257,742 research outputs found
Weak Transversality and Partially Invariant Solutions
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
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
We give a geometrical characterization of -prolongations of vector
fields, and hence of -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 , and we speak of -prolongations of vector fields
and -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
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
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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