Numerical binary black hole mergers in dynamical Chern-Simons gravity: Scalar field

Abstract

Testing general relativity in the nonlinear, dynamical, strong-field regime of gravity is one of the major goals of gravitational wave astrophysics. Performing precision tests of general relativity (GR) requires numerical inspiral, merger, and ringdown waveforms for binary black hole (BBH) systems in theories beyond GR. Currently, GR and scalar-tensor gravity are the only theories amenable to numerical simulations. In this article, we present a well-posed perturbation scheme for numerically integrating beyond-GR theories that have a continuous limit to GR. We demonstrate this scheme by simulating BBH mergers in dynamical ChernSimons gravity (dCS), to linear order in the perturbation parameter. We present mode waveforms and energy fluxes of the dCS pseudoscalar field from our numerical simulations. We find good agreement with analytic predictions at early times, including the absence of pseudoscalar dipole radiation. We discover new phenomenology only accessible through numerics: a burst of dipole radiation during merger. We also quantify the self-consistency of the perturbation scheme. Finally, we estimate bounds that GR-consistent LIGO detections could place on the new dCS length scale, approximately l ≲ Oð10Þ km.

Numerical binary black hole collisions in dynamical Chern-Simons gravity

“…The GR BBH background is evolved using a well-posed generalized harmonic formalism, with details given in [22][23][24][25]. The first-order scalar field is evolved using the formalism detailed in [11]. Finally, the metric perturbation is evolved using the formalism given in [13], a well-posed perturbed analogue of the generalized harmonic formalism.…”

“…We give details on perturbed gauge choices in Appendix B. We use the boundary conditions detailed in [11,13,26,27].…”

“…In addition to an instantaneous regime of validity, our computations will also have a secular regime of validity. This arises from our perturbative scheme and is discussed in detail in [11]. In order for the perturbation scheme to remain valid, we want the perturbation that is going as ∼ te −iω (0) t in Eqs.…”

“…Computing the evolution of a binary system requires first specifying suitable initial conditions. Because the well-posedness of the initial value problem in full dCS gravity is unknown [10], we work instead in a well-posed order-reduction scheme, in which we perturb the metric and scalar field around a GR background [11]. The leading-order modification to the spacetime metric, and hence gravitational radiation, * mokounko@tapir.caltech.edu occurs at second order, which is precisely the order we consider in this study, building on our previous work [11][12][13].…”

Beyond Lovelock gravity: Higher derivative metric theories

“…Indeed, since it leads to equations of motion with higher-order derivatives, it is expected to contain Ostrogradsky modes if treated as a complete theory (i.e., not as a perturbative expansion). For the so-called dynamical Chern-Simons gravity (where also an explicit kinetic term for ϕ is present), the authors of [36] showed that there is at least a ghost instability above a certain momentum cutoff and the authors of [37] provided evidence that the theory does not admit a well-posed initial value formulation (see also [38] for numerical simulations using the perturbative approach). However, to the best of our knowledge, a proper canonical analysis of this theory has never been performed in order to count the number of DOF at the nonlinear level.…”