208 research outputs found
Incompressible Stars and Fractional Derivatives
Fractional calculus is an effective tool in incorporating the effects of
non-locality and memory into physical models. In this regard, successful
applications exist rang- ing from signal processing to anomalous diffusion and
quantum mechanics. In this paper we investigate the fractional versions of the
stellar structure equations for non radiating spherical objects. Using
incompressible fluids as a comparison, we develop models for constant density
Newtonian objects with fractional mass distributions or stress conditions. To
better understand the fractional effects, we discuss effective values for the
density, gravitational field and equation of state. The fractional ob- jects
are smaller and less massive than integer models. The fractional parameters are
related to a polytropic index for the models considered
Missing Mass and the Acceleration of the Universe. Is Quintessence the only Explanation?
Detailed observations of the temperature fluctuations in the microwave
background radiation indicate that we live in an open universe. From the size
of these fluctuations it is concluded that the geometry of the universe is
quite close to Euclidean. In terms Friedmann models, this implies a mass
density within 10% of the critical density required for a flat universe.
Observed mass can only account for 30% of this mass density. Recently, an
outstanding observation revealed that cosmos is accelerating. This motivated
some astronomers to explain the missing 70% as some exotic dark energy called
quintessence. In this essay, we present an alternative explanation to these
cosmological issues in terms of the Friedmann Thermodynamics. This model has
the capability of making definite predictions about the geometry of the
universe, the missing mass problem, and the acceleration of the universe
in-line with the recent observations. For future observations, we also predict
where this model will start differing from the quintessence models.
(This essay received an honorable mention in the Annual Essay Competition of
the Gravity Research Foundation for the year 2002-- Ed)Comment: Accepted for publication in IJMP-D December 200
Fractional Boundaries for Fluid Spheres
A single Israel layer can be created when two metrics adjoin with no
continuous metric derivative across the boundary. The properties of the layer
depend only on the two metrics it separates. By using a fractional derivative
match, a family of Israel layers can be created between the same two metrics.
The family is indexed by the order of the fractional derivative. The method is
applied to Tolman IV and V interiors and a Schwarzschild vacuum exterior. The
method creates new ranges of modeling parameters for fluid spheres. A thin
shell analysis clarifies pressure/tension in the family of boundary layers.Comment: to appear in J. Math. Phy
A Singularity-Free Cosmological Model with a Conformally Coupled Scalar Field
We explore the possibility of describing our universe with a
singularity--free, closed, spatially homogeneous and isotropic cosmological
model, using only general relativity and a suitable equation of state which
produces an inflationary era. A phase transition to a radiation--dominated era
occurs as a consequence of boundary conditions expressing the assumption that
the temperature cannot exceed the Planck value. We find that over a broad range
of initial conditions, the predicted value of the Hubble parameter is
approximately km~s~Mpc. Inflation is driven by a
scalar field, which must be conformally coupled to the curvature if the
Einstein equivalence principle has to be satisfied. The form of the scalar
field potential is derived, instead of being assumed a priori.Comment: 19 pages, figures and tables available from the author
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