The symmetry algebra of asymptotically flat spacetimes at null infinity in four dimensions in the sense of Newman and Unti is revisited. As in the Bondi-Metzner-Sachs gauge, it is shown to be isomorphic to the direct sum of the abelian algebra of infinitesimal conformal rescalings with bms 4 . The latter algebra is the semi-direct sum of infinitesimal supertranslations with the conformal Killing vectors of the Riemann sphere. Infinitesimal local conformal transformations can then consistently be included. We work out the local conformal properties of the relevant Newman-Penrose coefficients, construct the surface charges and derive their algebra.

Asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner. In agreement with a recent conjecture, one finds a Virasoro-Kac-Moody type algebra not only in three dimensions but also in the four dimensional asymptotically flat case.

Abstract:The dS/CFT correspondence postulates the existence of a Euclidean CFT dual to a suitable gravity theory with Dirichlet boundary conditions asymptotic to de Sitter spacetime. A semi-classical model of such a correspondence consists of Einstein gravity with positive cosmological constant and without matter which is dual to Euclidean Liouville theory defined at the future conformal boundary. Here we show that Euclidean Liouville theory is also dual to Einstein gravity with Dirichlet boundary conditions on a fixed timelike slice in the static patch. Intriguingly, the spacetime interpretation of Euclidean Liouville time is the physical time of the static observer. As a prerequisite of this correspondence, we show that the asymptotic symmetry algebra which consists of two copies of the Virasoro algebra extends everywhere into the bulk.

The transport equation describing the flow of solute across a membrane has been modified on the basis of theoretical studies calculating the drag of a sphere moving in a viscous liquid undergoing Poiseuille flow inside a cylinder. It is shown that different frictional resistance terms should be introduced to calculate the contributions of diffusion and convection. New sieving equations are derived to calculate r and A,/Ax (respectively, the pore radius and the total area of the pores per unit of path length). These equations provide a better agreement than the older formulas between the calculated and the experimental glomerular sieving coefficients for [6I]polyvinylpyrrolidone (PVP) fractions with a mean equivalent radius between 19 and 37 A. From r and A,/Ax, the mean effective glomerular filtration pressure has been calculated, applying Poiseuille's law. A value of 15.4 mm Hg has been derived from the mean sieving curve obtained from 23 experiments performed on normal anesthetized dogs.In 1951, Pappenheimer et al. developed the so-called "pore theory" to account for the transcapillary transport of uncharged, lipid-insoluble solutes in mammalian muscles (24). According to this theory, convective flow and net diffusion contribute to solute flow across the membrane, in this case the capillary walls, both processes being impeded by the steric hindrance at the entrance of the "pores" (supposed to exist between the cells) and by frictional forces within the pores (20,22,23,25).The solute flow due to diffusion was calculated as D(c -c 2 )AW/Ax X A,/A, where D is the free diffusion coefficient, cl and c 2 , respectively, the solute concentrations in filtrand and filtrate and A,/Ax the pore area freely available to water per unit of length. The term A,/A, describes the restriction to the motion and can be calculated as 1/K 1 X SD where SD = [1 -(a,/r)]2 is the steric hindrance term (a, is the radius of the solute molecules

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Three-dimensional Einstein-Maxwell theory with non trivial asymptotics at null infinity is solved. The symmetry algebra is a Virasoro-Kac-Moody type algebra that extends the bms3 algebra of the purely gravitational case. Solution space involves logarithms and provides a tractable example of a polyhomogeneous solution space. The associated surface charges are non-integrable and non-conserved due to the presence of electromagnetic news. As in the four-dimensional purely gravitational case, their algebra involves a field-dependent central charge.

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We derive a canonical analysis of a double null 2+2 Hamiltonian description of General Relativity in terms of complex self-dual 2-forms and the associated SO(3) connection variables. The algebra of first class constraints is obtained and forms a Lie algebra that consists of two constraints that generate diffeomorphisms in the two surface, a constraint that generates diffeomorphisms along the null generators and a constraint that generates self-dual spin and boost transformations.