256 research outputs found
Comment on "Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions"
In a recent paper (Phys. Rev. D 94, 125016 (2016)), the authors argued that
the singularities of the two-point functions on the Poincar\'e domain of the
-dimensional anti-de Sitter spacetime () have the Hadamard
form, regardless of which (Robin) boundary condition is chosen at the conformal
boundary. However, the argument used to prove this statement was based on an
incorrect expression for the two-point function , which was
obtained by demanding invariance for the vacuum state. In this
comment I show that their argument works only for Dirichlet and Neumann
boundary conditions and that the full symmetry cannot be respected
by nontrivial Robin conditions (i.e., those which are neither Dirichlet nor
Neumann). By studying the conformal scalar field on , I find the
correct expression for and show that, notwithstanding this
problem, it still have the Hadamard form.Comment: 3 page
Quantum Singularities in Spacetimes with Spherical and Cylindrical Topological Defects
Exact solutions of Einstein equations with null Riemman-Christoffel curvature
tensor everywhere, except on a hypersurface, are studied using quantum
particles obeying the Klein-Gordon equation. We consider the particular cases
when the curvature is represented by a Dirac delta function with support either
on a sphere or on a cylinder (spherical and cylindrical shells). In particular,
we analyze the necessity of extra boundary conditions on the shells.Comment: 7 page,1 fig., Revtex, J. Math. Phys, in pres
Quantum Singularities in Static Spacetimes
We review the mathematical framework necessary to understand the physical
content of quantum singularities in static spacetimes. We present many examples
of classical singular spacetimes and study their singularities by using wave
packets satisfying Klein-Gordon and Dirac equations. We show that in many cases
the classical singularities are excluded when tested by quantum particles but
unfortunately there are other cases where the singularities remain from the
quantum mechanical point of view. When it is possible we also find, for
spacetimes where quantum mechanics does not exclude the singularities, the
boundary conditions necessary to turn the spatial portion of the wave operator
into self-adjoint and emphasize their importance to the interpretation of
quantum singularities.Comment: 14 pages, section Quantum Singularities has been improve
Vacuum Fluctuations and the Small Scale Structure of Spacetime
We show that vacuum fluctuations of the stress-energy tensor in
two-dimensional dilaton gravity lead to a sharp focusing of light cones near
the Planck scale, effectively breaking space up into a large number of causally
disconnected regions. This phenomenon, called "asymptotic silence" when it
occurs in cosmology, might help explain several puzzling features of quantum
gravity, including evidence of spontaneous dimensional reduction at short
distances. While our analysis focuses on a simplified two-dimensional model, we
argue that the qualitative features should still be present in four dimensions.Comment: 4 pages, revte
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