Constant threshold correction to electrically charged dilatonic black holes

We investigate the effect of a constant threshold correction to a general nonextreme, static, spherically symmetric, electrically charged black hole solution of the dilatonic Einstein-Maxwell Lagrangian, with an arbitrary coupling β between the electromagnetic tensor and the dilaton field. For a small β, an exact analytical solution is obtained. For an arbitrary β, a close form solution, up to first order in the constant threshold correction, of the metric and the dilaton are presented. In the extremal limit, the close form solution is reduced to an exact analytical form. Dilaton, i.e., scalar field without self-interactions, arise naturally in basic theories that unify gravity with other interactions, including certain supergravity theories, and effective theory from superstrings. In general, it couples to the gauge field kinetic energy as well as to the matter potential. It is therefore of interest to address dilatonic topological configurations in such theories. The dilatonic charged black hole solutions without threshold correction are known [1] [2]. The presence of the coupling between dilaton and the electromagnetic tensor produces black hole solutions drastically different from the Reissner-Nordstrom solutions. In addition to the dilaton, there are moduli fields which are generically present in string theories. They are stringy modes in a vacuum associated with compactification of the extra dimensions. In general, they act as threshold corrections to the scalar function that couples to the gauge field kinetic energy [3] [4]. Such scalar function determines the strength of the effective gauge coupling constant. Effects of stringy threshold corrections on charged spherically symmetric dilatonic configurations without gravity have been studied in [5]. The present work is to generalize the ∗E-mail address: [email protected] 1 study to charged black hole configurations, i.e., by including gravitational effects. The most general bosonic Lagrangian for the dilatonic Einstein-Maxwell theory with just one moduli field is of the following form: L = ∫