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#### Hairy binary black holes in Einstein-Maxwell-dilaton theory and their effective-one-body description

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##### Citation

Khalil, M., Sennett, N., Steinhoff, J., Vines, J., & Buonanno, A. (2018). Hairy
binary black holes in Einstein-Maxwell-dilaton theory and their effective-one-body description.* Physical
Review D,* *98*(10): 104010. doi:10.1103/PhysRevD.98.104010.

Cite as: https://hdl.handle.net/21.11116/0000-0002-4AF1-B

##### 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.

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.