135,406 research outputs found
Vector-Field Domain Walls
We argue that spontaneous Lorentz violation may generally lead to metastable
domain walls related to the simultaneous violation of some accompanying
discrete symmetries. Remarkably, such domain wall solutions exist for
space-like Lorentz violation and do not exist for the time-like violation.
Because a preferred space direction is spontaneously induced, these domain
walls have no planar symmetry and produce a peculiar static gravitational field
at small distances, while their long-distance gravity appears the same as for
regular scalar-field walls. Some possible applications of vector-field domain
walls are briefly discussed.Comment: Published version, to appear in Physical Review
Vector Field and Inflation
We have investigated if the vector field can give rise to an accelerating
phase in the early universe. We consider a timelike vector field with a general
quadratic kinetic term in order to preserve an isotropic background spacetime.
The vector field potential is required to satisfy the three minimal conditions
for successful inflation: i) , ii) and iii) the slow-roll
conditions. As an example, we consider the massive vector potential and small
field type potential as like in scalar driven inflation.Comment: 1+7pages, 3figures, To appear in the Proceedings of the CospA 2008,
Kore
Stability properties of divergence-free vector fields
A divergence-free vector field satisfies the star property if any
divergence-free vector field in some C1-neighborhood has all singularities and
all periodic orbits hyperbolic. In this paper we prove that any divergence-free
vector field defined on a Riemannian manifold and satisfying the star property
is Anosov. It is also shown that a C1-structurally stable divergencefree vector
field can be approximated by an Anosov divergence-free vector field. Moreover,
we prove that any divergence-free vector field can be C1-approximated by an
Anosov divergence-free vector field, or else by a divergence-free vector field
exhibiting a heterodimensional cycle.Comment: 24 page
Vector field theories in cosmology
Recently proposed theories based on the cosmic presence of a vectorial field
are compared and contrasted. In particular the so called Einstein aether theory
is discussed in parallel with a recent proposal of a strained space-time theory
(Cosmic Defect theory). We show that the latter fits reasonably well the cosmic
observed data with only one, or at most two, adjustable parameters, whilst
other vector theories use much more. The Newtonian limits are also compared.
Finally we show that the CD theory may be considered as a special case of the
aether theories, corresponding to a more compact and consistent paradigm.Comment: 19 pages, 1 figure, to appear on Phys. Rev.
Vector field construction of Segre sets
A CR generic real analytic CR manifold M carries two families of Segre
varieties and conjugate Segre varieties. We observe in this article that their
complexifications give rise to two families of foliations of the
complexification of M which coincide with the flow foliations induced by the
complexified CR (1,0) and (0,1) vector fields tangent to M. As an application,
we derive a new proof of the characterization of finite type in terms of Segre
sets.Comment: Completely rewritten version, 42 pages Sujclass: Complex Variable
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