How to calculate backreaction in AdS space?
Answers
This might be a very straight forward and basic question in GR. I am interested in calculating backreaction due to certain matter field (say, scalar) in AdS space.
Should I put the energy-momentum tensor (Tμν) for the scalar field into the Einstein equation with negative cosmological constant and try to solve it subject to some symmetries? (I feel this can be a difficult task!)
Can I somehow use the original AdS metric and see how the matter field (perturbatively) change it. I think this is the original idea of backreaction on some particular background. But don't have any idea how to implement it practically.
Is there any subtlety involved due to non-trivial asymptotic behavior of AdS space compared to Minkowski space.
Any further simplification to this computation if I work specifically in AdS3.