Ronald Kantowski, Bin Chen, Xinyu Dai
We present a much simplified version of the embedded point mass lens theory and then make the obvious extension of this theory to any embedded transparent lens. Embedding a lens effectively reduces the gravitational potential's range, i.e., partially shields the lensing potential because the lens mass is made a contributor to the mean mass density of the universe and not simply superimposed upon it. This presentation results from simplifying previous formulations of the embedded point mass theory and is quite similar to the standard theory. We are then able to re-derive the simplified point mass theory by applying Fermat's least-time principle to the time-delay function. Even though rigorous derivations are only made for the point mass, the lens equation to the lowest order for any distributed lens, is obvious. We find from this simplified theory that embedding can introduce corrections at the few percent level in weak lensing shears caused by large clusters but only at large impacts. The potential part of the time delay is also affected in strong lensing at the few percent level. Additionally we are surprised to find that the cosmological constant is only present in this theory at a higher order.
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http://arxiv.org/abs/1303.6648
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