Localization and Reference Frames in κ\kappa-Minkowski Spacetime

We study the limits to the localizability of events and reference frames in the $\kappa$-Minkowski quantum spacetime. Our main tool will be a representation of the $\kappa$-Minkowski commutation relations between coordinates, and the operator and measurement theory borrowed from ordinary quantum mechanics. Spacetime coordinates are described by operators on a Hilbert space, and a complete set of commuting observables cannot contain the radial coordinate and time at the same time. The transformation between the complete sets turns out to be the Mellin transform, which allows us to discuss the localizability properties of states both in space and time. We then discuss the transformation rules between inertial observers, which are described by the quantum $\kappa$-Poincar\'e group. These too are subject to limitations in the localizability of states, which impose further restrictions on the ability of an observer to localize events defined in a different observer's reference frame.Comment: 35 pages, 4 figure

Exotic matter driving wormholes

We develop an iterative approach to span the whole set of exotic matter models able to drive a traversable wormhole. The method reduces the Einstein equation to an infinite set of algebraic conditions and easily allows the implementation of further conditions linking the stress-energy tensor components among each other, like symmetry conditions or equations of state

Spin, torsion and violation of null energy condition in traversable wormholes

The static spherically symmetric traversable wormholes are analysed in the Einstein- Cartan theory of gravitation. In particular, we computed the torsion tensor for matter fields with different spin S = 0; 1/2; 1; 3/2. Interestingly, only for certain values of the spin the torsion contribution to Einstein-Cartan field equation allows one to satisfy both faring-out condition and Null Energy Condition. In this scenario traversable wormholes can be produced by using usual (non-exotic) spinning matter.Comment: 13 page

The Momentum Spaces of κ\kappa-Minkowski noncommutative spacetime

A useful concept in the development of physical models on the $\kappa$-Minkowski noncommutative spacetime is that of a curved momentum space. This structure is not unique: several inequivalent momentum space geometries have been identified. Some are associated to a different assumption regarding the signature of spacetime (i.e. Lorentzian vs. Euclidean), but there are inequivalent momentum spaces that can be associated to the same signature and even the same group of symmetries. Moreover, in the literature there are two approaches to the definition of these momentum spaces, one based on the right- (or left-)invariant metrics on the Lie group generated by the $\kappa$-Minkowski algebra. The other is based on the construction of $5$-dimensional matrix representation of the $\kappa$-Minkowski coordinate algebra. Neither approach leads to a unique construction. Here, we find the relation between these two approaches and introduce a unified approach, capable of describing all momentum spaces, and identify the corresponding quantum group of spacetime symmetries. We reproduce known results and get a few new ones. In particular, we describe the three momentum spaces associated to the $\kappa$-Poincar\'e group, which are half of a de Sitter, anti-de Sitter or Minkowski space, and we identify what distinguishes them. Moreover, we find a new momentum space with the geometry of a light cone, associated to a $\kappa$-deformation of the Carroll group.Comment: Completely rewritten version. Past results by other authors have been taken into account, and a new and better formulation has been introduced, which allows to connect the different approaches to the momentum space of kappa-Minkowski, and identify new, previously undiscovered, cases, like the momentum space associated to the kappa-Carroll grou

Observers and Momenta in κ-Minkowski space-time

We study the limits to the localizability and the role of observers in κ-Minkowski quantum spacetime. Inspired by Quantum Mechanincs, we develop an interpretations of the non-commutativity in coordinates and of the deformations of transformation between observers. Space-time coordinates are operators on a Hilbert space. The transformation between the complete sets is realized by Mellin transform. Transformation rules between inertial observers are described by the quantum κ-Poincaré group. There are restrictions on the observer possibility to localize events. We also discuss the geometry of the curved momentum space dual to k-Minkowski coordinates, which turns out to be not unique. It can have any signature: Euclidean, Lorentzian, and (+,+,-,-), as well as degenerate cases. For any choice of a four dimensional metric there is a quantum group of symmetries of κ-Minkowski preserving it. We associate a momentum space to each nondegenerate choice of such metric. These momentum spaces are all maximally symmetric, and the isotropy subgroup of their isometries coincides with the homogeneous part of the quantum group. We also discuss the degenerate cases.

Characterising exotic matter driving wormholes

In this paper, we develop an iterative approach to span the whole set of exotic matter models able to drive a traversable wormhole. The method, based on a Taylor expansion of metric and stress-energy tensor components in a neighbourhood of the wormhole throat, reduces the Einstein equation to an infinite set of algebraic conditions, which can be satisfied order by order. The approach easily allows the implementation of further conditions linking the stress-energy tensor components among each other, like symmetry conditions or equations of state. The method is then applied to some relevant examples of exotic matter characterised by a constant energy density and that also show an isotropic behaviour in the stress-energy tensor or obeying to a quintessence-like equation of state

Hypertension and migraine comorbidity: prevalence and risk of cerebrovascular events: evidence from a large, multicenter, cross-sectional survey in Italy (MIRACLES study)

OBJECTIVES: To estimate the prevalence of hypertension-migraine comorbidity; to determine their demographic and clinical characteristics versus patients with hypertension or migraine alone; and to see whether a history of cerebrovascular events was more common in the comorbidity group. METHODS: The MIRACLES, multicenter, cross-sectional, survey included 2973 patients with a known diagnosis of hypertension or migraine in a general practitioner setting in Italy. RESULTS: Five hundred and seventeen patients (17%) suffered from hypertension-migraine comorbidity, whereas 1271 (43%) suffered from hypertension only, and 1185 (40%) from migraine only. In the comorbidity group, the onset of comorbidity occurred at about 45 years of age, with migraine starting significantly later than in the migraine-only group, and hypertension significantly before than in the hypertension-only group; a familial history of both hypertension and migraine had a significantly higher frequency as compared with the hypertension and migraine group. Compared to hypertension (3.1%) and migraine (0.7%), the comorbidity group had a higher prevalence (4.4%) of history of cerebrovascular events, with an odds ratio of a predicted history of stroke/transient ischemic attack (TIA) of 1.76 [95% confidence interval (CI) 1.01-3.07] compared to the hypertension group. In patients without other recognized risk factors for stroke, stroke/TIA occurred more frequently in the comorbidity group, compared to the hypertension group. In the age range 40-49 years, prevalence of history of stroke/TIA was five-fold greater (4.8% in comorbidity vs. 0.9% in hypertension group). CONCLUSION: This cross-sectional study indicates that the prevalence of comorbidity hypertension-migraine is substantial and that patients with comorbidity have a higher probability of history of cerebrovascular events, compared to hypertensive patient