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Abstract

In General Relativity and many modified theories of gravity, isolated black
holes (BHs) cannot source massless scalar fields. Einstein-Maxwell-dilaton
(EMd) theory is an exception: through couplings both to electromagnetism and
(non-minimally) to gravity, a massless scalar field can be generated by an
electrically charged BH. In this work, we analytically model the dynamics of
binaries comprised of such scalar-charged ("hairy") BHs. While BHs are not
expected to have substantial electric charge within the Standard Model of
particle physics, nearly-extremally charged BHs could occur in models of
minicharged dark matter and dark photons. We begin by studying the test-body
limit for a binary BH in EMd theory, and we argue that only very compact
binaries of nearly-extremally charged BHs can manifest non-perturbative
phenomena similar to those found in certain scalar-tensor theories. Then, we
use the post-Newtonian approximation to study the dynamics of binary BHs with
arbitrary mass ratios. We derive the equations governing the conservative and
dissipative sectors of the dynamics at next-to-leading order, use our results
to compute the Fourier-domain gravitational waveform in the stationary-phase
approximation, and compute the number of useful cycles measurable by the
Advanced LIGO detector. Finally, we construct two effective-one-body (EOB)
Hamiltonians for binary BHs in EMd theory: one that reproduces the exact
test-body limit and another whose construction more closely resembles similar
models in General Relativity, and thus could be more easily integrated into
existing EOB waveform models used in the data analysis of gravitational-wave
events by the LIGO and Virgo collaborations.