We present ongoing work on the computation of the local force due to back-reaction effects caused by the spin of the lesser component in an extreme mass-ratio binary

In this brief talk, several aspects at the interface between EOB theory and the Small Mass Ratio (SMR) approximation will be reviewed. The light ring problem will be discussed and an outline of its resolution presented. The state-of-the-art EOBSMR model will then be introduced, followed by a sketch of the roadmap for its further improvements.

In this talk we will review the expected event rate for Extreme Mass Ratio Inspiral (EMRIs) in the LISA band. We discuss the astrophysical uncertainties which influence the event rate and distribution of source parameters. Then we describe the simulation of the LISA data with gravitational wave (GW) signal from EMRI system in the coming LISA data challenge and future plans. Finally, we will overview the main methods for detecting EMRI signal.

The detection of gravitational waves by terrestrial interferometers has ushered in the era of gravitational-wave astronomy. This will be even more true when space-based detectors will come of age and measure the mass and spin of massive black holes with exquisite precision and up to very high redshifts, thus allowing for better understanding of the symbiotic evolution of black holes with galaxies, and for high-precision tests of General Relativity in strong-field, highly dynamical regimes. Such ambitious goals require that astrophysical environmental pollution of gravitational-wave signals be constrained to negligible levels, so that neither detection nor estimation of the source parameters are significantly affected. Here, we consider the main sources for space-based detectors -- the inspiral, merger and ringdown of massive black-hole binaries and extreme mass-ratio inspirals -- and account for various effects on their gravitational waveforms, including electromagnetic fields, cosmological evolution, accretion disks, dark matter, "firewalls" and possible deviations from General Relativity. We discover that the black-hole quasinormal modes are sharply different in the presence of matter, but the ringdown signal observed by interferometers is typically unaffected. The effect of accretion disks and dark matter depends critically on their geometry and density profile, but is negligible for most sources, except for few special extreme mass-ratio inspirals. Electromagnetic fields and cosmological effects are always negligible. We finally explore the implications of our findings for proposed tests of General Relativity with gravitational waves, and conclude that environmental effects will not prevent the development of precision gravitational-wave astronomy.

In this work we have derived the evolution equation for gravitational perturbation in four dimensional spacetime in presence of a spatial extra dimension. The evolution equation is derived by perturbing the effective gravitational field equations on the four dimensional spacetime, which inherits non-trivial higher dimensional effects. The gravitational perturbation has further been decomposed into a purely four dimensional part and another piece depending on extra dimensions. The four dimensional gravitational perturbation now admits massive propagating degrees of freedom, courtesy to the existence of higher dimensions. We have also studied the influence of these massive propagating modes on the quasi-normal mode frequencies, signalling the higher dimensional nature of the spacetime and have contrasted these massive modes with the massless modes in general relativity. Surprisingly, it turns out that the massive modes experience much smaller damping compared to the massless modes in general relativity and may even dominate over and above the general relativity contribution if one observes the ring down phase of a black hole merger event at sufficiently late times. Furthermore, the whole analytical framework has been supplemented by the fully numerical Cauchy evolution problem as well. In this context we have shown that except for minute details the overall features of the gravitational perturbations are captured in both the Cauchy evolution as well as in the analysis of quasi-normal modes. The implications are also discussed.

Despite being associated with massless particles, electromagnetic and gravitational waves do not propagate strictly on the null cone in curved spacetimes. They also develop tails, traveling inside the light cone. This tail effect provides a contribution to the self-force of compact bodies orbiting super-massive black holes, which in turn are believed to be important sources of gravitational waves for future space based detectors like LISA, TianQin and Taiji. I will summarize my efforts -- which were inspired by the EMRI self-force problem -- to explore novel methods to understand the tail effect in curved geometries, primarily in cosmological spacetimes. Some of the spin-offs include the (small) discovery of new type of gravitational wave memory effect induced by tails.

Last year the European Space Agency selected the LISA mission for the L3 launch slot in its future science program. LISA will open the low-frequency spectrum for gravitational wave astronomy, listening to sources such as supermassive black holes and extreme mass ratio inspirals. The industrial Phase-A study has just begun to prepare for a launch in the early 2030s.

I will describe the progress made in performing self-consistent evolution of a scalar charge in orbit around a Schwarzschild black hole. I will briefly describe the main technical obstacle that was overcome, the obstacles that remain and show the first preliminary comparison between self-consistent and geodesic evolution. I will finally outline the plans for future development.

Abstract: The low-energy dynamics of any system admitting a continuum of static configurations is approximated by slow motion in moduli (configuration) space. In the talk I will describe how this moduli space approximation can be utilized to study collisions of two maximally charged Reissner–Nordstrom black holes of arbitrary masses, and to compute analytically the gravitational radiation generated by their scattering or coalescence. Notably, the motion remains slow even though the fields are strong, and the leading radiation is quadrupolar. A simple expression for the gravitational waveform will be presented and compared at early and late times to expectations.

In this talk I will give an overview of the current astrophysical results arising from searching for compact binary mergers in data taken from second-generation gravitational-wave observatories. I will give a description of the search techniques, and illustrate how highly-accurate waveform models are critical for us to observe, and understand, compact binary mergers. I will give an outlook on how we expect gravitational-wave astronomy to evolve in the coming years. I will also discuss some of the areas where our current methods could be improved, and how improved waveform models, especially at high mass ratios, will greatly help gravitational-wave astronomy today.

While the Capra community has traditionally been motivated by astrophysics, many of the tools we have developed are much more general: They can and should be applied to also understand other areas of physics. One interesting class of problems are those associated with motion in two spatial dimensions, as relevant for various condensed-matter and fluid-mechanical systems. Tail effects are much stronger here than in any "ordinary" 3+1D system, implying the existence of extremely persistent memory effects. These provide a far richer and less intuitive phenomenology than we're used to. For example, there is a sense in which mechanics takes on an almost-Aristotelian (instead of Newtonian) character.

The self-force mode-sum technique has proven itself the current leading technique in self-force calculations. The removal of a singular field via regularization parameters is a crucial part of this method. We show a covariant form of the Detweiler-Whiting singular field in the scalar case. We give a rotated coordinate system which allows for the production of high order regularization parameters in generic Kerr spacetime. We show the success of our parameters and outline the steps towards the gravity case.

The metric describing a two-body system in general relativity can be approximated (at lowest order) as a known background solution due to the more-massive body. A first-order metric perturbation (and the associated self-force), proportional to the mass-ratio of the two bodies, can be found by solving the linearized Einstein equations. This first-order solution serves as (part of) the source of the second-order problem. In recent decades, great strides have been made toward solving the first-order problem in a wide variety of parameter space. In this talk, I will review the state of first-order gravitational self-force analysis with particular attention paid to practical calculations.

The effective-one-body (EOB) model continually proves to be a flexible platform for combining information from numerical relativity and post-Newtonian theory into a comparatively simple form. This has allowed it to become one of the most widely used tools in waveform generation for LIGO. In this talk I will overview the EOB method, and how the developments in conservative self-force calculations have allowed considerable overlap between EOB, PN and self-force.

In General Relativity, it is known that a particle moving in curved spacetime undergoes a force which results from the interaction of the particle with its own field; namely, a self-force or radiation reaction force. In this talk, I discuss the effects of the self-force on the orbital motion of a small object about a black hole: e.g. a test particle orbiting a small black hole (of about a solar mass), a small black hole (of about a solar mass) orbiting a supermassive black hole (of about a million solar masses), etc.. This study can be applied to construction of accurate theoretical gravitational waveforms from binary systems consisting of a small black hole and a supermassive black hole (so called extreme-mass-ratio binaries), which are possible target sources of gravitational waves for eLISA detection.

The LISA mission will be outstanding for discovering and characterizing many moderate-frequency gravitational wave sources. Among these sources, there is special interest in binary black hole coalescences in which the primary has overwhelmingly greater mass than the secondary (extreme mass ratio inspirals) or substantially greater mass than the secondary (intermediate mass ratio inspirals), because the secondaries in such systems will spend a large number of cycles in the extreme gravity realms near the primaries. Several scenarios for such events have been proposed, including high-eccentricity cases driven largely by two-body relaxation, lower-eccentricity but arbitrary-inclination cases driven by tidal separation of a stellar-mass binary, and low-eccentricity and low-inclination cases driven by the dragging of a stellar-mass black hole toward the primary via an accretion disk. Although rates for all scenarios are still highly uncertain, each mechanism will have its own signature and astrophysical importance. I will discuss these possibilities and their variants.

Due to the precision requirements for waveform templates important for LISA data analysis, one of the significant goals of the Capra community is to compute waveforms that track the phase of the long evolution of EMRIs to a precision far better than one radian. The multiscale approximation method is a well-documented mathematical technique which performs a perturbative expansion in an enlarged domain, taking advantage of a near-periodicity in the system and of the separation of scales of the slow radiation-reaction time and the fast orbital time. I will discuss in detail the mathematical techniques of the multiscale approximation method. I will also present an update on recent work with Eanna Flanagan, Tanja Hinderer, and Adam Pound to lay the foundations of a computational scheme to compute the dynamics to post-adiabatic accuracy. This involves combining the multiscale approximation with three other approximations, each valid in different regions of spacetime. The full approximation framework uses several important results from the Capra community, including the detailed form of the second order self force and puncture, metric reconstruction, near-identity transformations, and post-Minkowski dynamics.

We calculate the first-order scalar self-force acting on a scalar-charged particle on a generic, bound geodesic in a background Kerr spacetime. To perform these calculations, we wrote a frequency domain code in Mathematica. By using spectral integration and the MST function expansion formalism, our code makes calculations with arbitrary numerical precision. We present scalar self-force results for several inclined, eccentric orbits, with inclinations ranging from ι = 0 to ι = π/3 and eccentricities ranging from e = 0 to e = 0.8. In these results, we also observe previously reported quasinormal mode excitations in the self-force for highly-eccentric orbits around a highly-spinning black hole.

We model the quasicircular inspiral of a compact object into a more massive charged black hole. Extreme and intermediate mass-ratio inspirals are considered through a small mass-ratio approximation. Reissner-Nordström spacetime is used to describe the charged black hole. The effect of radiation reaction on the smaller body is quantified through calculation of electromagnetic and gravitational energy fluxes via solution of Einstein's and Maxwell's equations. Inspiral trajectories are determined by matching the orbital energy decay rate to the rate of radiative energy dissipation. We observe that inspirals into a charged black hole evolve more rapidly than comparable inspirals into a neutral black hole. Through analysis of a variety of inspiral configurations, we conclude that electric charge is an important effect concerning gravitational wave observations when the charge exceeds the threshold |Q|/M > 0.071 √ ε, where ε is the mass ratio. Journal reference: Phys. Rev. D 97 (2018) 104058; arxiv reference: 1802.00836

In most textbook references, the Einstein Quadrupole formula for gravitational radiation is derived by approximating the source motion as non-relativistic. We relax that assumption in order to incorporate ultra-relativistic point masses such as blobs from jets emanating from the accretion discs around black holes, as sources of gravitational radiation, by deriving in a manifestly Lorentz- covariant manner, a new energy momentum tensor from gauge-invariant projected linearized metric perturbations. In this approach the gravitational radiation from an ultra-relativistic point mass is analyzed, in analogy with that for the relativistic point charge in Maxwell electrodynamics. Our eventual purpose is to calculate the radiation reaction due to linearized gravity by computing the exact radiated four-momentum and thus present a complete analysis of a gravitationally radiating ultra-relativistic point mass, in the linearized approximation. We also plan to investigate the existence or otherwise of pathologies like runaway modes, and to trace them if they do exist, to our use of linearized general relativity.

In this work we propose the modelling of static wormholes within the $f(R,T)$ extended theory of gravity perspective. We present some models of wormholes, which are constructed from different hypothesis for their matter content, i.e., different relations for their pressure components (radial and lateral) and different equations of state. The solutions obtained for the shape function of the wormholes obey the necessary metric conditions. They show a behaviour similar to those found in literature about wormholes, which also happens to our solutions for the energy density of such objects. We also apply the energy conditions for the wormholes physical content.

This work explores the gravitational wave polarization modes for some particular f(R) models using Newman-Penrose formalism. We find two extra scalar modes of gravitational wave (longitudinal and transversal modes) in addition to two tensor modes of general relativity. We conclude that gravitational waves correspond to class II_{6} under the Lorentz-invariant E(2) classification of plane null waves for these f(R) models.

We discuss progress towards first-order gravitational self-force regularization performed in the Regge-Wheeler and Easy gauges for circular orbits in Schwarzschild.

Time-domain evolutions of Lorenz-gauge metric perturbations (on black hole backgrounds) suffer from an $\ell=1$ gauge instability. I will describe this instability and review various techniques for avoiding it.

Motion of point charge with radiation reaction in flat spacetime is described by Lorenz-Dirac (LD) equation, while in curved spacetime - by DeWitt-Brehme (DWB) equation containing the Ricci term and the tail term. I will show that for the motion of elementary particles in vacuum metrics the DWB equation can be reduced to the covariant form of LD equation and covariant Landau-Lifshitz (LL) equation. In the ultrarelativistic case, identical results of integration of LD and LL equations imply the smallness of the third-order Schott term. As an example, I will demonstrate the trajectories of radiating charged particles orbiting Schwarzschild black hole immersed into external asymptotically uniform magnetic field. Depending on the orientation of Lorentz force, the charged particle either spirals down to the black hole, or stabilizes the motion by decaying its oscillations. The latter case leads to an interesting new effect of shifting of the orbit of charged particle outwards from the black hole. I will also discuss the astrophysical relevance of the presented approach and show the estimates of the main parameters of the model applied to some particular black hole candidates.

I will present the first result for calculating the first order self-force on generic bound geodesics in Kerr spacetime.

The Mathisson-Papapetrou-Dixon equations, governing the motion of an extended test body in a curved background, depend on the body's infinite series of multipole moments. From the quadrupolar level and up, the multipole tensors are completely unconstrained in the MPD analysis; they would be determined by the body's internal structure and dynamics. Is there a particular form for the MPD multipoles appropriate for a "test black hole"---an extended test body with spin-induced (and tidally induced?) multipoles matching those of black hole? We will explore this question in the context of an effective action approach to the MPD dynamics, and will mention some intriguing relationships to questions about scattering amplitudes for higher-spin quantum particles.

We present a new, fast method for computing the inspiral trajectory and gravitational waves from extreme mass-ratio inspirals that can incorporate all known (and future) self-force results. Using near-identity (averaging) transformations we formulate equations of motion that do not explicitly depend upon the orbital phases of the inspiral, making them fast to evaluate, and whose solutions track the evolving constants of motion, orbital phases and waveform phase of a full self-force inspiral to O(η), where η is the (small) mass ratio. As a concrete example, we implement these equations for inspirals of non-spinning (Schwarzschild) binaries. Our code computes inspiral trajectories in milliseconds which is a speed up of 2-5 orders of magnitude (depending on the mass-ratio) over previous self-force inspiral models which take minutes to hours to evaluate. Computing two-year duration waveforms using our new model we find a mismatch better than ~10e−4 with respect to waveforms computed using the (slower) full self-force models. The speed of our new approach is comparable with kludge models but has the added benefit of easily incorporating self-force results which will, once known, allow the waveform phase to be tracked to sub-radian accuracy over an inspiral.

The equations of motion of a spinning body in curved space-time are known as the Mathisson-Papapetrou-Dixon equations. However, these equations are not closed and need additional supplementary spin conditions (SSCs) to be imposed. I review these equations and the properties of the system under various commonly used SSCs. After that, I will present Hamiltonians for most of the SSCs and I will present canonical coordinates on the phase space of the entire spin tensor. Finally, I will show some preliminary numerical and perturbational results for spinning bodies near black holes.

The recent observations of gravitational waves has opened a new window to test general relativity. In the future, extreme-mass-ratio inspirals (EMRIs), in which a stellar-mass compact object of mass \mu spirals into a supermassive black holes of mass M, are expected to be observed by LISA. Such systems can be expressed by using the BH perturbation approach, where we expand equations in the mass ratio \mu/M. However, in order to extract physical parameters from GW observations, the second-order perturbations must be considered. In this talk, we will discuss the behavior of the second-order perturbations near the event horizon of the SMBH.

We present a systematic analytical approach to field perturbations of extreme Kerr based on the formalism of Mano, Suzuki and Takasugi (MST) for the Teukolsky equation. Complete analytical expressions for the radial solutions and frequency-domain Green function in terms of infinite series of special functions are presented. As an application, we compute the leading late-time behavior due to the branch point at zero frequency of scalar, gravitational, and electromagnetic field perturbations on and off the event horizon.