Measuring stochastic gravitational-wave energy beyond general relativity

Gravity theories beyond general relativity (GR) can change the properties of gravitational waves: their polarizations, dispersion, speed, and, importantly, energy content are all heavily theory- dependent. All these corrections can potentially be probed by measuring the stochastic gravitational- wave background. However, most existing treatments of this background beyond GR overlook modifications to the energy carried by gravitational waves, or rely on GR assumptions that are invalid in other theories. This may lead to mistranslation between the observable cross-correlation of detector outputs and gravitational-wave energy density, and thus to errors when deriving observational constraints on theories. In this article, we lay out a generic formalism for stochastic gravitational- wave searches, applicable to a large family of theories beyond GR. We explicitly state the (often tacit) assumptions that go into these searches, evaluating their generic applicability, or lack thereof. Examples of problematic assumptions are: statistical independence of linear polarization amplitudes; which polarizations satisfy equipartition; and which polarizations have well-defined phase velocities. We also show how to correctly infer the value of the stochastic energy density in the context of any given theory. We demonstrate with specific theories in which some of the traditional assumptions break down: Chern-Simons gravity, scalar-tensor theory, and Fierz-Pauli massive gravity. In each theory, we show how to properly include the beyond-GR corrections, and how to interpret observational results.Comment: 18 pages (plus appendices), 1 figur

Black-hole kicks from numerical-relativity surrogate models

Binary black holes radiate linear momentum in gravitational waves as they merge. Recoils imparted to the black-hole remnant can reach thousands of km/s, thus ejecting black holes from their host galaxies. We exploit recent advances in gravitational waveform modeling to quickly and reliably extract recoils imparted to generic, precessing, black hole binaries. Our procedure uses a numerical-relativity surrogate model to obtain the gravitational waveform given a set of binary parameters, then from this waveform we directly integrate the gravitational-wave linear momentum flux. This entirely bypasses the need of fitting formulae which are typically used to model black-hole recoils in astrophysical contexts. We provide a thorough exploration of the black-hole kick phenomenology in the parameter space, summarizing and extending previous numerical results on the topic. Our extraction procedure is made publicly available as a module for the Python programming language named SURRKICK. Kick evaluations take ~0.1s on a standard off-the-shelf machine, thus making our code ideal to be ported to large-scale astrophysical studies.Comment: More: https://davidegerosa.com/surrkick - Source: https://github.com/dgerosa/surrkick - pypi: https://pypi.python.org/pypi/surrkick - Published in PR

Extremal Black Holes in Dynamical Chern-Simons Gravity

Rapidly rotating black hole solutions in theories beyond general relativity play a key role in experimental gravity, as they allow us to compute observables in extreme spacetimes that deviate from the predictions of general relativity. Such solutions are often difficult to find in beyond-general-relativity theories due to the inclusion of additional fields that couple to the metric non-linearly and non-minimally. In this paper, we consider rotating black hole solutions in one such theory, dynamical Chern-Simons gravity, where the Einstein-Hilbert action is modified by the introduction of a dynamical scalar field that couples to the metric through the Pontryagin density. We treat dynamical Chern-Simons gravity as an effective field theory and work in the decoupling limit, where corrections are treated as small perturbations from general relativity. We perturb about the maximally-rotating Kerr solution, the so-called extremal limit, and develop mathematical insight into the analysis techniques needed to construct solutions for generic spin. First we find closed-form, analytic expressions for the extremal scalar field, and then determine the trace of the metric perturbation, giving both in terms of Legendre decompositions. Retaining only the first three and four modes in the Legendre representation of the scalar field and the trace, respectively, suffices to ensure a fidelity of over 99% relative to full numerical solutions. The leading-order mode in the Legendre expansion of the trace of the metric perturbation contains a logarithmic divergence at the extremal Kerr horizon, which is likely to be unimportant as it occurs inside the perturbed dynamical Chern-Simons horizon. The techniques employed here should enable the construction of analytic, closed-form expressions for the scalar field and metric perturbations on a background with arbitrary rotation.Comment: 25+9 pages (single column), 10 figures, 1 table; matches published versio