  Based on the observation that the exterior space-times of Schwarzschild-type
solutions allow two symmetric slicings, a static spherically symmetric one and
a timelike homogeneous one, modifications of gravitational dynamics suggested
by symmetry-reduced models of quantum cosmology can be used to derive
corresponding modified spherically symmetric equations. Generally covariant
theories are much more restricted in spherical symmetry compared with
homogeneous slicings, given by $1+1$-dimensional dilaton models if they are
local. As shown here, modifications used in loop quantum cosmology do not have
a corresponding covariant spherically symmetric theory. Models of loop quantum
cosmology therefore violate general covariance in the form of slicing
independence. Only a generalized form of covariance with a non-Riemannian
geometry could consistently describe space-time in models of loop quantum
gravity.
