Oslo-TP-4-94, USITP-94-5 gr-qc/9403060 Scattering of Fermions off Dilaton Black Holes

We discuss how various properties of dilaton black holes depend on the dilaton coupling constant a. In particular we investigate the a-dependence of certain mass parameters both outside and in the extremal limit and discuss their relation to thermodynamical quantities. To further illuminate the role of the coupling constant a we look at a massless point particle in a dilaton black hole geometry as well as the scattering of (neutral) fermions. In this latter case we find that the scattering potential vanishes for the zero angular momentum mode which seems to indicate a catastrophic deradiation when a > 1. PACS numbers: 03.65.Sq , 04.20.Cv , 04.60.+n Typeset using REVTEX Electronic address: [email protected] Electronic address: [email protected] and [email protected] 1 Dilaton black holes are studied because they arise as solutions to the low-energy string effective field theory [1], and because they shed new light on the old question of black holes as elementary particles [2]. The dilaton black holes are solutions to field equations that describe a scalar (dilaton) field and an electromagnetic field coupled to Einstein gravity. It has proven useful to let the dilaton coupling depend on a non-negative parameter a. The value a = 0 corresponds to the usual Einstein theory whereas the coupling a = 1 is the value dictated by string theory. Furthermore, the value a = √ 3 seems to be special. For this value of a rotating solutions [3] as well as a string black hole [4] have been found. It also arises in dimensional reduction of d = 5 supergravity studied in the context of supersymmetric solitons [5]. In general many features of the solution (but not all) depend on the value of a. The present work corroborates this picture. The main problem treated in this note is the scattering of spinning particles off of dilaton black holes. We derive the corresponding potential and discuss its behaviour as a function of a. In particular we find that it generally diverges at the horizon in the extremal limit for a > 1. For a = √ 3 there is an additional pole, interestingly enough, although the relation to the abovementioned rotating solution, string solution or soliton solutions is unclear. This note also contains a derivation and discussion of certain mass-parameters: the ADMmass, the Tolman mass and the mass of the black hole. Although we relate the usual definition of the temperature and entropy of the black hole to its ADM mass, we use the vanishing of the black hole mass as the main indication for the vanishing of the black hole in the extremal limit. This is because it has been argued that the thermo-dynamical description breaks down in that limit [6,2].