Hello everyone,
I did some research on the internet about analogies between nonlinear optics (NLO) and general relativity (GR), e.g. https://arxiv.org/pdf/0711.4796.pdf. That's already a very nice result, but is it possible to go even futher? It's a stupid idea, but since both GR and NLO are nonlinear field theories, is there any mapping between these two say at least for special solutions to the Einstein field equations? So more generally asking: Is it possible to simulate and study black holes (or other GR scenarios) with nonlinear optical setups in a earth-based laboratory? I'm really excited about this. Thanks a lot!
Philip
Yes it's possible and there has been considerable work on it since, in fact before as well as after the paper mentioned.
It's not true that any two non-linear field theories can be mapped to each other; what's relevant are the symmetries. The symmetries that are relevant for gravitational theories are diffeomorphisms and it's not true that any nonlinear field theory is invariant under diffeomorphisms. How this symmetry can emerge is being quite intensively studied using the so-called holographic correspondence.
Many thanks for your great answer! I know a little bit on AdS/CFT correspondence and the holographic principle. What about concrete examples? Are you aware of any results, where people succeeded to establish a mapping between a certain type of scalar field theory similar to NLO and a graviational theory?
Yes, now there are really too many and one can easily get lost.
A good starting point might be Article Introduction to AdS-CFT
and, perhaps, also: https://web.science.uu.nl/drstp/Postgr.courses/SPTCM/2015/adscmtreview.pdf This might be closer to issues on non-linear optics.On the other hand, it's not hard to see that by replacing, in Maxwell's equations, the Minkowski metric, ημν, by a curved metric, gμν=ημν+hμν , it's possible to describe the effects in a medium-in particular those relevant for non-linear optics. Indeed it's possible to generalize this approach to the case of perturbations about a black hole metric, which is how many experiments in so-called analog gravity are designed.
A recent overview, ``Optical analogues of black hole horizons", might be useful, too: Article Optical analogues of black-hole horizons
, whose fulltext is available on the arXiv: https://arxiv.org/pdf/2002.04216.pdf
There are a few optical analogues of black hole features, mostly based on nonlinear optics, see for example: https://opg.optica.org/oe/fulltext.cfm?uri=oe-30-5-8063&id=469831 and references within