Mass And Force Relations For Einstein-Maxwell-Dilaton Black Holes

Abstract

We investigate various properties of extremal dyonic static black holes in Einstein-Maxwell-Dilaton theory. Using the fact that the long-range force between two identical extremal black holes always vanishes, we obtain a simple first-order ordinary differential equation for the black hole mass in terms of its electric and magnetic charges. Although this equation appears not to be solvable explicitly for general values of the strength a of the dilatonic coupling to the Maxwell field, it nevertheless provides a powerful way of characterising the black hole mass and the scalar charge. We make use of these expressions to derive general results about the long-range force between two non-identical extremal black holes. In particular, we argue that the force is repulsive whenever a>1 and attractive whenever a<1 (it vanishes in the intermediate BPS case a=1). The sign of the force is also correlated with the sign of the binding energy between extremal black holes, as well as with the convexity or concavity of the surface characterizing the extremal mass as a function of the charges. Our work is motivated in part by the Repulsive Force Conjecture and the question of whether long range forces between non-identical states can shed new light on the Swampland.

arXiv comment34 pages, 3 figures. Typos fixed, footnote 3 added

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Cited by in corpus (3)

• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• On the interactions and equilibrium between Einstein-Maxwell-Dilaton black holes
• Spinning extremal dyonic black holes in $\gamma =1$ Einstein-Maxwell-dilaton theory