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

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.

arXiv commentLatex2e file, 38 pages, no figures

References in corpus (25)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Supersymmetry as a Cosmic Censor
• Moduli, Scalar Charges, and the First Law of Black Hole Thermodynamics
• Black Holes as Elementary Particles
• The Collision of Two Black Holes
• Quantum Hair on Black Holes
• Topology, Entropy and Witten Index of Dilaton Black Holes
• The Head-On Collision of Two Equal Mass Black Holes Peter Anninos
• Stationary Axion/Dilaton Solutions and Supersymmetry
• Charge Quantization of Axion-Dilaton Black Holes
• Black Hole Dynamics in Einstein-Maxwell-Dilaton Theory
• On the motion of hairy black holes in Einstein-Maxwell-dilaton theories
• Gravitational radiation from compact binary systems in Einstein-Maxwell-dilaton theories
• Smarr Formula for Lovelock Black Holes: a Lagrangian approach
• Dyonic dilaton black holes
• Komar integrals for theories of higher order in the curvature and black-hole chemistry
• The General, Duality-Invariant Family of Non-BPS Black-Hole Solutions of N=4, d=4 Supergravity
• Scalar charge of black holes in Einstein-Maxwell-dilaton theory
• On scalar charges and black-hole thermodynamics
• Komar integral and Smarr formula for axion-dilaton black holes versus S duality
• Super-Geometrodynamics
• "Triangular" extremal dilatonic dyons
• TIME-SYMMETRIC INITIAL DATA SETS IN 4--D DILATON GRAVITY
• Mass And Force Relations For Einstein-Maxwell-Dilaton Black Holes
• The Head-On Collision of Two Equal Mass Black Holes: Numerical Methods