Answer from an expert in astronomical simulations: --------------------------------------------------
Do the current galaxy gravitational simulations take into account the following phenomenon?
Gravitational lensing produces distortions when viewing distant objects. Presumably gravitational lensing also distorts the transmission of the gravitational force itself.
I am not an expert in lensing (but there are some at UCSC!), but I'll try to answer to your question. Gravitational lensing is due to a distorsion of the space-time continuum because of the effect of gravity, and an exact calculation requires a general relativity framework. Within such framework, everything is treated self-consistently, so the description of the system should be OK. I see that with your question you think to something along the lines of a quantum theory of gravity (where gravity is mediated by a graviton particle that transmits the info). Unfortunately, we have no such theory currently, so no exact answer to offer. But if we were to consider a source of gravitational waves behind a lens (e.g. a BH-BH merger), then I would expect that a GR calculation of the propagation of the wavefront will take into account correctly the distorsion because of the gravitational lens. I can run this question with a friend who is an expert on GR and gravitational waves and in case get back to you if I hear a better insight.
Do current galaxy gravitational simulations take into account the gravitational lensing effect of the black hole(s) in the center of the galaxy?
Short answer is no: The direct gravitational effect of the black hole is already limited to only a small portion of the galaxy, that is in the central region that has a mass comparable to the black hole mass (and therefore something of the order of 0.001 of the total galaxy mass). This effect, can be included in the simulations if needed by adding the BH as a point particle. For many problems, a 0.001 effect is already negligible (unless one is interested in the dynamics of the central region, of course). I do not think that even if there were any high-order corrections because of a lensing effect, these would ever go into a regime where they would be higher than the typical numerical issues of finite spatial/temporal/mass resolution and then roundoff accuracy. Hope this helps. Let me know if you have any other question. Michele Trenti Kavli Fellow Institute of Astronomy University of Cambridge Madingley Road Phone: +44 (0)1223 337526 Cambridge CB3 0HA Fax: +44 (0)1223 337523 United Kingdom E-mail: trenti@ast.cam.ac.uk