ABSTRACT

If string theory describes nature, then charged black holes are not described by the Reissner-Nordström solution. This solution must be modified to include a massive dilaton. In the limit of vanishing dilaton mass, the new solution can be found by a generalization of the Harrison transformation for the Einstein-Maxwell equations. These two solution generating transformations and the resulting black holes are compared. It is shown that the extremal black hole with massless dilaton can be viewed as the “square root” of the extremal Reissner-Nordström solution. When the dilaton mass is included, extremal black holes are repulsive, and it is energetically favorable for them to bifurcate into smaller holes.

INTRODUCTION

It is a pleasure to honor Dieter Brill on the occasion of his sixtieth birthday. Over the years, Dieter has worked on many aspects of general relativity. But two of his recent interests are negative energy (in higher dimensional theories) (Brill and Pfister 1989; Brill and Horowitz 1991), and the possibility that extremal charged black holes can quantum mechanically bifurcate (Brill 1992). I would like to describe some recent work which touches on both of these areas.

For many years, it has been widely believed that static charged black holes in nature are accurately described by the Reissner-Nordström solution.