  As a preparation for a mathematically consistent study of the physics of
symmetric spacetimes in a noncommutative setting, we study symmetry reductions
in deformed gravity. We focus on deformations that are given by a twist of a
Lie algebra acting on the spacetime manifold. We derive conditions on those
twists that allow a given symmetry reduction. A complete classification of
admissible deformations is possible in a class of twists generated by commuting
vector fields. As examples, we explicitly construct the families of vector
fields that generate twists which are compatible with
Friedmann-Robertson-Walker cosmologies and Schwarzschild black holes,
respectively. We find nontrivial isotropic twists of FRW cosmologies and
nontrivial twists that are compatible with all classical symmetries of black
hole solutions.
