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, ‘Sam and Julia hugged’ is assumed to entail both ‘Sam hugged Julia’ and ‘Julia hugged Sam’. 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, ‘Sam and Julia hugged’ is assumed to entail both ‘Sam hugged Julia’ and ‘Julia hugged Sam’. 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