On the influence of the cosmological constant on gravitational lensing in small systems

The cosmological constant Lambda affects gravitational lensing phenomena. The contribution of Lambda to the observable angular positions of multiple images and to their amplification and time delay is here computed through a study in the weak deflection limit of the equations of motion in the Schwarzschild-de Sitter metric. Due to Lambda the unresolved images are slightly demagnified, the radius of the Einstein ring decreases and the time delay increases. The effect is however negligible for near lenses. In the case of null cosmological constant, we provide some updated results on lensing by a Schwarzschild black hole.Comment: 8 pages, 1 figure; v2: extended discussion on the lens equation, references added, results unchanged, in press on PR

Freight Efficiency Strategies: Information Technology

This White Paper presents recommendations for using information technology solutions to increase the efficiency of California\u2019s multi modal freight system. These recommendations resulted from a consensus based process by working group committee members. The authors address two problems: information problems in the goods movement supply chain, and information problems in statewide trucking