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

New method for determining the light travel time in static, spherically symmetric spacetimes. Calculation of the terms of order G3G^3

A new iterative method for calculating the travel time of a photon as a function of the spatial positions of the emitter and the receiver in the field of a static, spherically symmetric body is presented. The components of the metric are assumed to be expressible in power series in $m/r$, with $m$ being half the Schwarzschild radius of the central body and $r$ a radial coordinate. The procedure exclusively works for a light ray which may be described as a perturbation in powers of $G$ of a Minkowskian null geodesic, with $G$ being the Newtonian gravitational constant. It is shown that the expansion of the travel time of a photon along such a ray only involves elementary integrals whatever the order of approximation. An expansion of the impact parameter in power series of $G$ is also obtained. The method is applied to explicitly calculate the perturbation expansions of the light travel time and the impact parameter up to the third order. The full expressions yielding the terms of order $G^3$ are new. The expression of the travel time confirms the existence of a third-order enhanced term when the emitter and the receiver are in conjunction relative to the central body. This term is shown to be necessary for determining the post-Newtonian parameter $\gamma$ at a level of accuracy of $10^{-8}$ with light rays grazing the Sun.Comment: 24 pages; Eq. (114) corrected; published in Classical and Quantum Gravity with a Corrigendu

Black holes in which the electrostatic or scalar equation is solvable in closed form

We show that the method used in the Schwarzschild black hole for finding the elementary solution of the electrostatic equation in closed form cannot extend in higher dimensions. By contrast, we prove the existence of static, spherically symmetric geometries with a non-degenerated horizon in which the static scalar equation can be solved in closed form. We give the explicit results in 6 dimensions. We determine moreover the expressions of the electrostatic potential and of the static scalar field for a point source in the extremal Reissner-Nordstrom black holes in higher dimensions.Comment: 20 pages, no figur

Electrostatics in a simple wormhole revisited

The electrostatic potential generated by a point charge at rest in a simple static, spherically symmetric wormhole is given in the form of series of multipoles and in closed form. The general potential which is physically acceptable depends on a parameter due to the fact that the monopole solution is arbitrary. When the wormhole has Z2-symmetry, the potential is completely determined. The calculation of the electrostatic self-energy and of the self-force is performed in all cases considered.Comment: 16 pages, no figure

Particle Creation If a Cosmic String Snaps

We calculate the Bogolubov coefficients for a metric which describes the snapping of a cosmic string. If we insist on a matching condition for all times {\it and} a particle interpretation, we find no particle creation.Comment: 10 pages, MRC.PH.17/9

Time transfer and frequency shift to the order 1/c^4 in the field of an axisymmetric rotating body

Within the weak-field, post-Newtonian approximation of the metric theories of gravity, we determine the one-way time transfer up to the order 1/c^4, the unperturbed term being of order 1/c, and the frequency shift up to the order 1/c^4. We adapt the method of the world-function developed by Synge to the Nordtvedt-Will PPN formalism. We get an integral expression for the world-function up to the order 1/c^3 and we apply this result to the field of an isolated, axisymmetric rotating body. We give a new procedure enabling to calculate the influence of the mass and spin multipole moments of the body on the time transfer and the frequency shift up to the order 1/c^4. We obtain explicit formulas for the contributions of the mass, of the quadrupole moment and of the intrinsic angular momentum. In the case where the only PPN parameters different from zero are beta and gamma, we deduce from these results the complete expression of the frequency shift up to the order 1/c^4. We briefly discuss the influence of the quadrupole moment and of the rotation of the Earth on the frequency shifts in the ACES mission.Comment: 17 pages, no figure. Version 2. Abstract and Section II revised. To appear in Physical Review

Frequency of cancer in children residing in Mexico City and treated in the hospitals of the Instituto Mexicano del Seguro Social (1996–2001)

BACKGROUND: The objective of this article is to present the frequency of cancer in Mexican children who were treated in the hospitals of the Instituto Mexicano del Seguro Social in Mexico City (IMSS-MC) in the period 1996–2001. METHODS: The Registry of Cancer in Children, started in 1996 in the IMSS-MC, is an on-going, prospective register. The data from 1996 through 2001 were analyzed and the different types of cancer were grouped according to the International Classification for Cancer in Children (ICCC). From this analysis, the general and specific frequencies by age and by sex were obtained for the different groups of neoplasms. Also, the frequency of the stage of the disease that had been diagnosed in cases of children with solid tumors was obtained. RESULTS: A total of 1,702 new cases of children with cancer were registered, with the male/female ratio at 1.1/1. Leukemias had the highest frequency with 784 cases (46.1%) and, of these, acute lymphoblastic leukemias were the most prevalent with 614 cases (78.3%). Thereafter, in descending order of frequency, were tumors of the central nervous system (CNST) with 197 cases (11.6%), lymphomas with 194 cases (11.4%), germinal cell tumors with 110 cases (6.5%), and bone tumors with 97 cases (5.7%). The highest frequency of cancer was found in the group of one to four year-olds that had 627 cases (36.8%). In all the age groups, leukemias were the most frequent. In the present work, the frequency of Hodgkin's disease (~4%) was found to be lower than that (~10%) in previous studies and the frequency of tumors of the sympathetic nervous system was low (2.3%). Of those cases of solid tumors for which the stage of the disease had been determined, 66.9% were diagnosed as being Stage III or IV. CONCLUSIONS: The principal cancers in the children treated in the IMSS-MC were leukemias, CNST, and lymphomas, consistent with those reported by developed countries. A 2.5-fold reduction in the frequency of Hodgkin's disease was found. Of the children, the stage of whose disease had been determined, two thirds were diagnosed as having advanced stages of the disease