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Wolfgang Rindler

Publications and source records attributed to Wolfgang Rindler.

4 recordsLinked to original sources
arXiv2010

The Relevance of the Cosmological Constant for Lensing

This review surveys some recent developments concerning the effect of the cosmological constant on the bending of light by a spherical mass in Kottler (Schwarzchild-de Sitter) spacetime. Some proposals of how such an effect may be put into a setting of gravitational lensing in cosmology are also discussed. The picture that emerges from this review is that it seems fair to assert that the contribution of $Λ$ to the bending of light has by now been well established, while putting the $Λ$ light-bending terms into a cosmological context is still subject to some interpretation and requires further work and clarification.

astro-ph.CO↗
arXiv2010

More on Lensing by a Cosmological Constant

The question of whether or not the cosmological constant affects the bending of light around a concentrated mass has been the subject of some recent papers. We present here a simple, specific and transparent example where $Λ$ bending clearly takes place, and where it is clearly neither a coordinate effect nor an aberration effect. We then show that in some recent works using perturbation theory the $Λ$ contribution was missed because of initial too-stringent smallness assumptions. Namely: Our method has been to insert a Kottler (Schwarzschild with $Λ$) vacuole into a Friedmann universe, and to calculate the total bending within the vacuole. We assume that no more bending occurs outside. It is important to observe that while the mass contribution to the bending takes place mainly quite near the lens, the $Λ$ bending continues throughout the vacuole. Thus if one deliberately restricts one's search for $Λ$ bending to the immediate neighborhood of the lens, one will not find it. Lastly, we show that the $Λ$ bending also follows from standard Weyl focusing, and so again, it cannot be a coordinate effect.

astro-ph↗
arXiv2008

A New Independent Limit on the Cosmological Constant/Dark Energy from the Relativistic Bending of Light by Galaxies and Clusters of Galaxies

We derive new limits on the value of the cosmological constant, $Λ$, based on the Einstein bending of light by systems where the lens is a distant galaxy or a cluster of galaxies. We use an amended lens equation in which the contribution of $Λ$ to the Einstein deflection angle is taken into account and use observations of Einstein radii around several lens systems. We use in our calculations a Schwarzschild-de Sitter vacuole exactly matched into a Friedmann-Robertson-Walker background and show that a $Λ$-contribution term appears in the deflection angle within the lens equation. We find that the contribution of the $Λ$-term to the bending angle is larger than the second-order term for many lens systems. Using these observations of bending angles, we derive new limits on the value of $Λ$. These limits constitute the best observational upper bound on $Λ$ after cosmological constraints and are only two orders of magnitude away from the value determined by those cosmological constraints.

astro-ph↗