Effect of a cylindrical thin-shell of matter on the electrostatic self-force on a charge

The electrostatic self-force on a point charge in cylindrical thin-shell space-times is interpreted as the sum of a $bulk$ field and a $shell$ field. The $bulk$ part corresponds to a field sourced by the test charge placed in a space-time without the shell. The $shell$ field accounts for the discontinuity of the extrinsic curvature ${\kappa^p}_q$. An equivalent electric problem is stated, in which the effect of the shell of matter on the field is reconstructed with the electric potential produced by a non-gravitating charge distribution of total image charge $Q$, to interpret the shell field in both the interior and exterior regions of the space-time. The self-force on a point charge $q$ in a locally flat geometry with a cylindrical thin-shell of matter is calculated. The charge is repelled from the shell if ${\kappa^{p}}_{p}=\kappa<0$ (ordinary matter) and attracted toward the shell if $\kappa>0$ (exotic matter). The total image charge is zero for exterior problems, while for interior problems $Q/q=-\kappa \, r_e$, with $r_e$ the external radius of the shell. The procedure is general and can be applied to interpret self-forces in other space-times with shells, e.g., for locally flat wormholes we found $Q_{\mp}^{wh}/q=-1/ (\kappa_{wh} r_{\pm})$.Comment: (15 pages, 6 figures; the work had been extended, corrected and reformulated from version v1 to v2, and minor misprints corrected from v2 to v3

On G/N-Hilb of N-Hilb

In this paper we consider the iterated G-equivariant Hilbert scheme G/N-Hilb(N-Hilb) and prove that G/N-Hilb(N-Hilb(C^3)) is a crepant resolution of C^3/G isomorphic to the moduli space of \theta-stable representations of the McKay quiver for certain stability condition \theta. We provide several explicit examples to illustrate this construction. We also consider the problem of when G/N-Hilb(N-Hilb) is isomorphic to G-Hilb showing the fact that these spaces are most of the times different.Comment: Final version. Explanations improved throughout the paper and mistakes in some statements have been corrected; (old) sections 2.2 and 3.1 have been expanded into new sections; (old) section 5 have been reorganised and several results in it have been extended. To appear in Kyoto Journal of Mathematic

Perturbative dynamics of thin-shell wormholes beyond general relativity: An alternative approach

Recent studies relating the approximations for the equations-of-state for thin shells and their consequent perturbative evolution are extended to thin-shell wormholes in theories beyond general relativity and more than four spacetime dimensions. The assumption of equations-of-state of the same form for static and slowly evolving shells appears as a strong restriction excluding the possibility of oscillatory evolutions. Then the new results considerably differ from previous ones obtained within the usual linearized approach.Fil: Rubín de Celis, Emilio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Tomasini, Cecilia. Universidad de Buenos Aires; ArgentinaFil: Simeone, Claudio Mauricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentin

Probing global aspects of a geometry by the self-force on a charge: Spherical thin-shell wormholes

The self-interaction for a static point charge in the space-time of a thin-shell wormhole constructed connecting two identical Schwarzschild geometries is calculated in a series expansion. The electrostatic self-force is evaluated numerically. It is found to be attractive towards the throat except for some values of the throat radius proximate to the value of the Schwarzschild horizon for which the force is repulsive or attractive depending on the position of the charge. The result differs from the self-force in the space-time of the Schwarzschild black hole, where it is always repulsive from the center. Although these wormhole and black hole geometries are locally indistinguishable, the different topologies of both backgrounds are manifested in the electrostatic field of a point charge.Comment: 17 pages, 4 figue

Combining causal model and focus group discussions experiences learned from a socio-anthropological research on the differing perceptions of caretakers and health professionals on children's health (Bolivia/Peru)

The paper discusses the utility of constructing causal models in focus groups. This was experienced as a complement to an in-depth ethnographic research on the differing perceptions of caretakers and health professionals on child's growth and development in Peru and Bolivia. The rational, advantages, difficulties and necessary adaptations of combining the two techniques are discussed on the basis of concrete examples. Authors conclude that the building of a causal model in a focus group session can be useful in comparing lay etiologies of diseases as perceived by different categories of caretakers and health professionals and in identifying specific health risks faced by children. Causal model building in a focus group can help renew discussions and participants'interest but its use is only justified when the study concerns the perception of the causality of a given phenomenon

Reconstruction Algebras of Type D (I)

This is the second in a series of papers which give an explicit description of the reconstruction algebra as a quiver with relations; these algebras arise naturally as geometric generalizations of preprojective algebras of extended Dynkin diagrams. This paper deals with dihedral groups G=D_{n,q} for which all special CM modules have rank one, and we show that all but four of the relations on such a reconstruction algebra are given simply as the relations arising from a reconstruction algebra of type A. As a corollary, the reconstruction algebra reduces the problem of explicitly understanding the minimal resolution (=G-Hilb) to the same level of difficulty as the toric case.Comment: 31 pages, final versio