1,533,120 research outputs found
Singular Perturbation Problem in Boundary/Fractional Combustion
Motivated by a nonlocal free boundary problem, we study uniform properties of
solutions to a singular perturbation problem for a boundary-reaction-diffusion
equation, where the reaction term is of combustion type. This boundary problem
is related to the fractional Laplacian. After an optimal uniform H\"older
regularity is shown, we pass to the limit to study the free boundary problem it
leads to
Boundary conditions in the Unruh problem
We have analyzed the Unruh problem in the frame of quantum field theory and
have shown that the Unruh quantization scheme is valid in the double Rindler
wedge rather than in Minkowski spacetime. The double Rindler wedge is composed
of two disjoint regions (- and -wedges of Minkowski spacetime) which are
causally separated from each other. Moreover the Unruh construction implies
existence of boundary condition at the common edge of - and -wedges in
Minkowski spacetime. Such boundary condition may be interpreted as a
topological obstacle which gives rise to a superselection rule prohibiting any
correlations between - and - Unruh particles. Thus the part of the field
from the -wedge in no way can influence a Rindler observer living in the
-wedge and therefore elimination of the invisible "left" degrees of freedom
will take no effect for him. Hence averaging over states of the field in one
wedge can not lead to thermalization of the state in the other. This result is
proved both in the standard and algebraic formulations of quantum field theory
and we conclude that principles of quantum field theory does not give any
grounds for existence of the "Unruh effect".Comment: 31 pages,1 figur
Boundary Value Problem for Black Rings
We study the boundary value problem for asymptotically flat stationary black
ring solutions to the five-dimensional vacuum Einstein equations. Assuming the
existence of two additional commuting axial Killing vector fields and the
horizon topology of , we show that the only asymptotically flat
black ring solution with a regular horizon is the Pomeransky-Sen'kov black ring
solution.Comment: 21 pages, 1 figur
Boundary Terms for Massless Fermionic Fields
Local supersymmetry leads to boundary conditions for fermionic fields in
one-loop quantum cosmology involving the Euclidean normal to the boundary and a
pair of independent spinor fields. This paper studies the corresponding
classical properties, i.e. the classical boundary-value problem and boundary
terms in the variational problem. Interestingly, a link is found with the
classical boundary-value problem when spectral boundary conditions are imposed
on a 3-sphere in the massless case. Moreover, the boundary term in the action
functional is derived.Comment: 8 pages, plain-tex, recently appearing in Foundations of Physics
Letters, volume 7, pages 303-308, year 199
- …