Abstract
We study the nonlinear dynamics of black holes that carry scalar hair and binaries composed of such black holes. The scalar hair is due to a linear or exponential coupling between the scalar and the Gauss--Bonnet invariant. We work perturbatively in the coupling constant of that interaction but nonperturbatively in the fields. We first consider the dynamical formation of hair for isolated black holes of arbitrary spin and determine the final state. This also allows us to compute for the first time the scalar quasinormal modes of rotating black holes in the presence of this coupling. We then study the evolution of nonspinning black-hole binaries with various mass ratios and produce the first scalar waveform for a coalescence. An estimate of the energy loss in scalar radiation and the effect this has on orbital dynamics and the phase of the GWs (entering at quadratic order in the coupling) show that GW detections can set the most stringent constraint to date on theories that exhibit a coupling between a scalar field and the Gauss--Bonnet invariant.
Highlights
The history of alternative theories of gravity is almost as old as that of general relativity (GR) itself
Based on the previous discussion, the choice of f0ð0Þ completely determines the form of the field equation for the scalar field up to order OðεÞ, cf
CANUDA5 is a novel numerical relativity library that is compatible with the open-source EINSTEIN TOOLKIT [87,88,89], and it is capable of simulating black holes (BHs) in extensions of GR; see, e.g., [68,79,90]
Summary
The history of alternative theories of gravity is almost as old as that of general relativity (GR) itself (see, e.g., [1,2]). For more than a century, each astrophysical revolution and the corresponding observational opportunity led to a new milestone test of gravity. While the recent GW events are all consistent with General Relativity (GR) [7,8], the constraints one can extract on alternative theories are rather weak [7], due to the lack of complete waveforms that correspond to binary evolution and mergers in these theories. Obtaining such waveforms is necessary to go beyond performing null tests of GR.
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