257,742 research outputs found

    Weak Transversality and Partially Invariant Solutions

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    New exact solutions are obtained for several nonlinear physical equations, namely the Navier-Stokes and Euler systems, an isentropic compressible fluid system and a vector nonlinear Schroedinger equation. The solution methods make use of the symmetry group of the system in situations when the standard Lie method of symmetry reduction is not applicable.Comment: 23 pages, preprint CRM-284

    Solutions to the Massive HLW IIA Supergravity

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    We find new supersymmetric solutions of the massive supergravity theory which can be constructed by generalized Scherk-Schwarz dimensional reduction of eleven dimensional supergravity, using the scaling symmetry of the equations of motion. Firstly, we construct field configurations which solve the ten dimensional equations of motion by reducing on the radial direction of Ricci-flat cones. Secondly, we will extend this result to the supersymmetric case by performing a dimensional reduction along the flow of a homothetic Killing vector which is the Euler vector of the cone plus a boost.Comment: 10 pages,v2: Reference added, some points clarified, v3: final versio

    On the geometry of lambda-symmetries, and PDEs reduction

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    We give a geometrical characterization of λ\lambda-prolongations of vector fields, and hence of λ\lambda-symmetries of ODEs. This allows an extension to the case of PDEs and systems of PDEs; in this context the central object is a horizontal one-form μ\mu, and we speak of μ\mu-prolongations of vector fields and μ\mu-symmetries of PDEs. We show that these are as good as standard symmetries in providing symmetry reduction of PDEs and systems, and explicit invariant solutions

    New D=6, N=(1,1) Gauged Supergravity with Supersymmetric (Minkowski)_4 X S^2 Vacuum

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    We obtain a new gauged D=6, N=(1,1) pure supergravity by a generalised consistent Kaluza-Klein reduction of M-theory on K3 \times R. The reduction requires a conspiratory gauging of both the Cremmer-Julia type global (rigid) symmetry and the homogeneous rescaling symmetry of the supergravity equations of motion. The gauged supergravity is different from the Romans D=6 gauged supergravity in that the four vector fields in our new theory are all abelian. We show that it admits a supersymmetric (Minkowski)_4\times S^2 vacuum, which can be lifted to D=11 where it becomes the near-horizon geometry of two intersecting M5-branes wrapping on a supersymmetric two-cycle of K3.Comment: latex, 13 pages, typo correcte

    Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes

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    As a preparation for a mathematically consistent study of the physics of symmetric spacetimes in a noncommutative setting, we study symmetry reductions in deformed gravity. We focus on deformations that are given by a twist of a Lie algebra acting on the spacetime manifold. We derive conditions on those twists that allow a given symmetry reduction. A complete classification of admissible deformations is possible in a class of twists generated by commuting vector fields. As examples, we explicitly construct the families of vector fields that generate twists which are compatible with Friedmann-Robertson-Walker cosmologies and Schwarzschild black holes, respectively. We find nontrivial isotropic twists of FRW cosmologies and nontrivial twists that are compatible with all classical symmetries of black hole solutions.Comment: LaTeX, 20 pages, no figures, minor modifications, reference added, to appear in JHE
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