On the interactions and equilibrium between Einstein-Maxwell-Dilaton black holes

TL;DR

This paper investigates the interactions and equilibrium conditions of non-rotating Einstein-Maxwell-Dilaton black holes, analyzing known and new solutions, and clarifying how scalar hair and interaction energies influence black hole dynamics.

Contribution

It introduces methods to distinguish between static and dynamical black hole configurations using initial data and interaction energies, including new insights into scalar hair effects.

Findings

Self-interaction energy relates to scalar hair and dynamical black holes.

Interaction energies between black holes follow Newtonian and Coulombian forms with scalar charge contributions.

Removing self-interaction energies isolates forces between black holes, showing scalar charges add an attractive component.

Abstract

We study the interactions and the conditions for the equilibrium of forces between generic non-rotating black holes of the Einstein-Maxwell-Dilaton (EMD) theory. We study known (and some new) solutions of the time-symmetric initial-data problem escribing an arbitrary number of those black holes, some of them with primary scalar hair. We show how one can distinguish between initial data corresponding to dynamical situations in which the black holes (one or many) are not in equilibrium and initial data which are just constant-time slices of a static solution of the full equations of motion describing static black holes using (self-)interaction energies. For a single black hole, non-vanishing self-interaction energy is always related to primary scalar hair and to a dynamical black hole. Removing the self-interaction energies in multi-center solutions we get interaction energies related to the attractive and repulsive forces acting on the black holes. As shown by Brill and Lindquist, for widely separated black holes, these take the standard Newtonian and Coulombian forms plus an additional interaction term associated with the scalar charges which is attractive for like charges.