PRIMARY SCALAR HAIR OF BLACK HOLES IN EFFECTIVE STRING THEORY

Abstract

Black holes in string theories can be studied by means of effective gravity-matter actions. These contain, among others, non-minimally coupled scalar fields, as the dilaton and moduli arising from the compactification of the extra dimensions1. The presence of non-minimal couplings prevents the application of the well known no-hair theorems2, so that it is possible to find regular black hole solutions with scalar hair. Solutions with non-trivial dilaton hair are known for Maxwell3 and Gauss-Bonnet4 black holes. In these cases the dilaton charge is a function of the other parameters of the solutions (secondary hair). However, it has recently been shown that when moduli fields are taken into account as well, one can obtain solutions where the scalar charges of the moduli are independent parameters (primary scalar hair)5,6. The thermodynamics of these black holes has been investigated. In particular, in the Maxwell case a condition for extremality has been obtained, which sets a lower bound for the mass in terms of the magnetic and scalar charges7. Similarly in the Gauss-Bonnet case, a minimal allowed value for the mass has been found, which depends only on the scalar charges and can be interpreted as a ground state for the Hawking evaporation process of the black hole6.