Stringy black holes and energy conditions

The energy condition inequalities for the matter stress energy comprised of the dilaton and Maxwell fields in the dilaton-Maxwell gravity theories emerging out of string theory are examined in detail. In the simplistic $\mathrm{}(1+1)\mathrm{}$-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 behavior of the matter stress energy with respect to the violation or 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 nonasymptotically 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.