Scalar Waveform Research Articles

Nonlinear studies of binary black hole mergers in Einstein-scalar-Gauss-Bonnet gravity

We study the nonlinear dynamics of binary black hole systems with scalar charge by numerically evolving the full equations of motion for shift-symmetric Einstein scalar Gauss-Bonnet gravity. We consider quasi-circular binaries with different mass-ratios, varying the Gauss-Bonnet coupling and quantifying its impact on the emitted scalar and gravitational waves. We compare our numerical results to post-Newtonian calculations of the radiation emitted during the inspiral. We demonstrate the accuracy of the leading-order terms in post-Newtonian theory in modeling the amplitude of the scalar waveform, but find that, at least for the last few orbits before merger, the currently available post-Newtonian theory is not sufficient to model the dephasing of the gravitational wave signal in this theory. We further find that there is non-negligible nonlinear enhancement in the scalar field at merger, but that the effect on the peak gravitational wave emission is small.

Post-Newtonian gravitational and scalar waves in scalar-Gauss–Bonnet gravity

Gravitational waves emitted by black hole binary inspiral and mergers enable unprecedented strong-field tests of gravity, requiring accurate theoretical modeling of the expected signals in extensions of general relativity. In this paper we model the gravitational wave emission of inspiralling binaries in scalar Gauss–Bonnet gravity theories. Going beyond the weak-coupling approximation, we derive the gravitational waveform to relative first post-Newtonian order beyond the quadrupole approximation and calculate new contributions from nonlinear curvature terms. We also compute the scalar waveform to relative 0.5PN order beyond the leading −0.5PN order terms. We quantify the effect of these terms and provide ready-to-implement gravitational wave and scalar waveforms as well as the Fourier domain phase for quasi-circular binaries. We also perform a parameter space study, which indicates that the values of black hole scalar charges play a crucial role in the detectability of deviation from general relativity. We also compare the scalar waveforms to numerical relativity simulations to assess the impact of the relativistic corrections to the scalar radiation. Our results provide important foundations for future precision tests of gravity.

Nonlinear curvature effects in gravitational waves from inspiralling black hole binaries

Gravitational waves (GWs) from merging black holes allow for unprecedented probes of strong-field gravity. Testing gravity in this regime requires accurate predictions of gravitational waveform templates in viable extensions of general relativity. We concentrate on scalar Gauss-Bonnet gravity, one of the most compelling classes of theories appearing as the low-energy limit of quantum gravity paradigms, which introduces quadratic curvature corrections to gravity coupled to a scalar field and allows for black hole solutions with scalar charge. Focusing on inspiraling black hole binaries, we compute the leading-order corrections due to curvature nonlinearities in the GW and scalar waveforms, showing that the new contributions, beyond merely the effect of scalar field, appear at first post-Newtonian order in GWs. We provide ready-to-implement GW polarizations and phasing. Computing the GW phasing in the Fourier domain, we perform a parameter-space study to quantify the detectability of deviations from general relativity. Our results lay important foundations for future precision tests of gravity with both parametrized and theory-specific searches.

Black holes and binary mergers in scalar Gauss-Bonnet gravity: Scalar field dynamics

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.

Gravitational radiation from compact binary systems in Einstein-Maxwell-dilaton theories

We derive the energy fluxes radiated by compact binary systems, including “hairy” black holes, in Einstein-Maxwell-dilaton theories, for circular orbits and at quadrupolar order. This enables to include in their resummed effective-one-body (EOB) dynamics the effect of the radiation reaction force at the origin of their inspiral and merger. We also exhibit typical examples of the resulting tensor and scalar waveforms.

Compact binary systems in scalar-tensor gravity. III. Scalar waves and energy flux

We derive the scalar waveform generated by a binary of nonspinning compact objects (black holes or neutron stars) in a general class of scalar-tensor theories of gravity. The waveform is accurate to 1.5 post-Newtonian order [$O((v/c)^3)$] beyond the leading-order tensor gravitational waves (the "Newtonian quadrupole"). To solve the scalar-tensor field equations, we adapt the direct integration of the relaxed Einstein equations formalism developed by Will, Wiseman, and Pati. The internal gravity of the compact objects is treated with an approach developed by Eardley. We find that the scalar waves are described by the same small set of parameters which describes the equations of motion and tensor waves. For black hole--black hole binaries, the scalar waveform vanishes, as expected from previous results which show that these systems in scalar-tensor theory are indistinguishable from their general relativistic counterparts. For black hole--neutron star binaries, the scalar waveform simplifies considerably from the generic case, essentially depending on only a single parameter up to first post-Newtonian order. With both the tensor and scalar waveforms in hand, we calculate the total energy flux carried by the outgoing waves. This quantity is computed to first post-Newtonian order relative to the "quadrupole formula" and agrees with previous, lower order calculations.

Body surface mapping of counterclockwise and clockwise typical atrial flutter: a comparative analysis with endocardial activation sequence mapping

OBJECTIVESThis study was directed at developing spatial 62-lead electrocardiogram (ECG) criteria for classification of counterclockwise (CCW) and clockwise (CW) typical atrial flutter (Fl) in patients with and without structural heart disease.BACKGROUNDElectrocardiographic classification of CCW and CW typical atrial Fl is frequently hampered by inaccurate and inconclusive scalar waveform analysis of the 12-lead ECG.METHODSElectrocardiogram signals from 62 torso sites and multisite endocardial recordings were obtained during CCW typical atrial Fl (12 patients), CW typical Fl (3 patients), both forms of typical Fl (4 patients) and CCW typical and atypical atrial Fl (1 patient). All the Fl wave episodes were divided into two or three successive time periods showing stable potential distributions from which integral maps were computed.RESULTSThe initial, intermediate and terminal CCW Fl wave map patterns coincided with: 1) caudocranial activation of the right atrial septum and proximal-to-distal coronary sinus activation, 2) craniocaudal activation of the right atrial free wall, and 3) activation of the lateral part of the subeustachian isthmus, respectively. The initial, intermediate and terminal CW Fl wave map patterns corresponded with : 1) craniocaudal right atrial septal activation, 2) activation of the subeustachian isthmus and proximal-to-distal coronary sinus activation, and 3) caudocranial right atrial free wall activation, respectively. A reference set of typical CCW and CW mean integral maps of the three successive Fl wave periods was computed after establishing a high degree of quantitative interpatient integral map pattern correspondence irrespective of the presence or absence of organic heart disease.CONCLUSIONSThe 62-lead ECG of CCW and CW typical atrial Fl in man is characterized by a stereotypical spatial voltage distribution that can be directly related to the underlying activation sequence and is highly specific to the direction of Fl wave rotation. The mean CCW and CW Fl wave integral maps present a unique reference set for improved clinical detection and classification of typical atrial Fl.

Gravitational wave radiation from compact binary systems in the Jordan-Brans-Dicke theory

In this paper we analyze the signal emitted by a compact binary system in the Jordan-Brans-Dicke theory. We compute the scalar and tensor components of the power radiated by the source and study the scalar waveform. Eventually we consider the detectability of the scalar component of the radiation by interferometers and resonant-mass detectors.

Waveform response to the morphology of 2-D subducted slabs

Summary To evaluate waveform responses to morphological variations of the subducted lithospheric slab, scalar waveform solutions are computed for 2-D slab models perpendicular to the arc. The dependence of the waveforms on the background 1-D velocity model and on the wavelet frequency is analysed. The waveform variation due to the background velocity model is characterized by gradual changes in amplitude and traveltime over the take-off angle; such variation can be distinguished from the slab-generated waveform anomaly, which is restricted to a narrow take-off angle range and often severely alters the wavelet frequency. Therefore, much information can be gained through the waveform modelling of slabs in a homogeneous background velocity model. The characteristics of the waveform anomaly, such as slab-diffracted waveform broadening, depend on the ratio between the wavelength of the main source wavelet and the thickness of the slab. The slab-diffracted broadening, which has low-frequency characteristics, may be described more accurately as a wavelet broadening rather than a pulse-width broadening. When the wavelength is shorter than about one-half of the slab's thickness, a restoration of normal amplitude that is accompanied by waveform distortion is observed for waves propagating parallel and down-dip to the slab. Considerable waveform variations in arrival time, amplitude and wavelet-width exist among different morphological models of the slab, and may provide some useful guidance in inferring the real slab morphology from waveform data.