Stringy black holes and energy conditions

TL;DR

This paper investigates the energy conditions in string theory-derived dilaton-Maxwell gravity, analyzing their implications for black hole solutions and geodesic focusing in various dimensions.

Contribution

It provides a detailed analysis of energy condition inequalities in dilaton-Maxwell theories, revealing unique behaviors of matter stress energy in black hole spacetimes within string theory.

Findings

In 1+1 dimensions, Ricci scalar must be non-positive for geodesic focusing.

In 3+1 dimensions, matter constraints influence dilaton functional forms.

In charged dilaton black holes, matter satisfies the weak energy condition in the string frame.

Abstract

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, $R\le 0$ (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.