Stringy Black Holes and Energy Conditions

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, the negativity of the Ricci curvature, turns out to be the requirement for ensuring focussing of timelike geodesics whereas null geodesics always focus irrespective of the choice of the metric. 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 black hole metric, strangely, matter satisfies the Weak Energy condition in the string frame whereas the magnetic black hole satisfies the Null Energy condition. Finally, the Averaged Null Energy Condition is evaluated along radial null geodesics for each of these black hole spacetimes.