What is *uplift* in respect to extra dimensions and their stability? What is uplift in respect to extra dimensions and their stability?
It's notoriously hard to find something on this, as all possible keyword combinations pull up plethora of unrelated Google hits.
 A: To uplift a solution to the field equations (such as Einstein's equations or their generalizations) or to uplift any other construction or argument means to find a solution of a higher-dimensional theory (or the analogous construction or argument) given the known solution of a lower-dimensional theory.
This is possible if the lower-dimensional theory may be derived as a "dimensional reduction" of the higher-dimensional theory. The dimensional reduction is a result of compactification of some excess dimensions of the higher-dimensional theory in which the size of these extra dimensions are sent to vanishingly small values so that nothing can depend on them anymore and they effectively disappear. The uplifting is a reverse process. Those higher-dimensional fields that are directly inherited by the lower-dimensional theory are set to the appropriate values (usually constant as functions of the excess dimensions, but sometimes more general Fourier-like analysis is needed).
Physicists sometimes jokingly use a special name for the addition of the extra dimensions, "dimensional oxidation", because at least in chemistry, the opposite of reduction is oxidation.
