arXiv subjects

Barry Wardell

Publications and source records attributed to Barry Wardell.

At least 37 records · Page 2Linked to original sources

arXiv2022

Comparing second-order gravitational self-force, numerical relativity and effective one body waveforms from inspiralling, quasi-circular and nonspinning black hole binaries

We present the first systematic comparison between gravitational waveforms emitted by inspiralling, quasi-circular and nonspinning black hole binaries computed with three different approaches: second-order gravitational self-force (2GSF) theory, as implemented in the 1PAT1 model; numerical relativity (NR), as implemented by the SXS collaboration; and the effective one body (EOB) formalism, as implemented in the TEOBResumS waveform model. To compare the models we use both a standard, time-domain waveform alignment and a gauge-invariant analysis based on the dimensionless function $Q_ω(ω)\equiv ω^2/\dotω$, where $ω$ is the gravitational wave frequency. We analyse the domain of validity of the 1PAT1 model, deriving error estimates and showing that the effects of the final transition to plunge, which the model neglects, extend over a significantly larger frequency interval than one might expect. Restricting to the inspiral regime, we find that, while for mass ratios $q = m_1/m_2\le 10$ TEOBResumS is largely indistinguishable from NR, 1PAT1 has a significant dephasing $\gtrsim 1$rad; conversely, for $q\gtrsim 100$, 1PAT1 is estimated to have phase errors $<0.1$rad on a large frequency interval, while TEOBResumS develops phase differences $\gtrsim1$rad with it. Most crucially, on that same large frequency interval we find good agreement between TEOBResumS and 1PAT1 in the intermediate regime $15\lesssim q\lesssim 64$, with $<0.5$rad dephasing between them. A simple modification to the TEOBResumS flux further improves this agreement for $q\gtrsim 30$, reducing the dephasing to $\approx0.27$rad even at $q=128$. Our results pave the way for the construction of GSF-informed EOB models for both intermediate and extreme mass ratio inspirals for the next generation of gravitational wave detectors.

gr-qc↗

arXiv2022

Comparing second-order gravitational self-force and effective one body waveforms from inspiralling, quasi-circular and nonspinning black hole binaries II: the large-mass-ratio case

We compare recently computed waveforms from second-order gravitational self-force (GSF) theory to those generated by a new, GSF-informed, effective one body (EOB) waveform model for (spin-aligned, eccentric) inspiralling black hole binaries with large mass ratios. We focus on quasi-circular, nonspinning, configurations and perform detailed GSF/EOB waveform phasing comparisons, either in the time domain or via the gauge-invariant dimensionless function $Q_ω\equiv ω^2/\dotω$, where $ω$ is the gravitational wave frequency. The inclusion of high-PN test-mass terms within the EOB radiation reaction (notably, up to 22PN) is crucial to achieve an EOB/GSF phasing agreement below 1~rad up to the end of the inspiral for mass ratios up to 500. For larger mass ratios, up to $5\times 10^4$, the contribution of horizon absorption becomes more and more important and needs to be accurately modeled. Our results indicate that our GSF-informed EOB waveform model is a promising tool to describe waveforms generated by either intermediate or extreme mass ratio inspirals for future gravitational wave detectors

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arXiv2022

Hyperboloidal method for frequency-domain self-force calculations

Gravitational self-force theory is the leading approach for modeling gravitational wave emission from small mass-ratio compact binaries. This method perturbatively expands the metric of the binary in powers of the mass ratio. The source for the perturbations depends on the orbital configuration, calculational approach, and the order of the perturbative expansion. These sources fall into three broad classes: (i) distributional, (ii) worldtube, and (iii) unbounded support. The latter, in particular, is important for emerging second-order (in the mass ratio) calculations. Traditional frequency domain approaches employ the variation of parameters method and compute the perturbation on standard time slices with numerical boundary conditions supplied at finite radius from series expansions of the asymptotic behavior. This approach has been very successful, but the boundary conditions calculations are tedious, and the approach is not well suited to unbounded sources where homogeneous solutions must be computed at all radii. This work develops an alternative approach where hyperboloidal slices foliate the spacetime, and compactifying coordinates simplify the boundary treatment. We implement this approach with a multi-domain spectral solver with analytic mesh refinement and use the scalar-field self-force on circular orbits around a Schwarzschild black hole as an example problem. The method works efficiently for all three source classes encountered in self-force calculations and has distinct advantages over the traditional approach. For example, our code efficiently computes the perturbation for orbits with extremely large orbital radii ($r_{p}>10^5M$) or modes with very high spherical harmonic mode index ($\ell \ge 100$). Our results indicate that hyperboloidal methods can play an essential role in self-force calculations.

gr-qc↗

arXiv2022

Gravitational perturbations of rotating black holes in Lorenz gauge

Perturbations of Kerr spacetime are typically studied with the Teukolsky formalism, in which a pair of invariant components of the perturbed Weyl tensor are expressed in terms of separable modes that satisfy ordinary differential equations. However, for certain applications it is desirable to construct the full metric perturbation in the Lorenz gauge, in which the linearized Einstein field equations take a manifestly hyperbolic form. Here we obtain a set of Lorenz-gauge solutions to the vacuum field equations in terms of homogeneous solutions to the spin-2, spin-1 and spin-0 Teukolsky equations; and completion pieces that represent perturbations to the mass and angular momentum of the spacetime. The solutions are valid in vacuum Petrov type-D spacetimes that admit a conformal Killing-Yano tensor.

gr-qc↗

arXiv2021

Self-Force Calculations with a Spinning Secondary

We compute the linear metric perturbation to a Schwarzschild black hole generated by a spinning compact object, specialising to circular equatorial orbits with an (anti-)aligned spin vector. We derive a two-timescale expansion of the field equations, with an attendant waveform-generation framework, that includes all effects through first post-adiabatic order, and we use the Regge-Wheeler-Zerilli formalism in the frequency domain to generate waveforms that include the complete effect of the spin on the waveform phase. We perform the calculations using expansions at fixed orbital frequency, increasing the computational efficiency and simplifying the procedure compared to previous approaches. Finally, we provide the first fully relativistic, first-principles regularisation procedure for gauge invariant self-force quantities to linear order in spin. We use this procedure to produce the first strong-field, conservative self-force calculation including the spin of the secondary -- computing Detweiler's redshift invariant.

gr-qc↗

arXiv2021

Gravitational-wave energy flux for compact binaries through second order in the mass ratio

Within the framework of self-force theory, we compute the gravitational-wave energy flux through second order in the mass ratio for compact binaries in quasicircular orbits. Our results are consistent with post-Newtonian calculations in the weak field and they agree remarkably well with numerical-relativity simulations of comparable-mass binaries in the strong field. We also find good agreement for binaries with a spinning secondary or a slowly spinning primary. Our results are key for accurately modelling extreme-mass-ratio inspirals and will be useful in modelling intermediate-mass-ratio systems.

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arXiv2021

Applying the effective-source approach to frequency-domain self-force calculations: Lorenz-gauge gravitational perturbations

With a view to developing a formalism that will be applicable at second perturbative order, we devise a new practical scheme for computing the gravitational self-force experienced by a point mass moving in a curved background spacetime. Our method works in the frequency domain and employs the effective-source approach, in which a distributional source for the retarded metric perturbation is replaced with an effective source for a certain regularized self-field. A key ingredient of the calculation is the analytic determination of an appropriate puncture field from which the effective source and regularized residual field can be calculated. In addition to its application in our effective-source method, we also show how this puncture field can be used to derive tensor-harmonic mode-sum regularization parameters that improve the efficiency of the traditional mode-sum procedure. To demonstrate the method, we calculate the first-order-in-the-mass-ratio self-force and redshift invariant for a point mass on a circular orbit in Schwarzschild spacetime.

gr-qc↗

arXiv2021

Analytical high-order post-Newtonian expansions for extreme mass ratio binaries

We present analytic computations of gauge invariant quantities for a point mass in a circular orbit around a Schwarzschild black hole, giving results up to 15.5 post-Newtonian order in this paper and up to 21.5 post-Newtonian order in an online repository. Our calculation is based on the functional series method of Mano, Suzuki and Takasugi (MST) and a recent series of results by Bini and Damour. We develop an optimised method for generating post-Newtonian expansions of the MST series, enabling significantly faster computations. We also clarify the structure of the expansions for large values of $\ell$, and in doing so develop an efficient new method for generating the MST renormalised angular momentum, $ν$.

gr-qc↗

arXiv2021

Analytical high-order post-Newtonian expansions for spinning extreme mass ratio binaries

We present an analytic computation of Detweiler's redshift invariant for a point mass in a circular orbit around a Kerr black hole, giving results up to 8.5 post-Newtonian order while making no assumptions on the magnitude of the spin of the black hole. Our calculation is based on the functional series method of Mano, Suzuki and Takasugi, and employs a rigorous mode-sum regularization prescription based on the Detweiler-Whiting singular-regular decomposition. The approximations used in our approach are minimal; we use the standard self-force expansion to linear order in the mass ratio, and the standard post-Newtonian expansion in the separation of the binary. A key advantage of this approach is that it produces expressions that include contributions at all orders in the spin of the Kerr black hole. While this work applies the method to the specific case of Detweiler's redshift invariant, it can be readily extended to other gauge invariant quantities and to higher post-Newtonian orders.

gr-qc↗

arXiv2021

Characteristic formulation of the Regge-Wheeler and Zerilli Green functions

We present a characteristic initial value approach to calculating the Green function of the Regge-Wheeler and Zerilli equations. We combine well-known numerical methods with newly derived initial data to obtain a scheme which can in principle be generalised to any desired order of convergence. We demonstrate the approach with implementations up to sixth-order in the grid spacing. By combining the results of our numerical code with late-time tail expansions and methods of subtracting the direct part of the Green function, we show that the scalar self-force in Schwarzschild spacetime can be computed to better accuracy than previous Green-function based approaches. We also demonstrate agreement with frequency-domain methods for computing the Green function in the gravitational case. Finally, we apply the Regge-Wheeler and Zerilli Green functions to the computation of the gravitational energy flux.

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arXiv2020

Dissipation in extreme-mass ratio binaries with a spinning secondary

We present the gravitational-wave flux balance law in an extreme mass-ratio binary with a spinning secondary. This law relates the flux of energy (angular momentum) radiated to null infinity and through the event horizon to the local change in the secondary's orbital energy (angular momentum) for generic (non-resonant) bound orbits in Kerr spacetime. As an explicit example we compute these quantities for a spin-aligned body moving on a circular orbit around a Schwarzschild black hole. We perform this calculation both analytically, via a high-order post-Newtonian expansion, and numerically in two different gauges. Using these results we demonstrate explicitly that our new balance law holds.

gr-qc↗

arXiv2020

Transport Equation Approach to Calculations of Hadamard Green functions and non-coincident DeWitt coefficients

Building on an insight due to Avramidi, we provide a system of transport equations for determining key fundamental bi-tensors, including derivatives of the world-function, σ(x,x'), the square root of the Van Vleck determinant, Δ^{1/2}(x,x'), and the tail-term, V(x,x'), appearing in the Hadamard form of the Green function. These bi-tensors are central to a broad range of problems from radiation reaction to quantum field theory in curved spacetime and quantum gravity. Their transport equations may be used either in a semi-recursive approach to determining their covariant Taylor series expansions, or as the basis of numerical calculations. To illustrate the power of the semi-recursive approach, we present an implementation in \textsl{Mathematica} which computes very high order covariant series expansions of these objects. Using this code, a moderate laptop can, for example, calculate the coincidence limit a_7(x,x) and V(x,x') to order (σ^a)^{20} in a matter of minutes. Results may be output in either a compact notation or in xTensor form. In a second application of the approach, we present a scheme for numerically integrating the transport equations as a system of coupled ordinary differential equations. As an example application of the scheme, we integrate along null geodesics to solve for V(x,x') in Nariai and Schwarzschild spacetimes.

gr-qc↗

arXiv2019

Second-order self-force calculation of the gravitational binding energy in compact binaries

Self-force theory is the leading method of modeling extreme-mass-ratio inspirals (EMRIs), key sources for the gravitational-wave detector LISA. It is well known that for an accurate EMRI model, second-order self-force effects are critical, but calculations of these effects have been beset by obstacles. In this letter we present the first implementation of a complete scheme for second-order self-force computations, specialized to the case of quasicircular orbits about a Schwarzschild black hole. As a demonstration, we calculate the gravitational binding energy of these binaries.

gr-qc↗

arXiv2019

Excitation of Kerr quasinormal modes in extreme--mass-ratio inspirals

If a small compact object orbits a black hole, it is known that it can excite the black hole's quasinormal modes (QNMs), leading to high-frequency oscillations ("wiggles") in the radiated field at $\mathcal{J}^+$, and in the radiation-reaction self-force acting on the object after its orbit passes through periapsis. Here we survey the phenomenology of these wiggles across a range of black hole spins and equatorial orbits. In both the scalar-field and gravitational cases we find that wiggles are a generic feature across a wide range of parameter space, and that they are observable in field perturbations at fixed spatial positions, in the self-force, and in radiated fields at $\mathcal{J}^+$. For a given charge or mass of the small body, the QNM excitations have the highest amplitudes for systems with a highly spinning central black hole, a prograde orbit with high eccentricity, and an orbital periapsis close to the light ring. The QNM amplitudes depend smoothly on the orbital parameters, with only very small amplitude changes when the orbit's (discrete) frequency spectrum is tuned to match QNM frequencies. The association of wiggles with QNM excitations suggest that they represent a situation where the \emph{nonlocal} nature of the self-force is particularly apparent, with the wiggles arising as result of QNM excitation by the compact object near periapsis, and then encountered later in the orbit. Astrophysically, the effects of wiggles at $\mathcal{J}^+$ might allow direct observation of Kerr QNMs in extreme-mass-ratio inspiral (EMRI) binary black hole systems, potentially enabling new tests of general relativity.

gr-qc↗

arXiv2019

Regularized calculation of the retarded Green function in Schwarzschild spacetime

The retarded Green function for linear field perturbations of black hole spacetimes is notoriously difficult to calculate. One of the difficulties is due to a Dirac-$δ$ divergence that the Green function possesses when the two spacetime points are connected by a "direct" null geodesic. We present a procedure which notably aids its calculation in the case of Schwarzschild spacetime by separating this direct $δ$-divergence from the remainder of the retarded Green function. More precisely, the method consists of calculating the multipolar $\ell$-modes of the direct $δ$-divergence and subtracting them from the corresponding modes of the retarded Green function. We illustrate the usefulness of the method with some specific calculations in the case of the scalar Green function and self-field for a point scalar charge in Schwarzschild spacetime.

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arXiv2019

Probing the Nature of Black Holes: Deep in the mHz Gravitational-Wave Sky

Black holes are unique among astrophysical sources: they are the simplest macroscopic objects in the Universe, and they are extraordinary in terms of their ability to convert energy into electromagnetic and gravitational radiation. Our capacity to probe their nature is limited by the sensitivity of our detectors. The LIGO/Virgo interferometers are the gravitational-wave equivalent of Galileo's telescope. The first few detections represent the beginning of a long journey of exploration. At the current pace of technological progress, it is reasonable to expect that the gravitational-wave detectors available in the 2035-2050s will be formidable tools to explore these fascinating objects in the cosmos, and space-based detectors with peak sensitivities in the mHz band represent one class of such tools. These detectors have a staggering discovery potential, and they will address fundamental open questions in physics and astronomy. Are astrophysical black holes adequately described by general relativity? Do we have empirical evidence for event horizons? Can black holes provide a glimpse into quantum gravity, or reveal a classical breakdown of Einstein's gravity? How and when did black holes form, and how do they grow? Are there new long-range interactions or fields in our universe, potentially related to dark matter and dark energy or a more fundamental description of gravitation? Precision tests of black hole spacetimes with mHz-band gravitational-wave detectors will probe general relativity and fundamental physics in previously inaccessible regimes, and allow us to address some of these fundamental issues in our current understanding of nature.

astro-ph.HE↗

arXiv2019

Gravitational Self-Force Regularization in the Regge-Wheeler and Easy Gauges

We present numerical results for the gravitational self-force and redshift invariant calculated in the Regge-Wheeler and Easy gauges for circular orbits in a Schwarzschild background, utilizing the regularization framework introduced by Pound, Merlin, and Barack. The numerical calculation is performed in the frequency domain and requires the integration of a single second-order ODE, greatly improving computation times over more traditional Lorenz gauge numerical methods. A sufficiently high-order, analytic expansion of the Detweiler-Whiting singular field is gauge-transformed to both the Regge-Wheeler and Easy gauges and used to construct tensor-harmonic mode-sum regularization parameters. We compare our results to the gravitational self-force calculated in the Lorenz gauge by explicitly gauge-transforming the Lorenz gauge self-force to the Regge-Wheeler and Easy gauges, and find that our results agree to a relative accuracy of $10^{-15}$ for an orbital radius of $r_0=6M$ and $10^{-16}$ for an orbital radius of $r_0=10M$.

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arXiv2019

Black holes, gravitational waves and fundamental physics: a roadmap

The grand challenges of contemporary fundamental physics---dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem---all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress.

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