The Wilson approximate dynamics and the Einstein dynamics are compared for binary systems. At the second post-Newtonian approximation, genuine two-body aspects are found to differ by up to 114%. In the regime of a formal innermost stable circular orbit (ISCO) the both dynamics differ by up to 7%. Recently Wilson and Mathews [1] proposed a truncated version of the Einstein field equations to tre...

We present solution generating methods which allow us to construct exact static solutions to the equations of four-dimensional Einstein-MaxwellDilaton gravity starting with arbitrary static solutions to the pure vacuum Einstein equations, Einstein-dilaton or Einstein-Maxwell equations. In four dimensions the field equations of the Einstein-Maxwell-dilaton gravity with arbitrary dilaton coupling...

We present solution generating methods which allow to construct exact static solutions to the equations of four-dimensional Einstein-Maxwell-Dilaton gravity starting with arbitrary static solutions to the pure vacuum Einstein equations, Einstein-dilaton or Einstein-Maxwell equations. In four dimensions the field equations of the Einstein-Maxwell-dilaton gravity with arbitrary dilaton coupling p...

We present an algorithm for computing Minkowski sums among surfaces of revolution and surfaces of linear extrusion, generated by slope-monotone closed curves. The special structure of these simple surfaces allows the process of normal matching between two surfaces to be expressed as an explicit equation. Based on this insight, we also present an efficient algorithm for computing the distance be...

We show that for polytopes P1, P2, . . . , Pr ⊂ R, each having ni ≥ d + 1 vertices, the Minkowski sum P1 + P2 + · · · + Pr cannot achieve the maximum of ∏ i ni vertices if r ≥ d. This complements a recent result of Fukuda & Weibel (2006), who show that this is possible for up to d − 1 summands. The result is obtained by combining methods from discrete geometry (Gale transforms) and topological ...

It is known that in the Minkowski sum of r polytopes in dimension d, with r < d, the number of vertices of the sum can potentially be as high as the product of the number of vertices in each summand [2]. However, the number of vertices for sums of more polytopes was unknown so far. In this paper, we study sums of polytopes in general orientations, and show a linear relation between the number o...

We consider the problem of traveling the contour of the set of all points that are within distance 1 of a connected planar curve arrangement P, forming an embedding of the graph G. We show that if the overall length of P is L, there is a closed roundtrip that visits all points of the contour and has length no longer than 2L + 2n. This result carries over in a more general setting: if R is a com...

Cecile Lahiri, Emory University Katherine B. Dugan, Emory University Xianhong Xie, Albert Einstein College of Medicine Laura Reimers, Albert Einstein College of Medicine Robert D. Burk, Albert Einstein College of Medicine Kathryn Anastos, Albert Einstein College of Medicine Stewart Massad, Washington University Isam-Eldin Eltoum, University of Alabama at Birmingham Xiaonan Xue, Albert Einstein ...

The aim of this paper is to characterize $3$-dimensional $N(k)$-paracontact metric manifolds satisfying certain curvature conditions. We prove that a $3$-dimensional $N(k)$-paracontact metric manifold $M$ admits a Ricci soliton whose potential vector field is the Reeb vector field $xi$ if and only if the manifold is a paraSasaki-Einstein manifold. Several consequences of this result are discuss...