I will describe a new separation-of-variables method for obtaining the metric perturbations of Kerr spacetime in Lorenz gauge. The metric perturbation is constructed in the frequency domain from (Teukolsky) scalars that satisfy decoupled ordinary differential equations. For the case of a particle moving on a circular equatorial orbit of Kerr spacetime, I will compare the results of the new...
We present an algebraic procedure for reconstructing the metric perturbation from scalar quantities in the Regge-Wheeler-Zerilli formalism. Starting with the work of Wald, and more recently through advances by Green, Hollands, and Zimmerman and others, the Teukolsky metric reconstruction formalism has been written in an elegant four-dimensional language of operator adjoints, Hertz potentials,...
Extreme-mass ratio inspirals are identified as one of the key targets for the upcoming LISA mission. They will serve as unique probes of black-hole physics and enable tests of general relativity with unparalleled precision. Modelling these systems with sufficient accuracy requires the calculation of up to second-order metric perturbation due to a point particle orbiting a Kerr black hole....
We compute the metric perturbation for a point particle on a bound geodesic in Kerr spacetime using the CCK and AAB reconstruction procedures. We discuss the numerical advantages and disadvantages of these different approaches, and present how other researchers can use the numerical tools from this work to construct their own Kerr metric perturbations.
We present a multi-domain elliptic solver in 2D based on spectral methods to solve typical self-force equations in an Effective Source m-mode scheme. The domain decomposition exploits two features to enhance accuracy. With a reference centred at the black hole, the horizon and wave zone regions are treated with a hyperboloidal approach, allowing asymptotic regions to be included in the...
Extreme mass-ratio inspirals (EMRIs) are expected to have considerable eccentricity when emitting gravitational waves (GWs) in the LISA band. Developing GW templates that remain phase accurate over these long inspirals requires the use of second-order self-force theory. Practical second-order self-force calculations are now emerging for quasi-circular EMRIs. These calculations rely on...
We are pursuing Lorenz gauge Kerr self-force calculations based on an m-mode scheme in the frequency domain. Prior hyperbolic partial differential equation (PDE) formulations encountered numerical instabilities involving unchecked growth in time; our method is based on elliptic PDEs, which do not exhibit instabilities of that kind. For proof of concept we calculated the self-force acting on a...
The only available 1PA waveform model, developed by the Southampton-UCD collaboration, is currently limited to the strong-field inspiral stage of quasicircular binaries. In this talk, I discuss progress toward developing a complete model that includes the early inspiral and the final merger and ringdown. A companion talk by Lorenzo Kuchler will provide further details of how we model the merger phase.
Within general relativity, the planar motion of a small body around a supermassive Schwarzschild black hole admits a quasi-circular inspiral followed by a transition across the innermost stable circular orbit (ISCO) and a final plunge behind the event horizon. Waveforms from second-order self-force theory compare remarkably well with numerical relativity simulations in the regime of...
To date, the only existing second-order self-force calculations have used some variant of a puncture scheme. In this scheme, one replaces the small object with a local singularity possessing the same curvature structure. This puncture field is truncated at some suitable distance from the particle and is then used as a source to solve for the residual field. From this, one can reconstruct the...
The trajectory of a point particle can be represented by a series of geodesics whose constants of motion slowly evolve over the inspiral. Flux-balance laws give the (averaged) evolution of these "conserved quantities" in terms of fluxes of conserved currents through the horizon and at null infinity. In the specific case of conserved quantities coming from spacetime isometries (for example,...
Calculations involving Kerr extreme-mass-ratio inspirals (EMRIs) often involve solving the s = -2 Teukolsky functions. In the cases where the s = +2 Teukolsky functions are warranted, they are usually obtained through the use of a Starobinsky transformation. In our work, we decided to directly construct post-Newtonian (PN) expansions of s = +2 Teukolsky functions using the MST method. First,...
High-accuracy theoretical predictions for the motion of compact binary systems are the most fundamental tools for interpreting data from present and future detectors, such as the LIGO-Virgo-Kagra, the Einstein Telescope and the LISA. I will talk about a novel framework aiming at efficiently calculating gravitational observables by employing cutting-edge technology from Quantum Field Theory and...
We describe an on-shell approach to discussing radiation reaction problems within the post-Minkowskian and self-force approximations to general relativity. In both cases, the notions of coherent states and eikonal exponentiation are key tools for accessing this physics in terms of on-shell amplitudes. We will explore a few applications and demonstrate how these tools can be used to relate...
I will describe the application of scattering amplitudes in quantum field theory to the description of the dynamics of binaries of spinning black holes or other compact objects
Calculations of the scatter angle in hyperbolic black hole encounters have been of recent cross-disciplinary interest, driven by its potential to advance post-Minkowskian theory and the effective-one-body model of binary dynamics. In this talk I will present our frequency-domain method for calculating the self-force acting on a scalar charge on a fixed scattering geodesic in Schwarzschild...
The asymptotic nature of hyperbolic orbits provides a clean environment for comparisons between different methods of calculating scattering observables. In this talk, we present details of a (numerical) calculation of the scalar self-force correction to the scattering angle and compare with analytical expressions up to fourth post-Minkowskian order obtained using scattering-amplitude methods....
While it is well accepted that generic EMRI waveform models must be fully relativistic, early 'kludge' waveform models often relied on weak-field (and other) approximations. Kludges were created in the absence of fully relativistic EMRI models to inform the science case for LISA. While it may be hoped that generic adiabatic self-force models are right around the corner, the same cannot be said...
Extreme mass ratio inspirals (EMRIs) are a prime gravitational wave source for the upcoming LISA mission and are expected to be both eccentric and inclined with respect to the equatorial plane of the primary. To this end, we develop a model for these inspirals using an action angle formulation of the method of osculating geodesics and a toy model of the gravitational self force (GSF). The...
Geodesic motion plays a fundamental role in the gravitational self-force approach to solving the relativistic dynamics of binary black holes. In this scheme, the zeroth approximation to the motion of the lighter secondary component is given by a geodesic in the Kerr geometry generated by the (heavier) primary black hole. At higher orders, this motion is corrected by an effective force term,...
EMRI data analysis faces a number of challenges. One issue is the high computational cost of waveforms, which arises due to the need to model complex physics over long timescales. Recent innovations in relativistic EMRI waveform generation have enabled them to be computed in less than a second, but further improvements are required if EMRI studies are to be made practical. Potentially millions...
I will discuss the covariant non-relativistic expansion of general relativity in powers of 1/c, using as an example the case of a compact perfect fluid matter source that can radiate gravitational waves. This is a well-studied scenario in the literature that is conventionally done by using the approach developed, amongst others, by Blanchet and Damour. This approach uses the harmonic gauge and...
The local geometry around a null geodesic in an arbitrary spacetime resembles the geometry of a plane wave (PW) spacetime at leading order. This idea is called the Penrose limit. Families of curves that stay within this local neighbourhood of the null geodesic can be thought of as being “ultrarelativistic” in some suitable sense, and their motion is largely determined by the structure of the...
As gravitational waves (GW) probe the strong field regime of gravity, they are an important tool for testing gravitational models. This requires an accurate description of the gravitational waveforms in modified gravity theories. In this work we focus on scalar Gauss Bonnet gravity (sGB), a promising extension of General Relativity (GR), to include finite size effects in the modelling of the...
We show that for the motion of elementary particles in vacuum metrics the DeWitt-Brehme equation can be reduced to the covariant form of the Landau-Lifshitz equation. Further we discuss the implications of this approach in the Schwarzschild and Kerr black hole metrics immersed into external uniform magnetic field. In the latter case one can observe energy gain of a radiating charged particle...
For many years, the idea that there may be more than three spatial dimensions in our universe has attracted people’s interest. The method by which extra dimensions are concealed, making spacetime essentially four-dimensional as far as known physics is concerned, is a key issue in multidimensional theories. Extra dimensions might be large or infinite, and they might then have consequences that...
I am interested in understanding radiation reaction(RR) and the post-Newtonian(PN) expansion in the presence of a cosmological constant. To this end, de Sitter spacetime provides a simple maximally symmetric background, where the in-in action that describes the RR can be computed. This in-in action has a natural interpretation through a 'doubled' static patch geometry associated with a...
Scalar-tensor theories are one of the long-standing alternatives to General Relativity (GR). These theories introduce an extra degree of freedom through a scalar field coupled to gravity, which affects the dynamics and internal composition of neutron stars. In this talk we use an effective field theory approach in order to describe an isolated body with size effects, characterised through the...
Self-force resonance is a resonance phenomenon that occurs when the ratio of orbital frequencies becomes a simple rational number. Its contribution appears at 0.5 post-adiabatic order, making it the next-to-leading effect after the adiabatic radiation reaction. Moreover,it is estimated that almost all EMRI systems experience this type of resonance, and so its theoretical prediction is...
Extreme mass ratio inspirals (EMRIs) are one of primary targets of space-borne gravititional wave detectors like LISA. Due to the long inspiral time and the large accumulated orbital phase of EMRIs in the LISA sensitive band, EMRIs are ideal tools for testing the fundmamental laws of gravity. Many previous studies have pointed out possible chaos of EMRI dynamics in non-GR gravity or non-Kerr...
The two-body problem is extensively studied in open systems and asymptotically flat spacetimes. However, there are many systems where radiation is trapped: they range from radiating charges in cavities to low-energy excitations of massive degrees of freedom, to anti-de Sitter spacetimes. Here, we study the problem of motion of a pointlike particle orbiting a massive compact object inside a...
We leverage recent breakthrough calculations using second-order gravitational self-force (2GSF) theory to improve both the gravitational-mode amplitudes and radiation-reaction force in effective-one-body~(EOB) waveform models. We achieve this by introducing new calibration parameters in the SEOBNRv5HM mode amplitudes, and matching them to the newly available 2GSF energy-flux multipolar data...
Building on previous work comparing effective-one-body (EOB) and gravitational self-force (GSF) waveforms for nonspinning black hole binaries on quasi-circular equatorial orbits, I will present an extension of this comparison to binaries with a spinning secondary. In particular, the comparison involves binaries with mass ratios ranging from 1:15 to 1:50000, and dimensionless spin on the...
It is commonly stated within the self force (SF) community that, in order to not significantly bias results, we require accurate tracking of the phase to within 1 radian. However, although frequently stated, this criterion is yet to be tested through a general Bayesian analysis. Armed with complete first order post-adiabatic (1PA) circular-Schwarzschild EMRI waveforms, we discuss the impact of...
Extreme mass ratio inspirals (EMRIs) and Intermediate mass ratio inspirals (IMRis) are prime targets for future space-borne interferometers like LISA. It is well-known that waveforms suitable for LISA data analysis must be accurate up to first-order post-adiabatic (1PA) corrections for both sources. But is it always the case? In this talk, we will try to answer this question by presenting the...
It has long been stated that in order to perform precision tests of general relativity (GR) by comparing gravitational wave (GW) models from black hole perturbation theory with observations, one must calculate the phase to the next-to-leading order in the small mass ratio (SMR) expansion. The extent to which this statement is true however needs to be tested. That is, how far can the SMR...
We present a systematic comparison between gravitational waveforms emitted by quasi-circular non-spinning binary black holes in both comparable and large mass ratio regimes, generated with two different classes of waveform models: (i) second-order gravitational self-force (GSF) theory and (ii) numerical relativity (NR) informed point particle black hole perturbation theory (ppBHPT) waveforms...
This talk outlines a fast, high-precision time-domain solver for scalar, elec- tromagnetic, and gravitational perturbations on hyperboloidal foliations of Kerr space- times. Time-domain Teukolsky equation solvers have typically used explicit methods, which numerically violate Noether symmetries and are Courant-limited. These re- strictions can limit the performance of explicit schemes when...
With the detection of first gravitational waves in 2015 by the laser interferometers at Laser Interferometer Gravitational wave Observatories (LIGO) located in Hanford and Livingston that was followed by a Nobel prize, there is an urgent need of more template waveforms for a bigger parameter space. The upcoming space borne detector Laser Interferometer Space Antenna (LISA) is primarily...
In 2034 LISA is due to be launched, which will provide the opportunity to extract physics from stellar objects and systems that would not otherwise be possible, among which are EMRIs. Unlike previous sources detected at LIGO, these sources can be simulated using an accurate computation of the gravitational self-force. Whereas the field has seen outstanding progress in the frequency domain,...
Binary black hole simulations become increasingly more computationally expensive with smaller mass ratios, partly because of the longer evolution time, and partly because the lengthscale disparity dictates smaller time steps. We explore a method for alleviating the scale disparity in simulations with mass ratios in the intermediate astrophysical range (10−4≲q≲10−2), where purely perturbative...
For the foreseeable future, numerical relativity waveforms for calibrating waveform models will be sparse in the parameter space of precessing (even more so for generic) black hole binaries, especially at high mass ratios. It is however well known that the extreme mass ratio limit can provide useful information even for the comparable mass ratio regime, and it can be hoped that using such...
The first confirmed detection of a 150 solar mass black hole in the form of the gravitational wave event, GW190521, did put an end to decades long debate concerning the existence of intermediate mass black holes. Black holes with masses typically in the range of 100-10,000 solar masses, when paired with stellar or supermassive black holes, become one of the most interesting sources for...
New ultralight fields are an exciting candidate for dark matter and can solve some of the small-scale tension between the standard CDM paradigm and observations. With the upcoming space-based LISA mission there is the prospect of detecting compact binaries in galactic centers, where dark matter structures are expected to be present. In this talk, we will present the first fully relativistic...
I will first discuss under which circumstances can black holes carry a scalar charge and what this implies for how that charge scales with the mass of the black hole. I will then use this insight to argue that EMRIs are an ideal system for searches of new fundamental scalars. I will lay out the framework for modelling EMRIs in this context and and present some first forecasts on LISA's ability...
Extreme Mass Ratio Inspirals (EMRIs), binary systems with a secondary stellar mass compact object inspiralling into a massive black hole, are among the main targets for LISA, as they harbour the potential for precise strong gravity tests. Although the description of these systems in modified theories of gravity can be drastically complex, for a vast class of theories with additional scalar...
For precise measurements of EMRIs with LISA data, first-post-adiabatic accuracy EMRI models will be required. Great effort is being expelled in pursuing first-post-adiabatic models in General Relativity. However, to test our fundamental theory of gravity, we also need models in alternative theories. Scalar fields are ubiquitous in alternative theories of gravity. In this talk, we provide a...
I have calculated gravitational wave memory effects generated by small mass ratio inspirals at second order in Schwarzschild spacetime and first order in Kerr spacetime. This is a step towards generating complete waveform templates for LIGO and LISA. I will present my results along with comparisons to PN results.
We introduce an action-angle formalism for bounded geodesic motion in Kerr black hole spacetime using canonical perturbation theory. Namely, we employ a Lie series technique to produce a series of canonical transformations on a Hamiltonian function describing geodesic motion in Kerr background written in Boyer-Lindquist coordinates to a Hamiltonian system written in action-angle variables....
We show that the motion of a spinning point particle in stationary spacetime is Hamiltonian when we include the spin-curvature coupling and the conservative piece of the self-force to first order in the mass ratio and spin of the secondary. We also report ongoing progress in attempts to extend this result to spinless particles at second order in the mass ratio. Problems involving the...
I will present a new Hamiltonian analysis of the motion of a spinning particle orbiting a Scwharzschild black hole. First I will reduce the Mathisson-Papapetrou equations at linear order in spin to a Poisson system. Second, I will present a reduction of this system to a 6 degrees-of-freedom (dof), constrained Hamiltonian system. Third, specialising to the Schwarzschild spacetime, a reduction...
The spin of the secondary in large mass ratio inspirals contributes to the inspiral phasing at the same order as the conservative self-force. Hence, treating the secondary spin at least to linear order is important for precise waveforms from these systems. In this talk I will present solutions of general motion of spinning test particles near a Schwarzschild black hole to linear order in spin...
Calculations involving compact objects, such as post-Newtonian (PN) or self-force calculations, are greatly simplified by treating the body as point particles. Going to higher orders in compactness introduces successively higher order multipolar structure to the compact object. Effective field theory methods provide a systematic tool to account for these finite size effects, by using an...
To a first approximation, objects in general relativity move along geodesics. Looked at more closely, a body's internal structure affects its motion, causing different objects to fall in different ways. This talk will explore which extended-body effects are possible and which are not. For example, can an appropriately-engineered spacecraft escape from a bound orbit without the use of a rocket?...
Accurate models of large mass-ratio systems must include post-geodesic corrections, which account for forces driving the small body away from the geodesic. An important post-geodesic effect is gravitational self-force, which describes the small body's interaction with its own spacetime curvature. This effect includes the backreaction due to gravitational-wave emission that leads to the...
This work provides gravitational wave energy and angular momentum asymptotic fluxes from a spinning body moving on generic orbits in a Kerr spacetime up to linear in spin approximation. To achieve this, we have developed a new frequency domain Teukolsky equation solver that calculates asymptotic amplitudes from generic orbits of spinning bodies with their spin aligned with the total orbital...
Although solutions to Teukolsky’s radial equation play a key role in black hole perturbation theory, there are limitations in our understanding that obscure our practical use and application of e.g. QNM overtone solutions. Towards addressing these limitations, I’ll present a collection of results that conclude with the tridiagonalization of Teukolsky's radial equation. In particular, I’ll...
Linear perturbations around black hole spacetimes can be quasinormal, quasibound or even superradiantly unstable, depending on the fields involved and the system's parameters. Recently, a bilinear form on perturbations of Kerr was proposed, and shown to give rise to an orthogonality relation between quasinormal modes. In this work, we extend the definition of the bilinear form and the...
The post-merger gravitational-wave waveform of binary black hole mergers can be well modeled by quasinormal modes during the late ringdown phase. The theoretical spectrum of modes that could be present in the ringdown is extensive, but in practice only a subset of them will be significantly excited. Focusing on non-precessing mergers, we determine the relevancy of different ringdown modes by...
Black hole (BH) perturbation theory is crucial in computing the quasinormal modes (QNMs) emitted by general binary BH merges and the gravitational waves (GWs) of extreme-mass-ratio-inspirals (EMRIs). These GWs carry essential information about the geometry around BHs and any potential deviations from General Relativity (GR). In recent years, there have been extensive studies of perturbations...
We present the first high-order regularisation parameters for generic orbits in Kerr spacetime in the gravitational case. Such parameters enable a jump in efficiency for mode-sum self-force calculation and have been shown to be of particular importance in the case of resonances. We also present the updated Regularisation Mathematica Package which includes both the gravitational and...
