In this talk, we consider the electromagnetic radiation-reaction/self-force process for a charged particle orbiting a rotating black hole. Our goal is to complement the existing results for the scalar and gravitational cases, to give a full picture of integer spins in the Kerr spacetime. As a first step, we restrict ourselves to the case of circular orbits. The dissipative and conservative components of the electromagnetic self-force are computed numerically, by solving the inhomogeneous Teukolsky equations using the BHperturbation toolkit. The dissipative part, which equals the flux radiated at infinity and through the horizon, is directly compared to the scalar and gravitational cases, while the conservative part of the self-force is compared to existing results in the literature via the examination of gauge-independent quantities.

Modelling EMRIs to the degree of accuracy necessary for detection by LISA requires knowledge of the self-force to at least second order in the small mass ratio, which depends on the metric perturbation to both first and second order. The self-force is better understood in the Lorenz gauge, and to second order is currently known only in the Lorenz gauge. Attempts that have been and are currently being explored to solve the first order metric perturbation in Lorenz gauge analytically for self-force calculations will be discussed.

The calculation of the trajectory of an object subject to a force in curved spacetime can be calculated using the method of osculating geodesics. However, the resulting equations of motion depend on both the long term evolution of the orbital elements (p,e,x) but also the short term radial and polar phases (qr, qz). This can be remedied by the use of near identity (averaging) transformations (NITs) which allow us to solve a simpler problem where the equations of motion where the equations of motion only depend on (p,e,x). This technique has been very successful for Schwarzschild inspirals, however, it cannot be applied to the Kerr osculating geodesic equations in their current form.We present an alternate form of the osculating geodesic equations and apply the NIT to them and solve the new equations of motion. Our preliminary findings which show that our NIT'd trajectories agree with those found from the full equations of motion to a high degree of accuracy, while the run time is reduced from minutes or hours to less than a second.

A vast majority of extreme-mass-ratio black hole binaries (EMRIs) will encounter at least one strong 𝑟𝜃-resonance as they evolve through LISA's passband. These resonances occur when the frequencies of the librating radial and polar motion of the EMRI's smaller body form a low-integer ratio, and they drive significant `kicks' in the amount of energy and angular momentum that EMRIs radiate through gravitational waves. These kicks, if not properly accounted for, can amplify errors in modeled EMRI waveforms by factors of ∼100. As a first step in quantifying these effects, we calculate the scalar self-force experienced by a scalar-charged particle following an 𝑟𝜃-resonant geodesic around a Kerr black hole. We present how local and global radiation-reaction effects vary with respect to initial conditions. We also demonstrate, numerically, that conservative self-force effects do not contribute to the leading-order evolution of the system, at least within the error tolerances of our results.

I will discuss some recent developments in modelling multiple stellar-mass objects orbiting around a galactic centre, supermassive black hole. This includes relativistic extension of the mean motion resonance, an effect extensively studied in planetary systems, e.g. in explaining the formation of orbital structure of Jupiter's moons and the rings in the gaps of Saturn. It turns out that this mechanism may generate locked pairs of stellar-mass black holes in AGN disks that migrate towards the supermassive black hole together. I will also show that, if there is a close third body near an extreme mass-ratio inspiral (EMRI) system, the gravitational force due to the third could generate observational signatures in the EMRI waveform through a new resonance effect.

"Impact of Resonances and Chaos on Extreme Mass Ratio Inspirals Extreme Mass Ratio Inspirals (EMRIs) are one of the prominent sources for gravitational wave detection by (LISA). However, there are physical factors introducing non-linear phenomena that might render EMRIs not detectable. We will address this issue by showing how factors like the spin of the inspiraling object and deviations from the Kerr background can induce effects like prolonged resonances and chaos. We will discuss what is the impact of these effects on the gravitational waves and EMRIs' detectability."

The rapid generation of accurate EMRI waveforms is a necessity for LISA data analysis, but is still very much an open problem. One of the key remaining obstacles is the efficient computation of amplitudes for the 10^3-10^5 harmonic modes that comprise a waveform in the usual angular and frequency-based decomposition. I report promising progress on this front for eccentric orbits in Schwarzschild, and introduce the first EMRI model with full harmonic content and millisecond-scale runtimes for analysis-length waveforms.

Computing EMRI waveforms is computationally difficult even with simplifying approximations. As the EMRI community advances towards higher fidelity waveforms, accelerated computational methods will be required to both scale these calculations and build models for fast online waveform generation. In this talk, I will discuss the usage of Graphics Processing Units (GPU) in these calculations, which represents one way to address these challenges from the hardware perspective. I will showcase the modular implementation of our Fast EMRI Waveform (FEW) model and how the accelerator hardware has helped us achieve the high performance observed. Additionally, one of the main goals of this talk is to encourage those in the EMRI modeling community to consider where accelerated techniques could help execute or scale calculations. This would allow for better and more efficient linkage between EMRI modeling efforts and their implementations in data analysis-related waveform generation, which is crucial to the success of EMRI science with LISA.

Modelling extreme-mass-ratio inspirals with sufficient accuracy for LISA science requires going to second (or post-adiabatic) order in self-force theory. Such second-order calculations are now the overriding challenge facing the self-force community. In this talk I discuss ongoing work toward calculating the second-order self-force and generating post-adiabatic waveforms. I present preliminary results for the waveforms from a quasicircular inspiral into a Schwarzschild black hole.

Precise parameter extraction from EMRI signals requires, among other things, the dissipative piece of the second-order self-force in a Kerr background. The second-order Teukolsky equation is an existing avenue for second-order calculations; however, in its traditional form, application to the self-force problem produces an ill-defined source. We present a new form of the second-order Teukolsky equation—whose source we show to be distributionally well defined (in a Highly Regular gauge) for self-force calculations. Following that, we discuss schemes for achieving gauge-invariant second-order solutions via gauge fixing. We find fixing to a single, well-behaved gauge throughout a spacetime proves challenging. Instead, we propose fixing to unique good gauges in each physically significant region of the spacetime: the supermassive black hole horizon, the worldline of the inspiraling object, and future null infinity. We give a practical method for fixing to a good gauge at future null infinity, the Bondi–Sachs gauge, and also discuss a method for fixing the corresponding BMS frame.

To perform accurate EMRI science with LISA, we require self-force calculations at second order in perturbation theory. A major obstacle in these calculations is the strong divergences that are encountered on the worldline of the small object. These appear in a generic gauge (including the Lorenz gauge) and result from the second-order singular field having the form ~ m^2/r^2, where r measures distance from the worldline. This divergence creates a severe computational cost and hinders the rapid calculations that are required for waveform analysis. Previously, it was shown by Pound [Phys. Rev. D 95, 104056 (2017)] that a highly regular gauge exists in which the singular field takes the less singular form ~ m^2/r. By reducing the strength of the divergence, this gauge promises to enable more efficient numerical simulations. However, only the singular field's leading behaviour was presented in Pound's paper. In this talk, I will present results for the singular field to sufficient order for numerical implementation. Additionally, I will show how we can use this new gauge to rigorously derive a pointlike second-order stress-energy tensor for the small object.

"A critical ingredient for high-fidelity EMRI waveforms is the time-averaged dissipative part of the second-order self-force. The dissipative contribution to self-force effects must be obtained to high accuracy due to the secular change of orbital parameters over the long inspiral. In this talk, I present the first derivation of a second-order flux-balance law: the relationship between the local orbital evolution of a small object and distant waveform amplitudes to post-adiabatic order. The asymptotic amplitudes can be obtained from a second-order Teukolsky formalism, meaning these balance laws hold the promise of dramatically improving the efficiency of post-adiabatic inspiral calculations by alleviating the need for metric reconstruction at second order.

Collaborators: Jordan Moxon, Eanna Flanagan, Adam Pound, and Jonathan Thompson."

"State-of-the-art second-order self-force calculations are now enabling high-precision modelling of compact binaries in the small-mass-ratio regime. Along with the asymptotically observable waveforms, these calculations allow precise characterizations of the local properties of the central black hole over the course of an inspiral. Such characterizations have already proved critical in the comparison of second-order self-force calculations with predictions from the first law of binary mechanics [1]. Motivated by this development, we study the apparent and event horizons of a perturbed Schwarzschild black hole at second order in perturbation theory. Starting from basic assumptions, we derive practical formulas for the second-order perturbations to the locations and surface areas of the horizons. We also present work in progress regarding the gauge dependence of these quantities.
[1] A. Pound, B. Wardell, N. Warburton, J. Miller. "Second-order self-force calculation of the gravitational binding energy in compact binaries". Phys. Rev. Lett. 124, 021101 (2020).
Supervisor: Dr. Adam Pound (University of Southampton)."

In order to model extreme-mass-ratio inspirals (EMRIs) for the gravitational-wave detector LISA one must consider the effects of second-order self-force. Following on from the ground-breaking first implementation of a second-order self-force by Pound et Al (2019) that specialised to circular orbits in Schwarzschild spacetime, we look to extend this to eccentric orbits. We present a new frequency domain method of applying the effective-source technique to eccentric orbits - extended effective sources - within the the context of the scalar-field problem. This simplified model allows us to understand the problems one might encounter when considering the more mathematically complex, but inherently similar, gravitational problem. Finally, we consider preliminary results in applying the effective-source scheme for gravitational perturbations from circular orbits in terms of the Teukolsky formalism.

Intermediate-mass-ratio inspirals (IMRIs) remain an important open problem in the field. Such binary systems are possible sources for Advanced LIGO and LISA, and their observation would provide fundamental insights into black hole formation and astrophysical populations. Whilst extreme-mass-ratio inspirals are well modelled by black hole perturbation theory, and numerical relativity has seen much success modelling comparable-mass inspirals, neither approach works well on its own for IMRIs. It is not clear how adequate a purely perturbative treatment can be at intermediate mass ratios of 1:100-1:1000, and the length-scale disparity remains large enough to pose a serious challenge for numerical relativity. We are working to provide accurate modelling of such binaries through a combination of black-hole perturbation and numerical relativity techniques. Our approach matches an approximate analytical solution (formed from the tidally perturbed metric of the smaller black hole) to a fully nonlinear numerical solution in the bulk of the spacetime. This talk will give an overview of our method and results from a scalar toy model.

In a linear field theory, self-interaction can be understood by constructing a certain 2-point "propagator," typically the Detweiler-Whiting Green function. Forces and torques exerted by the fields associated with this propagator can be removed by renormalization, so the laws of motion may be written in terms of the (much simpler) difference field. I will discuss how this picture changes for bodies coupled to nonlinear fields. At each order n in the field strength, there turn out to be n relevant propagators which generalize the Detweiler-Whiting Green function. One of these is a 2-point function, the next involves 3 points, the next 4-points, and so on: There is a tower of m-point distributions which determine the self-force and self-torque. This works at all orders and for finitely-sized bodies with arbitrary multipole structure.

Is 1/4 a "small" number?

While second order self-force calculations are an essential ingredient to accurately model EMRI evolutions for LISA, the precision needed at second order is greatly supressed to that needed for first order, adiabatic inspirals. Thus the potential utility of analytical approximations at post-adiabatic order, such a post-Newtonian self-force expansions, could be greatly increased. In this talk I will discuss prospects and early progress towards doing PN self-force at second order in the mass ratio.

We develop a formalism to treat higher order (nonlinear) metric perturbations of the Kerr spacetime in a Teukolsky framework. We first show that solutions to the linearized Einstein equation with nonvanishing stress tensor can be decomposed into four terms: a pure gauge term, an infinitesimal perturbation of the black hole mass and spin, a perturbation arising from a Hertz potential, and a ”corrector tensor.” The Hertz potential is a solution to the spin -2 Teukolsky equation with a source. This source, as well as the tetrad components of the corrector tensor, are obtained by solving certain decoupled ordinary differential equations involving the stress tensor. In outgoing Kerr-Newman coordinates, solving these ordinary differential equations reduces simply to integrations in the r coordinate. Since higher order perturbations are subject to a linearized Einstein equation with a stress tensor obtained from the lower order perturbations, our method applies iteratively to higher order metric perturbations. We discuss possible applications, including to analyze perturbations generated by a pointlike body in Kerr.

We begin a program to apply a newly developed, nonvacuum Teukolsky formalism to the problem of extreme mass ratio inspirals. In vacuum, a radiation gauge metric perturbation may be generated from the Weyl scalars by the so-called ``metric reconstruction'' procedure. The presence of an inspiralling body, when treated as point particle, violates the vacuum condition and the reconstructed radiation gauge metric must be ``corrected'' in order to satisfy the field equations. Recently, it has been shown that this ``correction'' tensor satisfies ODEs along outgoing principal null geodesics and is completely determined by the source. For a point particle source, the correction yields a distributional solution which displays string singularities extending from the worldline to future null infinity. As the correction tensor satisfies similar equations in Kerr as in flat spacetime, the simpler, flat context provides valuable intuition, especially as a probe for the second-order problem. As a warm up, we are therefore led to study the "corrected'' solution for a point particle in flat spacetime. We find that the solution exhibits the expected string singularities, which we expect to "gauge away", leaving a metric with irregularity confined to a sphere intersecting the particle. We discuss whether a regularized version of this metric is a suitable second-order source and how our results generalize to Kerr.

The tidal deformability of a self-gravitating body can be characterized by a set of so-called tidal Love numbers (TLN). Existing and future gravitational-wave measurements of TLN in binary inspirals provide a novel way of testing compact objects and general relativity in the strong-field regime. In particular, the observation by the planned LISA mission of the gravitational-wave signals resulting from extreme mass ratio inspirals might place constraints on the TLN of the central object which are roughly eight orders of magnitude more stringent than current ones on neutron stars. All previous works so far suggest that the TLN of black holes vanish in general relativity. We report on recent work addressing the question of whether the TLN of a Kerr black hole vanish for an arbitrary spin.

We combine different techniques to extract information about the logarithmic contributions to the two-body conservative dynamics within the post-Newtonian (PN) approximation of general relativity. The logarithms come from the conservative part of nonlinear gravitational-wave tails and their iterations. Explicit, original expressions are found for conservative dynamics logarithmic tail terms up to 6PN order by adopting both traditional PN calculations and effective field theory methods. We also determine all logarithmic terms at 7PN order, fixing a sub-leading logarithm from a tail-of-tail-of-tail process by comparison with self-force results. Moreover, we use renormalization group techniques to obtain the leading logarithmic terms to generic power n, appearing at (3n+1)PN order, and we resum the infinite series in a closed form extending a previous self-force results which determined these logarithms up to 22PN order.

We present new advances in determining analytic PN series for various orbital features of non-spinning extreme-mass-ratio inspirals. We pursue quantities in both the dissipative and conservative sectors using an expansion procedure for the MST solutions in the RWZ formalism. On the dissipative side, these solutions immediately yield PN series for the time-averaged fluxes using standard formulas. Because the process requires only a finite number of modes, the results can be easily taken to high PN order, as well as high (if not arbitrary) order in the eccentricity of the orbit. However, local conservative changes involve an infinite number of modes, increasing the computational complexity by an order of magnitude. Nevertheless, we employ several computational simplifications to advance the state of the art for the redshift invariant. We conclude by discussing the spin-precession invariant and local self-force, as well as future application to the Kerr case.

Exploiting simple yet remarkable properties of relativistic gravitational scattering, we use first-order self-force (linear-in-mass-ratio) results to obtain arbitrary-mass-ratio results for the complete third-subleading post-Newtonian (4.5PN) corrections to the spin-orbit sector of spinning-binary conservative dynamics, for generic (bound or unbound) orbits and spin orientations. We thereby improve important ingredients of models of gravitational waves from spinning binaries, and we demonstrate the improvement in accuracy by comparing against numerical simulations of binary black holes. We lay out future work at the interface between post-Minkowskian gravity and self-force theory. Based on [arXiv:2003.11391].

Hyperbolic-type scattering orbits are excellent probes of the strong-field regime around black holes, and their analysis can inform the construction of an accurate two-body Hamiltonian. In particular, it has been shown that knowledge of the scattering angle through linear order in the mass ratio (as a function of initial velocity and impact parameter) completely determines the (yet-unknown) 4PM Hamiltonian. With this motivation in mind, we describe a programme to calculate the self-force correction to the scattering angle. Our method is based on on a numerical time-domain metric reconstruction from a Hertz potential in a radiation gauge. We describe a novel method for setting up such a calculation, and present intermediate results. We show a formulation of the conservative self-force correction to the scatter angle in Schwarzschild spacetime, and thus identify the necessary self-force input.

Using a recently introduced method which splits the conservative dynamics of gravitationally interacting binary systems into a non-local-in-time part and a local-in-time one, we show how to compute the local part of the dynamics at the 6PN accuracy. We also show recent results concerning the nonlocal part.

Time-domain evolutions of Lorenz-gauge metric perturbations (on black hole backgrounds) suffer from an $\ell=1$ gauge instability. The unstable gauge mode satisfies the Einstein equations and all physical boundary conditions at any finite time, but blows up in the limit $t \to \infty$. I have proposed an orthogonalization scheme to cancel out the effect of the instability in time-domain evolutions. I will describe recent progress towards applying this scheme in a (semi-)realistic GSF computation, and discuss the use of an independently-programmed computation of the Einstein tensor in validating and debugging a numerical code.

We perform a sequence of binary black hole simulations with increasingly small mass ratio, reaching a 1:128 binary that displays 13 orbits before merger. Based on a detailed convergence study of the $q=1/15$ nonspinning case, we apply additional mesh refinements levels on the smaller hole horizon to reach the $q=1/32$, $q=1/64$, and $q=1/128$ cases. Roughly linear strong computational scaling with $q$ is observed on 8 nodes simulations. We compute the remnant properties of the merger; final mass, spin, and recoil. We also compute the gravitational waveforms, peak frequency, amplitude, and luminosity. We compare those values with predictions of the corresponding phenomenological formulas, reproducing the particle limit, and we then use these new results to improve their fitting coefficients.

"Much effort has been devoted in order to develop a theory that describes dissipative fluid dynamics in the context of General Relativity. It is well known that much of the equations that describe those effects are of parabolic type, and thus the information propagates at infinite speed. This fact goes against the causality principles of Einstein's theory, that postulates that nothing can travel faster than speed of light. This problem makes the issue of describing dissipative fluids in the context of General Relativity a highly non-trivial task.In this talk I will present a novel theory for utrarelativistic fluids, that are invariant under conformal transformations of the background metric tensor. We show that such a theory is symmetric-hyperbolic, which implies that it has a well-posed initial value problem, and study causality and stability of equillibrium states. Finally, we comment on a original way for numerically evolve this class of theories, focusing on the difficulties that appear during evolution, and show some simulations at short and long times, within different dissipative regimes. This system can be directly adapted for simulating astrophysical fluid systems around compact objects like rotating black holes."

Gravitational wave signals from compact astrophysical sources such as those observed by LIGO and Virgo require a high-accuracy waveform model for the analysis of the recorded signal. Current inspiral-merger-ringdown (IMR) models are calibrated only up to moderate mass ratios, thereby limiting their applicability to signals from high-mass ratio binary systems. We describe reduced-order surrogate models for gravitational waveforms including several harmonic modes and with mass-ratios varying from 3 to 10,000 thus vastly expanding the parameter range beyond the current surrogate IMR models. This surrogate model is trained on waveform data generated by point-particle black hole perturbation theory (ppBHPT) both for large mass-ratio and comparable mass-ratio binaries. We observe that the gravitational waveforms generated through a simple application of ppBHPT to the comparable mass-ratio cases agree remarkably (and surprisingly) well with those from full numerical relativity after a rescaling of the ppBHPT's total mass parameter. These results will enable data analysis studies in the high-mass ratio regime, including potential intermediate mass-ratio signals from LIGO/Virgo and extreme-mass ratio events of interest to the future space-based observatory LISA.

Multiple approaches are required to study the evolution of black-hole binaries. While the post-Newtonian approximation is sufficient to describe the early inspiral (even from infinitely large orbital separation), only numerical relativity can capture the full complexity of the dynamics near the merger. We combine multi-timescale post-Newtonian integrations with numerical-relativity surrogate models, thus mapping the entire history of the binary from its asymptotic configuration at past-time infinity to the post-merger remnant. Our approach naturally allows us to assess the impact of the precessional and orbital phase on the properties -- mass, spin, and kick -- of the merger remnant. These phases impose a fundamental limit on the accuracy of models that aim to connect the properties of astrophysical black-hole binary progenitors to the parameters of their merger remnants. More on arxiv:2005.01747

The small body in an EMRI, in fact, could be a stellar-mass black hole binary. In this talk, I will review the astrophysical scenarios in which such binary-EMRIs could form. I will show that such sources emit both milli-Hertz and hundred-Hertz gravitational waves, so that they are perfect targets for future multi-band gravitational-wave astronomy. Because of the rich radiate spectrum, binary-EMRI opens up new possibilities of testing general relativity and fundamental physics.

"Numerous galaxies embodies a Massive Black hole (MBH) in the galactic center enclosed by stellar clusters with large verity of dense stellar population. Extreme mass ratio inspirals (EMRIs) and Intermediate mass ratio inspirals (IMRIs) are the most compelling sources of gravitational radiation detectable by Laser Interferometer Space Antenna (LISA) that will have competence to observe the entire sky probing for the gravitational universe. Sensitivity band of LISA lies in frequency range of about 10−4 to 10−1Hz with mass range ∼ 10^4 10^7M. EMRIs and IMRIs are the prime source for LISA encompasses the whirling of compact objects (COs), typically stellar mass black holes (BH), neutron stars (NS), white dwarfs (WD) and intermediate mass blackholes (IMBH) with mass ratio q 1 and prolonged cycles ∼ 10^4–10^5, emitting gravitational radiations lasting for several years.

We investigate the dependency of signal–to–noise ratios (SNRs) onto informative parameters and make inferences regarding the properties of Galactic EMRIs. Constraining the intrinsic parameters of Analytical Kludge (AK) waveform model we employ the well calibrated stellar properties of the MBH to extrapolate the scaling relation that contemplates fiducial fit for back–of–envelop computations of SNRs. The best–fit the radial parameter sweeps between 6.09rg < a < 11.18rg. Additionally, we enumerate the averaged probability of 1.43 EMRI events to occur in Milky Way (MW) hosting super massive black hole (SMBH), by employing the known astrophysical stellar dynamics of stellar population near the MBH and considering the detectors sensitivity."

The dynamics of precessing black-hole binaries in the post-Newtonian regime is deeply characterized by a timescale hierarchy: the orbital timescale is very short compared to the spin-precession timescale which, in turn, is much shorter than the radiation-reaction timescale on which the orbit is shrinking due to gravitational-wave emission. We present the development of a generic multi-timescale analysis which averages the dynamics over both the orbital and the precessional motions. Spin-precession cones can be treated “as a whole", without tracking the spin's secular motion. These solutions improve our understanding of spin precession in much the same way that the conical sections for Keplerian orbits provide additional insights beyond Newton's 1/r^2 law. Over the years, our multi-timescale approach led to an explosion of new predictions ranging from spin morphologies to new dynamical instabilities, resonances, and maximal nutations. Multi-timescale solutions are now at the backbone of state-of-the-art waveform templates used in gravitational-wave parameter estimation.

Binary black holes in which both spins are aligned with the orbital angular momentum do not precess. However, the up-down configuration, in which the spin of the heavier (lighter) hole is aligned (anti-aligned) with the orbital angular momentum, is unstable to spin precession at small orbital separations. Employing the multi-timescale post-Newtonian approach, we derive the instability onset by casting the spin dynamics in terms of a simple harmonic oscillator. Surprisingly, we find that the instability drives up-down binaries to precise endpoints - namely, they approach merger with the two spins aligned with each other and equally misaligned with the orbital angular momentum. For an astrophysically motivated population we find that the binaries approach this endpoint quickly and note that the measurement of two-spin effects in gravitational-wave emission is necessary to detect the phenomenon.

Even though rarely directly relevant for gravitational-wave physics, scattering has recently proven itself to be a useful proxy from which one can read off quantities relevant even for bound binaries. In this talk I will present analytical results for generic scattering of spinning test particles around Kerr black holes to linear perturbative order in the particle spin.

In this talk I will examine spin effects in EMRI self-force calculations. In particular, the work is specialised to perturbations of Schwazschild spacetime by a secondary with spin aligned to the orbital angular momentum in a quasi-circular orbit.

"Extreme mass-ratio inspirals detectable by the future Laser Interferometer Space Antenna provide a unique way to test general relativity and fundamental physics. Motivated by this possibility, we study in detail the EMRI dynamics in the presence of a spinning secondary, extending various results that appeared in previous work and also providing new relations for the first time. We present the results of a frequency-domain code that computes gravitational-wave fluxes and the adiabatic orbital evolution for the case of circular, equatorial orbits with (anti)aligned spins in Kerr spacetime. The spin of the secondary starts affecting the gravitational-wave phase to next-to-leading order in the mass ratio (being thus comparable to the leading-order conservative part and the second-order dissipative part of the self-force) and introduces a detectable dephasing, which can be used to measure it at 5-25% level, depending on individual spins. Finally, we discuss the implication of this effect for tests of the Kerr bound.

[1] G. A. Piovano, A. Maselli, P. Pani, ""Model independent tests of the Kerr bound with extreme mass ratio inspirals"", arXiv:2003.08448 [gr-qc]

[2] G. A. Piovano, A. Maselli, P. Pani, ""Extreme mass ratio inspirals with spinning secondary:a detailed study of equatorial circular motion"", arXiv:2004.02654 [gr-qc]"

We present the analytical description of the gravitational two-body problem in the spinning particle limit. Recently developed equations of motion and world-line perturbation theory for particles carrying spin are reviewed. Exact circular orbit solutions, eccentric-planar orbits, and the innermost stable circular orbit are found in the Kerr spacetime. Non-planar eccentric orbits including the precessional frequency of the plane are predicted in Schwarzschild spacetime. The calculations are performed with the complete spin of the particle and in a fully relativistic way.