More on Lensing by a Cosmological Constant

Understand

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 $\Lambda$ 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 $\Lambda$ contribution was missed because of initial too-stringent smallness assumptions.
• Namely: Our method has been to insert a Kottler (Schwarzschild with $\Lambda$) vacuole into a Friedmann universe, and to calculate the total bending within the vacuole.