Reference frames in General Relativity and the galactic rotation curves

The physical interpretation of the exact solutions of the Einstein field equations is, in general, a challenging task, part of the difficulties lying in the significance of the coordinate system. We discuss the extension of the International Astronomical Union (IAU) reference system to the exact theory. It is seen that such an extension, retaining some of its crucial properties, can be achieved in a special class of spacetimes, admitting non-shearing congruences of observers which, at infinity, have zero vorticity and acceleration. As applications, we consider the FLRW, Kerr and NUT spacetimes, the van Stockum rotating dust cylinder, spinning cosmic strings and, finally, we debunk the so-called Balasin-Grumiller (BG) model, and the claims that the galaxies' rotation curves can be explained through gravitomagnetic effects without the need for Dark Matter. The BG spacetime is shown to be completely inappropriate as a galactic model: its dust is actually static with respect to the asymptotic inertial frame, its gravitomagnetic effects arise from unphysical singularities along the axis (a pair of NUT rods, combined with a spinning cosmic string), and the rotation curves obtained are merely down to an invalid choice of reference frame -- the congruence of zero angular momentum observers, which are being dragged by the singularities.Comment: 29 pages, 10 figures. Slightly improved version, typos corrected, references added. Supplemental material is provided in the ancillary Mathematica files "NUTmetrics.nb" and "BGmetric.nb". Version to be submitte

Analytical properties of Einasto dark matter haloes

Recent high-resolution N-body CDM simulations indicate that nonsingular three-parameter models such as the Einasto profile perform better than the singular two-parameter models, e.g. the Navarro, Frenk and White, in fitting a wide range of dark matter haloes. While many of the basic properties of the Einasto profile have been discussed in previous studies, a number of analytical properties are still not investigated. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halo, is still lacking to date. To this aim, we used a Mellin integral transform formalism to derive a closed expression for the Einasto surface density and related properties in terms of the Fox H and Meijer G functions, which can be written as series expansions. This enables arbitrary-precision calculations of the surface density and the lensing properties of realistic dark matter halo models. Furthermore, we compared the S\'ersic and Einasto surface mass densities and found differences between them, which implies that the lensing properties for both profiles differ.Comment: 10 pages, 2 figures. Accepted for publication in Astronomy and Astrophysic

Analytical shear and flexion of Einasto dark matter haloes

N-body simulations predict that dark matter haloes are described by specific density profiles on both galactic- and cluster-sized scales. Weak gravitational lensing through the measurements of their first and second order properties, shear and flexion, is a powerful observational tool for investigating the true shape of these profiles. One of the three-parameter density profiles recently favoured in the description of dark matter haloes is the Einasto profile. We present exact expressions for the shear and the first and second flexions of Einasto dark matter haloes derived using a Mellin-transform formalism in terms of the Fox H and Meijer G functions, that are valid for general values of the Einasto index. The resulting expressions can be written as series expansions that permit us to investigate the asymptotic behaviour of these quantities. Moreover, we compare the shear and flexion of the Einasto profile with those of different mass profiles including the singular isothermal sphere, the Navarro-Frenk-White profile, and the S\'ersic profile. We investigate the concentration and index dependences of the Einasto profile, finding that the shear and second flexion could be used to determine the halo concentration, whilst for the Einasto index the shear and first and second flexions may be employed. We also provide simplified expressions for the weak lensing properties and other lensing quantities in terms of the generalized hypergeometric function.Comment: 14 pages, 3 figures. Accepted for publication in Astronomy and Astrophysic

Étude de la vasodilatation cutanée induite par la pression au cours d'un diabète expérimental avec ou sans neuropathie

Une altération de la réponse vasodilatatrice cutanée à une pression progressive et non douloureuse (PIV : Pressure-Induced-Vasodilation) appliquée localement a été observée chez des patients diabétiques de type 1. Le but de cette thèse a été d'évaluer l'atteinte de la PIV dans différents contextes de durée de diabète expérimental chez la souris. Dans les mêmes contextes de durée de diabète, nous avons étudié les effets d'inhibiteurs pharmacologiques sur l'atteinte de la PIV. Une prévention de l'atteinte de la PIV par l'acide alpha-lipoïque a été observée dans un diabète précoce n'exprimant qu'une microangiopathie. Une restauration de la PIV par le sorbinil a été observée dans un diabète tardif exprimant une neuropathie sévère associée à une microangiopathie. Ces études ouvrent des perspectives thérapeutiques intéressantes pour prévenir et améliorer les complications microcirculatoires cutanées liées à la pression chez les patients diabétiques.Pressure-induced vasodilation (PIV) is a mechanism whereby skin blood flow increases in response to progressive locally applied pressure. PIV decreases early in diabetic patients as a result of vascular and/or neural impairment. This work was designed to determine the effect of vascular changes and neurovascular changes on PIV in streptozotocin-induced diabetic mice. We determined whether the diabetes-induced PIV alteration could be prevented or restored by pharmacological agents in these different terms of diabetes. Alpha-lipoïc acid treatment was able to preserve PIV response in diabetic mice in short-term diabetes without neuropathy. Sorbinil treatment restored PIV response in a long-term diabetes with severe neuropathy. Alpha-lipoic acid and sorbinil treatments by preserving and by restoring the cutaneous PIV response respectively should preserve the normal reaction to pressure strain, which might limit the risk of pressure-induced ulcer in diabetic patients.ANGERS-BU Médecine-Pharmacie (490072105) / SudocPARIS-BIUP (751062107) / SudocSudocFranceF