  We review the constraints modified theories of gravity must satisfy to be
compatible with the spherically symmetric black hole solutions of semiclassical
gravity that describe the formation of an apparent horizon in finite time of a
distant observer. The constraints are satisfied in generic modified gravity
theories with up to fourth-order derivatives in the metric, indicating that the
semiclassical solutions correspond to zeroth-order terms in perturbative
solutions of these models. From an observational point of view, this result
implies that it may not be possible to distinguish between the semiclassical
theory and modifications including up to fourth-order derivatives based on the
observation of an apparent horizon alone.
