General spherically symmetric elastic stars in Relativity

The relativistic theory of elasticity is reviewed within the spherically symmetric context with a view towards the modeling of star interiors possessing elastic properties such as theones expected in neutron stars. Emphasis is placed on generality in the main sections of the paper, and the results are then applied to specific examples. Along the way, a few general results for spacetimes admitting isometries are deduced, and their consequences are fully exploited in the case of spherical symmetry relating them next to the the case in which the material content of the spacetime is some elastic material. This paper extends and generalizes the pioneering work by Magli and Kijowski [1], Magli [2] and [3], and complements, in a sense, that by Karlovini and Samuelsson in their interesting series of papers [4], [5] and [6].Comment: 23 page

The spectrum of endstates of gravitational collapse with tangential stresses

The final state--black hole or naked singularity--of the gravitational collapse of a marginally bound matter configuration in the presence of tangential stresses is classified, in full generality, in terms of the initial data and equation of state. If the tangential pressure is sufficiently strong, configurations that would otherwise evolve to a spacelike singularity, result in a locally naked singularity, both in the homogeneous and in the general, inhomogeneous density case.Comment: 9 pages, revtex4; accepted for publication in Phys. Rev.

On the fate of singularities and horizons in higher derivative gravity

We study static spherically symmetric solutions of high derivative gravity theories, with 4, 6, 8 and even 10 derivatives. Except for isolated points in the space of theories with more than 4 derivatives, only solutions that are nonsingular near the origin are found. But these solutions cannot smooth out the Schwarzschild singularity without the appearance of a second horizon. This conundrum, and the possibility of singularities at finite r, leads us to study numerical solutions of theories truncated at four derivatives. Rather than two horizons we are led to the suggestion that the original horizon is replaced by a rapid nonsingular transition from weak to strong gravity. We also consider this possibility for the de Sitter horizon.Comment: 15 pages, 3 figures, improvements and references added, to appear in PR

High-precision GPS survey of Via Appia: Archaeoastronomy-related aspects

Via Appia was built by the Romans around 312 BCE to connect Rome with Capua during the Samnite wars. The road is an astonishing engineering masterpiece. In particular, the segment which runs from Collepardo to Terracina – 61 km long – is renowned for being virtually straight; however this “straightness” was never investigated quantitatively. As a consequence, the techniques used by the ancient surveyors and their scope – whether it was only practical, or also symbolic – remain obscure. We report here a high-precision GPS survey of the road, performed with a u-blox receiver and further checked with a dual frequency receiver. We give a detailed analysis of the methods used and of the errors, which are shown to be less than 6’. To our knowledge it is the first time that such a long ancient manufactured structure has been surveyed with such a high accuracy. The results lead us to conclude that astronomy was certainly used in the construction of the road and in that of the associated grid, oriented to the setting of the star Castor and to the cardinal points respectively

Epithelium-Off Corneal Collagen Cross-linking Versus Transepithelial Cross-linking for Pediatric Keratoconus.

Abstract PURPOSE:: To compare efficiency and safety of epithelium-off corneal cross-linking (CXL) and transepithelial cross-linking (TE-CXL) in pediatric patients with progressive keratoconus. METHODS:: Uncorrected and corrected visual acuity, corneal topography and pachymetry (Pentacam; Oculus Pentacam), and in vivo confocal microscopy (HRT II, Rostock Cornea Module, Heidelberg Engineering, Heidelberg, Germany) were evaluated at baseline and at 3, 6, and 12 months. RESULTS:: In the epithelium-off CXL group (19 patients, 23 eyes; mean age, 14.75 ± 2.1 years), a significant improvement at month 12 was present for Kmax [-1.11 diopters (D), P = 0.01], Kmin (-3.2 D, P = 0.001), mean K (-1.47 D, P = 0.01), surface asymmetry index (-0.64 D, P = 0.001), inferior-superior symmetry index (-0.54 D, P = 0.01), index of height asymmetry (-2.97, P = 0.03), and anterior elevation at the thinnest location (-2.82 D, P = 0.01) and at the apex (-2.27 D, P = 0.01). Postoperative corneal edema lasted 3 months in 16 eyes (69.5%) and more than 6 months in 2 eyes (8.7%). In the TE-CXL group (10 patients, 14 eyes; mean age, 15 ± 4.2 years), a significant improvement at month 12 was present for Kmax (-1.14 D, P = 0.02), Kmin (-2.04 D, P = 0.01), mean K (-1.63 D, P = 0.01), surface asymmetry index (-0.86 D, P = 0.001), inferior-superior symmetry index (-0.55 D, P = 0.001), index of height asymmetry (-2.95, P = 0.01), and anterior elevation at the thinnest location (-2.96 D, P = 0.01) and at the apex (-2.19 D, P = 0.01). No postoperative corneal edema after TE-CXL was observed. Changes at month 12 from baseline were not significantly different between the 2 groups (P > 0.05). TE-CXE was significantly less painful than epithelium-off CXL. CONCLUSIONS:: In pediatric patients with progressive keratoconus, TE-CXL was less painful, provided similar effectiveness and fewer complications than epithelium-off CXL at 12-month follow-up

Gravitational collapse from smooth initial data with vanishing radial pressure

We study here the spherical gravitational collapse assuming initial data to be necessarily smooth, as motivated by the requirements based on physical reasonableness. A tangential pressure model is constructed and analyzed in order to understand the final fate of collapse explicitly in terms of the density and pressure parameters at the initial epoch from which the collapsedevelops. It is seen that both black holes and naked singularities are produced as collapse end states even when the initial data is smooth. We show that the outcome is decided entirely in terms of the initial data, as given by density, pressure and velocity profiles at the initial epoch, from which the collapse evolves.Comment: 10 pages,3 figures,revtex4,Revised Versio