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 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.

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

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.

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