The energy condition inequalities for the matter stress energy comprised out
of the dilaton and Maxwell fields in the dilaton-Maxwell gravity theories
emerging out of string theory are examined in detail. In the simplistic 1+1
dimensional models, R≤0 (where R is the Ricci scalar), turns out to be
the requirement for ensuring focusing of timelike geodesics. In 3+1 dimensions,
we outline the requirements on matter for pure dilaton theories-these in turn
constrain the functional forms of the dilaton. Furthermore, in charged dilaton
gravity a curious opposite behaviour of the matter stress energy w.r.t the
violation/conservation of the Weak Energy Condition is noted for the electric
and magnetic black hole metrics written in the string frame of reference. We
also investigate the matter that is necessary for creating certain specific
non-asymptotically flat black holes. For the electric and magnetic black hole
metrics, strangely, matter satisfies the weak energy condition in the string
frame. Finally, the Averaged Null Energy Condition is evaluated along radial
null geodesics for each of these black hole spacetimes.Comment: 23 pages, RevTex, no figures, corrected and extended,to appear in
Physical Review