  Gravitational theories with fixed background fields break local Lorentz and
diffeomorphism invariance either explicitly or spontaneously. In the case of
explicit breaking it is known that conflicts can arise between the dynamics and
geometrical constraints, while spontaneous breaking evades this problem. It is
for this reason that in the gravity sector of the Standard-Model Extension
(SME) it is assumed that the background fields (SME coefficients) originate
from spontaneous symmetry breaking. However, in other examples, such as
Chern-Simons gravity and massive gravity, diffeomorphism invariance is
explicitly broken by the background fields, and the potential conflicts between
the dynamics and geometry can be avoided in most cases. An analysis of how this
occurs is given, and the conditions that are placed on the metric tensor and
gravitational structure as a result of the presence of an explicit-breaking
background are described. The gravity sector of the SME is then considered for
the case of explicit breaking. However, it is found that a useful
post-Newtonian limit is only obtained when the symmetry breaking is
spontaneous.
