2,467 research outputs found
An extended version of the Cayley-Hamilton-Ziebur Theorem
The aim of this paper is to prove a Cayley-Hamilton-Ziebur Theorem for
non-autonomous semilinear matrix differential equations. Moreover, we show the
applicability of results like these to ODE theory.Comment: 10 page
Casimir-Polder interaction between an atom and a conducting wall in cosmic string spacetime
The Casimir-Polder interaction potential is evaluated for a polarizable
microparticle and a conducting wall in the geometry of a cosmic string
perpendicular to the wall. The general case of the anisotropic polarizability
tensor for the microparticle is considered. The corresponding force is a
function of the wall-microparticle and cosmic string-microparticle distances.
Depending on the orientation of the polarizability tensor principal axes the
force can be either attractive or repulsive. The asymptotic behavior of the
Casimir-Polder potential is investigated at large and small separations
compared to the wavelength of the dominant atomic transitions. We show that the
conical defect may be used to control the strength and the sign of the
Casimir-Polder force.Comment: 17 pages, 3 figure
Polarization of the fermionic vacuum by a global monopole with finite core
We study the vacuum polarization effects associated with a massive fermionic
field in a spacetime produced by a global monopole considering a nontrivial
inner structure for it. In the general case of the spherically symmetric static
core with finite support we evaluate the vacuum expectation values of the
energy-momentum tensor and the fermionic condensate in the region outside the
core. These quantities are presented as the sum of point-like global monopole
and core-induced contributions. The asymptotic behavior of the core-induced
vacuum densities are investigated at large distances from the core, near the
core and for small values of the solid angle corresponding to strong
gravitational fields. As an application of general results the flower-pot model
for the monopole's core is considered and the expectation values inside the
core are evaluated.Comment: 22 pages, 4 figure
Vacuum polarization induced by a cylindrical boundary in the cosmic string spacetime
In this paper we investigate the Wightman function, the renormalized vacuum
expectation values of the field square, and the energy-momentum tensor for a
massive scalar field with general curvature coupling inside and outside of a
cylindrical shell in the generalized spacetime of straight cosmic string. For
the general case of Robin boundary condition, by using the generalized
Abel-Plana formula, the vacuum expectation values are presented in the form of
the sum of boundary-free and boundary-induced parts. The asymptotic behavior of
the vacuum expectation values of the field square, energy density and stresses
are investigated in various limiting cases. The generalization of the results
to the exterior region is given for a general cylindrically symmetric static
model of the string core with finite support.Comment: 21 pages, 5 figure
Black hole formation in bidimensional dilaton gravity coupled to scalar matter systems
This work deals with the formation of black hole in bidimensional dilaton
gravity coupled to scalar matter fields. We investigate two scalar matter
systems, one described by a sixth power potential and the other defined with
two scalar fields containing up to the fourth power in the fields. The
topological solutions that appear in these cases allow the formation of black
holes in the corresponding dilaton gravity models.Comment: Latex, 9 pages. Published in Mod. Phys. Lett. A14 (1999) 268
Relativistic Quantum Scattering on a Cone
We study the relativistic quantum mechanical scattering of a bosonic particle
by an infinite straight cosmic string, considering the non-minimal coupling
between the bosonic field and the scalar curvature. In this case, an effective
two-dimensional delta-function interaction takes place besides the usual
topological scattering and a renormalization procedure is necessary in order to
treat the problem that appears in connection with the delta-function.Comment: 22 pages, LATEX fil
Self-forces in the Spacetime of Multiple Cosmic Strings
We calculate the electromagnetic self-force on a stationary linear
distribution of four-current in the spacetime of multiple cosmic strings. It is
shown that if the current is infinitely thin and stretched along a line which
is parallel to the strings the problem admits an explicit solution.Comment: This paper has been produced in Latex format and has 18 page
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