  Energy conditions, especially the null energy condition (NEC), are
generically imposed on solutions to retain a physically sensible classical
field theory and they also play an important role in the AdS/CFT duality. Using
this duality, we study non-trivially deformed strongly coupled quantum field
theories at large-$N_c$. The corresponding dual classical gravity constructions
entail the use of radially non-monotonic D-brane distributions. The gravity
backgrounds are supersymmetric and hence perturbatively stable, and do not
possess curvature singularities. There are no short-cuts through the bulk
spacetime for signal propagation which assures that the field theory duals are
causal. Nevertheless, some of our solutions violate the NEC in the gravity
dual. In these cases the non-monotonicity of the D-brane distributions is
reflected in the properties of the renormalization group flow: none of the
$c$-functions proposed in the literature are monotonic. This further suggests
that the non-monotonic behavior of the $c$-functions within previously known
anisotropic backgrounds does not originate from the breaking of Lorentz
invariance. We surmise that NEC violations induced by quantum corrections also
need to be considered in holographic duals, but can be studied already at the
classical level.
