20 research outputs found
An alternative well-posedness property and static spacetimes with naked singularities
In the first part of this paper, we show that the Cauchy problem for wave
propagation in some static spacetimes presenting a singular time-like boundary
is well posed, if we only demand the waves to have finite energy, although no
boundary condition is required. This feature does not come from essential
self-adjointness, which is false in these cases, but from a different
phenomenon that we call the alternative well-posedness property, whose origin
is due to the degeneracy of the metric components near the boundary.
Beyond these examples, in the second part, we characterize the type of
degeneracy which leads to this phenomenon.Comment: 34 pages, 3 figures. Accepted for publication in Class. Quantum Gra
Scalar Field Probes of Power-Law Space-Time Singularities
We analyse the effective potential of the scalar wave equation near generic
space-time singularities of power-law type (Szekeres-Iyer metrics) and show
that the effective potential exhibits a universal and scale invariant leading
x^{-2} inverse square behaviour in the ``tortoise coordinate'' x provided that
the metrics satisfy the strict Dominant Energy Condition (DEC). This result
parallels that obtained in hep-th/0403252 for probes consisting of families of
massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The
detailed properties of the scalar wave operator depend sensitively on the
numerical coefficient of the x^{-2}-term, and as one application we show that
timelike singularities satisfying the DEC are quantum mechanically singular in
the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We
also comment on some related issues like the near-singularity behaviour of the
scalar fields permitted by the Friedrichs extension.Comment: v2: 21 pages, JHEP3.cls, one reference adde
Quantum singularities in a model of f(R) Gravity
The formation of a naked singularity in a model of f(R) gravity having as
source a linear electromagnetic field is considered in view of quantum
mechanics. Quantum test fields obeying the Klein-Gordon, Dirac and Maxwell
equations are used to probe the classical timelike naked singularity developed
at r=0. We prove that the spatial derivative operator of the fields fails to be
essentially self-adjoint. As a result, the classical timelike naked singularity
remains quantum mechanically singular when it is probed with quantum fields
having different spin structures.Comment: 12 pages, final version. Accepted for publication in EPJ
Reciprocal predicates: a prototype model
Many languages have verbal stems like hug and marry whose intransitive realization is interpreted as reciprocal. Previous semantic analyses of such reciprocal intransitives rely on the assumption of symmetric participation. Thus, âSam and Julia huggedâ is assumed to entail both âSam hugged Juliaâ and âJulia hugged Samâ. In this paper we report experimental results that go against this assumption. It is shown that although symmetric participation is likely to be preferred by speakers, it is not a necessary condition for accepting sentences with reciprocal verbs. To analyze the reciprocal alternation, we propose that symmetric participation is a typical feature connecting the meanings of reciprocal and binary forms. This accounts for the optionality as well as to the preference of this feature. Further, our results show that agent intentionality often boosts the acceptability of sentences with reciprocal verbs. Accordingly, we propose that intentionality is another typical semantic feature of such verbs, separate from symmetric participation
Reciprocal predicates: a prototype model
Many languages have verbal stems like hug and marry whose intransitive realization is interpreted as reciprocal. Previous semantic analyses of such reciprocal intransitives rely on the assumption of symmetric participation. Thus, âSam and Julia huggedâ is assumed to entail both âSam hugged Juliaâ and âJulia hugged Samâ. In this paper we report experimental results that go against this assumption. It is shown that although symmetric participation is likely to be preferred by speakers, it is not a necessary condition for accepting sentences with reciprocal verbs. To analyze the reciprocal alternation, we propose that symmetric participation is a typical feature connecting the meanings of reciprocal and binary forms. This accounts for the optionality as well as to the preference of this feature. Further, our results show that agent intentionality often boosts the acceptability of sentences with reciprocal verbs. Accordingly, we propose that intentionality is another typical semantic feature of such verbs, separate from symmetric participation