the asymptotic region. They have frequency of order 1/r 0 , and are specific of each black hole. Our results for their frequencies are in excellent agreement with numerical calculations, in some cases even in D = 4.