Metric perturbations of Kerr spacetime in Lorenz gauge: Circular equatorial orbits

We construct the metric perturbation in Lorenz gauge for a compact body on a circular equatorial orbit of a rotating black hole (Kerr) spacetime, using a newly-developed method of separation of variables. The metric perturbation is formed from a linear sum of differential operators acting on Teukolsky mode functions, and certain auxiliary scalars, which are solutions to ordinary differential equations in the frequency domain. For radiative modes, the solution is uniquely determined by the $s=\pm2$ Weyl scalars, the $s=0$ trace, and $s=0,1$ gauge scalars whose amplitudes are determined by imposing continuity conditions on the metric perturbation at the orbital radius. The static (zero-frequency) part of the metric perturbation, which is handled separately, also includes mass and angular momentum completion pieces. The metric perturbation is validated against the independent results of a 2+1D time domain code, and we demonstrate agreement at the expected level in all components, and the absence of gauge discontinuities. In principle, the new method can be used to determine the Lorenz-gauge metric perturbation at a sufficiently high precision to enable accurate second-order self-force calculations on Kerr spacetime in future. We conclude with a discussion of extensions of the method to eccentric and non-equatorial orbits.Comment: 88 pages, 14 figure

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.Comment: 5 pages + supplemental material, 7 figure

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 $Q_\omega\equiv \omega^2/\dot{\omega}$, where $\omega$ 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 detectorsComment: 13 pages, 8 figures. Submitted to Phys. Rev.

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 $Q_\omega(\omega)\equiv \omega^2/\dot{\omega}$, where $\omega$ 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.Comment: 31 pages, 19 figures, submitted to Phys. Rev.

Hyperboloidal discontinuous time-symmetric numerical algorithm with higher order jumps for gravitational self-force computations in the time domain

Within the next decade the Laser Interferometer Space Antenna (LISA) is due to be launched, providing the opportunity to extract physics from stellar objects and systems, such as \textit{Extreme Mass Ratio Inspirals}, (EMRIs) otherwise undetectable to ground based interferometers and Pulsar Timing Arrays (PTA). Unlike previous sources detected by the currently available observational methods, these sources can \textit{only} be simulated using an accurate computation of the gravitational self-force. Whereas the field has seen outstanding progress in the frequency domain, metric reconstruction and self-force calculations are still an open challenge in the time domain. Such computations would not only further corroborate frequency domain calculations and models, but also allow for full self-consistent evolution of the orbit under the effect of the self-force. Given we have \textit{a priori} information about the local structure of the discontinuity at the particle, we will show how to construct discontinuous spatial and temporal discretisations by operating on discontinuous Lagrange and Hermite interpolation formulae and hence recover higher order accuracy. In this work we demonstrate how this technique in conjunction with well-suited gauge choice (hyperboloidal slicing) and numerical (discontinuous collocation with time symmetric) methods can provide a relatively simple method of lines numerical algorithm to the problem. This is the first of a series of papers studying the behaviour of a point-particle prescribing circular geodesic motion in Schwarzschild in the \textit{time domain}. In this work we describe the numerical machinery necessary for these computations and show not only our work is capable of highly accurate flux radiation measurements but it also shows suitability for evaluation of the necessary field and it's derivatives at the particle limit

Metric perturbations and their slow evolution for modelling extreme mass ratio inspirals via the gravitational self force approach

In 2015, gravitational waves (GWs) were observed by direct detection for the very first time, over one-hundred years since the publication of Einstein's theory of general relativity (GR). Since then, GWs produced by a variety of systems have been detected. The laser interferometer space antenna (LISA), due to be launched in 2037 by the European Space Agency, will be sensitive to a new frequency of the GW spectrum than we are currently capable of detecting with ground based interferometry. One of the most highly anticipated sources of GWs detectable to LISA, that we have so far been blind to, are extreme mass ratio inspirals (EMRIs). These are binary systems comprised of a massive black hole that is at least ten-thousand times more massive than its satellite. Provided our models are accurate enough, matched filtering between real and theoretical GW signals can provide a measure of precisely how well GR describes our Universe. To achieve this scientific goal, we must calculate the phase of GWs sourced by EMRIs to post-adiabatic order, which in turn requires knowledge of the gravitational self-force (GSF) and metric perturbation through second-order in the small mass ratio. This thesis aims to further our understanding of the evolution of EMRI spacetimes, by determining the phase and amplitude of the GWs they admit. Within the framework of GR, black hole perturbation theory (BHPT), gravitational self-force (GSF) theory, and the two-timescale approximation, this work presents a number of novel calculations as tools for modelling EMRI waveforms. In particular, the MST package was developed for the Black Hole Perturbation Toolkit (BHPToolkit), which solves the Regge-Wheeler (RW) and Teukolsky equations via the Mano-Suzuki-Takasugi method. Another major result in this thesis is the Lorenz gauge calculation of the slowly-evolving first-order metric perturbation for quasicircular, equatorial orbits on a Schwarzschild background during inspiral. This provides a key ingredient to the source of the second-order metric perturbation, and is already being used to generate post adiabatic EMRI waveforms via the GSF approach. Post-adiabatic waveforms presented in this thesis are also found to describe intermediate mass ratio inspirals (IMRIs) to a high degree of accuracy, systems which are already being detected by interferometers on the ground. Thus work presented here is deemed applicable for GW science now and in the future. The transition to plunge is also examined in detail, and waveforms are computed during the transition regime to adiabatic order, again for quasicircular, equatorial orbits around a Schwarzschild black hole. Perturbations to a Kerr black hole will also explored, and a final output of this work is the `pure gauge' contribution to the first-order Lorenz gauge metric perturbation, generated by a gauge vector

Gravitational waveforms for compact binaries from second-order self-force theory

We produce gravitational waveforms for nonspinning compact binaries undergoing a quasicircular inspiral. Our approach is based on a two-timescale expansion of the Einstein equations in second-order self-force theory, which allows first-principles waveform production in milliseconds. Although the approach is designed for extreme mass ratios, our waveforms agree remarkably well with those from full numerical relativity, even for comparable-mass systems. Our results will be invaluable in accurately modelling extreme-mass-ratio inspirals for the LISA mission and intermediate-mass-ratio systems currently being observed by the LIGO-Virgo-KAGRA Collaboration

Gravitational waveforms for compact binaries from second-order self-force theory

We produce gravitational waveforms for nonspinning compact binaries undergoing a quasicircular inspiral. Our approach is based on a two-timescale expansion of the Einstein equations in second-order self-force theory, which allows first-principles waveform production in milliseconds. Although the approach is designed for extreme mass ratios, our waveforms agree remarkably well with those from full numerical relativity, even for comparable-mass systems. Our results will be invaluable in accurately modelling extreme-mass-ratio inspirals for the LISA mission and intermediate-mass-ratio systems currently being observed by the LIGO-Virgo-KAGRA Collaboration

Gravitational waveforms for compact binaries from second-order self-force theory

We produce gravitational waveforms for nonspinning compact binaries undergoing a quasicircular inspiral. Our approach is based on a two-timescale expansion of the Einstein equations in second-order self-force theory, which allows first-principles waveform production in milliseconds. Although the approach is designed for extreme mass ratios, our waveforms agree remarkably well with those from full numerical relativity, even for comparable-mass systems. Our results will be invaluable in accurately modelling extreme-mass-ratio inspirals for the LISA mission and intermediate-mass-ratio systems currently being observed by the LIGO-Virgo-KAGRA Collaboration