A practical, covariant puncture for second-order self-force calculations

Accurately modeling an extreme-mass-ratio inspiral requires knowledge of the second-order gravitational self-force on the inspiraling small object. Recently, numerical puncture schemes have been formulated to calculate this force, and their essential analytical ingredients have been derived from first principles. However, the \emph{puncture}, a local representation of the small object's self-field, in each of these schemes has been presented only in a local coordinate system centered on the small object, while a numerical implementation will require the puncture in coordinates covering the entire numerical domain. In this paper we provide an explicit covariant self-field as a local expansion in terms of Synge's world function. The self-field is written in the Lorenz gauge, in an arbitrary vacuum background, and in forms suitable for both self-consistent and Gralla-Wald-type representations of the object's trajectory. We illustrate the local expansion's utility by sketching the procedure of constructing from it a numerically practical puncture in any chosen coordinate system.Comment: 23 pages, 1 figure, final version to be published in Phys Rev

Some stable homology calculations and Occam's razor for Hodge structures

Motivated by motivic zeta function calculations, Vakil and Wood in [VMW12] made several conjectures regarding the topology of subspaces of symmetric products. The purpose of this note is to prove two of these conjectures and disprove a strengthening of one of them.Comment: 7 page

BFKL Pomeron calculus: nucleus-nucleus scattering

In this paper the action of the BFKL Pomeron calculus is re-written in momentum representation, and the equations of motion for nucleus-nucleus collisions are derived, in this representation. We found the semi-classical solutions to these equations, outside of the saturation domain. Inside this domain these equations reduce to the set of delay differential equations, and their asymptotic solutions are derived.Comment: 22pp. 9 figures imn .eps file