4,831 research outputs found
On the embedding of spacetime in five-dimensional Weyl spaces
We revisit Weyl geometry in the context of recent higher-dimensional theories
of spacetime. After introducing the Weyl theory in a modern geometrical
language we present some results that represent extensions of Riemannian
theorems. We consider the theory of local embeddings and submanifolds in the
context of Weyl geometries and show how a Riemannian spacetime may be locally
and isometrically embedded in a Weyl bulk. We discuss the problem of classical
confinement and the stability of motion of particles and photons in the
neighbourhood of branes for the case when the Weyl bulk has the geometry of a
warped product space. We show how the confinement and stability properties of
geodesics near the brane may be affected by the Weyl field. We construct a
classical analogue of quantum confinement inspired in theoretical-field models
by considering a Weyl scalar field which depends only on the extra coordinate.Comment: 16 pages, new title and references adde
Deconfinement transition in protoneutron stars: analysis within the Nambu-Jona-Lasinio model
We study the effect of color superconductivity and neutrino trapping on the
deconfinement transition of hadronic matter into quark matter in a protoneutron
star. To describe the strongly interacting matter a two-phase picture is
adopted. For the hadronic phase we use different parameterizations of a
non-linear Walecka model which includes the whole baryon octet. For the quark
matter phase we use an Nambu-Jona-Lasinio effective model which
includes color superconductivity. We impose color and flavor conservation
during the transition in such a way that just deconfined quark matter is
transitorily out of equilibrium with respect to weak interactions. We find that
deconfinement is more difficult for small neutrino content and it is easier for
lower temperatures although these effects are not too large. In addition they
will tend to cancel each other as the protoneutron star cools and deleptonizes,
resulting a transition density that is roughly constant along the evolution of
the protoneutron star. According to these results the deconfinement transition
is favored after substantial cooling and contraction of the protoneutron star
Fermi-Frenet coordinates for space-like curves
We generalize Fermi coordinates, which correspond to an adapted set of
coordinates describing the vicinity of an observer's worldline, to the
worldsheet of an arbitrary spatial curve in a static spacetime. The spatial
coordinate axes are fixed using a covariant Frenet triad so that the metric can
be expressed using the curvature and torsion of the spatial curve. As an
application of Fermi-Frenet coordinates, we show that they allow covariant
inertial forces to be expressed in a simple and physically intuitive way.Comment: 7 page
Riemannian Geometry of Noncommutative Surfaces
A Riemannian geometry of noncommutative n-dimensional surfaces is developed
as a first step towards the construction of a consistent noncommutative
gravitational theory. Historically, as well, Riemannian geometry was recognized
to be the underlying structure of Einstein's theory of general relativity and
led to further developments of the latter. The notions of metric and
connections on such noncommutative surfaces are introduced and it is shown that
the connections are metric-compatible, giving rise to the corresponding Riemann
curvature. The latter also satisfies the noncommutative analogue of the first
and second Bianchi identities. As examples, noncommutative analogues of the
sphere, torus and hyperboloid are studied in detail. The problem of covariance
under appropriately defined general coordinate transformations is also
discussed and commented on as compared with other treatments.Comment: 28 pages, some clarifications, examples and references added, version
to appear in J. Math. Phy
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