Euclidean spinor Green's functions in the spacetime of a straight cosmic string

We determine generally the spinor Green's function and the twisted spinor Green's function in an Euclidean space with a conical-type line singularity. In particular, in the neighbourhood of the point source, we expree them as a sum of the usual Euclidean spinor Green's functin and a regular term. In four dimensions, we use these determinations to calculate the vacuum energy density and the twisted one for a massless spinor field in the spacetime of a straight cosmic string. In the Minkowski spacetime, we determine explicitly the vacuum energy density for a massive twisted spinor field.Comment: 20 pages, latex, no figure

Fine Structure Constant in the Spacetime of a Cosmic String

We calculate the fine structure constant in the spacetime of a cosmic string. In the presence of a cosmic string the value of the fine structure constant reduces. We also discuss on numerical results.Comment: 5 pages, Published in Phys. Lett.

Electrostatics in a wormhole geometry

We determine in closed form the electrostatic potential generated by a point charge at rest in a simple model of static spherically symmetric wormhole. From this, we deduce the electrostatic self-energy of this point charge.Comment: latex, 5 pages, a slight correctio

The south-pointing chariot on a surface

We examine closely the motion of the south-pointing chariot on a surface by taking into account the fact that both wheels have to roll without slipping. We firstly develop a procedure of successive approximations. In the limit where the distance between the wheels tends to zero, we find again the result due to Santander that the pointer is parallel transported. This is longer true generally within the first-order approximation. We secondly determine in an exact manner the motion of the south-pointing chariot on the sphere. Then, we define a pointer and we prove that this one is parallel transported exactly.Comment: Latex, 16 pages with 3 figure

Bending of a light ray within a dispersive medium in a uniform gravitational field

Recently, Dressel et al determined the vertical deflection of a light ray in a medium, with a strong frequency-dependent dispersion, at rest in a uniform gravitational field. We take up this question within the general relativistic theory of the propagation of light in a dispersive medium, due to Synge.Comment: Latex, 4 page

Time transfer functions in Schwarzschild-like metrics in the weak-field limit: A unified description of Shapiro and lensing effects

We present a complete analysis of the light rays within the linearized, weak-field approximation of a Schwarzschild-like metric describing the gravitational field of an isolated, spherically symmetric body. We prove in this context the existence of two time transfer functions and we obtain these functions in an exact closed-form. We are led to distinguish two regimes. In the first regime, the two time transfer functions correspond to rays which are confined in regions of spacetime where the weak-field approximation is valid. Such a regime occurs in gravitational lensing configurations with double images of a given source. We find the general expressions of the angular separation and the difference in light travel time between the two images. In the second regime, there exists only one time transfer function corresponding to a light ray remaining in a region of weak field. Performing a Taylor expansion of this function with respect to the gravitational constant, we obtain the Shapiro time delay completed by a series of so-called "enhanced terms". The enhanced terms beyond the third order are new.Comment: 12 pages, added one figure in section 3; a paragraph in Introduction rewritten without changing the argument; corrected typos; one reference added for section 2; Eq. (84) rewritten in a more elegant form; slightly revised argument in section 9, results unchange