35,465 research outputs found
Spinor Casimir densities for a spherical shell in the global monopole spacetime
We investigate the vacuum expectation values of the energy-momentum tensor
and the fermionic condensate associated with a massive spinor field obeying the
MIT bag boundary condition on a spherical shell in the global monopole
spacetime. In order to do that it was used the generalized Abel-Plana summation
formula. As we shall see, this procedure allows to extract from the vacuum
expectation values the contribution coming from to the unbounded spacetime and
explicitly to present the boundary induced parts. As to the boundary induced
contribution, two distinct situations are examined: the vacuum average effect
inside and outside the spherical shell. The asymptotic behavior of the vacuum
densities is investigated near the sphere center and surface, and at large
distances from the sphere. In the limit of strong gravitational field
corresponding to small values of the parameter describing the solid angle
deficit in global monopole geometry, the sphere-induced expectation values are
exponentially suppressed. As a special case we discuss the fermionic vacuum
densities for the spherical shell on background of the Minkowski spacetime.
Previous approaches to this problem within the framework of the QCD bag models
have been global and our calculation is a local extension of these
contributions.Comment: 20 pages, 4 figure
The characteristic initial value problem for colliding plane waves: The linear case
The physical situation of the collision and subsequent interaction of plane
gravitational waves in a Minkowski background gives rise to a well-posed
characteristic initial value problem in which initial data are specified on the
two null characteristics that define the wavefronts. In this paper, we analyse
how the Abel transform method can be used in practice to solve this problem for
the linear case in which the polarization of the two gravitational waves is
constant and aligned. We show how the method works for some known solutions,
where problems arise in other cases, and how the problem can always be solved
in terms of an infinite series if the spectral functions for the initial data
can be evaluated explicitly.Comment: 14 pages. To appear in Class. Quantum Gra
Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials
A geometric approach is used to study a family of higher-order nonlinear Abel
equations. The inverse problem of the Lagrangian dynamics is studied in the
particular case of the second-order Abel equation and the existence of two
alternative Lagrangian formulations is proved, both Lagrangians being of a
non-natural class (neither potential nor kinetic term). These higher-order Abel
equations are studied by means of their Darboux polynomials and Jacobi
multipliers. In all the cases a family of constants of the motion is explicitly
obtained. The general n-dimensional case is also studied
Nonlocal symmetries of Riccati and Abel chains and their similarity reductions
We study nonlocal symmetries and their similarity reductions of Riccati and
Abel chains. Our results show that all the equations in Riccati chain share the
same form of nonlocal symmetry. The similarity reduced order ordinary
differential equation (ODE), , in this chain yields
order ODE in the same chain. All the equations in the Abel chain also share the
same form of nonlocal symmetry (which is different from the one that exist in
Riccati chain) but the similarity reduced order ODE, , in
the Abel chain always ends at the order ODE in the Riccati chain.
We describe the method of finding general solution of all the equations that
appear in these chains from the nonlocal symmetry.Comment: Accepted for publication in J. Math. Phy
Computer Algebra Solving of First Order ODEs Using Symmetry Methods
A set of Maple V R.3/4 computer algebra routines for the analytical solving
of 1st. order ODEs, using Lie group symmetry methods, is presented. The set of
commands includes a 1st. order ODE-solver and routines for, among other things:
the explicit determination of the coefficients of the infinitesimal symmetry
generator; the construction of the most general invariant 1st. order ODE under
given symmetries; the determination of the canonical coordinates of the
underlying invariant group; and the testing of the returned results.Comment: 14 pages, LaTeX, submitted to Computer Physics Communications.
Soft-package (On-Line Help) and sample MapleV session available at:
http://dft.if.uerj.br/symbcomp.htm or ftp://dft.if.uerj.br/pdetool
Wightman function and vacuum fluctuations in higher dimensional brane models
Wightman function and vacuum expectation value of the field square are
evaluated for a massive scalar field with general curvature coupling parameter
subject to Robin boundary conditions on two codimension one parallel branes
located on -dimensional background spacetime
with a warped internal space . The general case of different Robin
coefficients on separate branes is considered. The application of the
generalized Abel-Plana formula for the series over zeros of combinations of
cylinder functions allows us to extract manifestly the part due to the bulk
without boundaries. Unlike to the purely AdS bulk, the vacuum expectation value
of the field square induced by a single brane, in addition to the distance from
the brane, depends also on the position of the brane in the bulk. The brane
induced part in this expectation value vanishes when the brane position tends
to the AdS horizon or AdS boundary. The asymptotic behavior of the vacuum
densities near the branes and at large distances is investigated. The
contribution of Kaluza-Klein modes along is discussed in various
limiting cases. As an example the case is considered,
corresponding to the bulk with one compactified dimension. An
application to the higher dimensional generalization of the Randall-Sundrum
brane model with arbitrary mass terms on the branes is discussed.Comment: 25 pages, 2 figures, discussion added, accepted for publication in
Phys.Rev.
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