Nearly 7 years in the making, we have finally finished our first paper describing our second-order gravitational self-force results:

Second-order self-force calculation of gravitational binding energy
Adam Pound, Barry Wardell, Niels Warburton, Jeremy Miller

Self-force theory is the leading method of modeling extreme-mass-ratio inspirals (EMRIs), key sources for the gravitational-wave detector LISA. It is well known that for an accurate EMRI model, second-order self-force effects are critical, but calculations of these effects have been beset by obstacles. In this letter we present the first implementation of a complete scheme for second-order self-force computations, specialized to the case of quasicircular orbits about a Schwarzschild black hole. As a demonstration, we calculate the gravitational binding energy of these binaries.

Check out our paper on arXiv.

The preprint of my latest paper with Niels Warburton is now available on the arXiv. The abstract for the article is below:

With a view to developing a formalism that will be applicable at second perturbative order, we devise a new practical scheme for computing the gravitational self-force experienced by a point mass moving in a curved background spacetime. Our method works in the frequency domain and employs the effective-source approach, in which a distributional source for the retarded metric perturbation is replaced with an effective source for a certain regularized self-field. A key ingredient of the calculation is the analytic determination of an appropriate puncture field from which the effective source and regularized residual field can be calculated. In addition to its application in our effective-source method, we also show how this puncture field can be used to derive tensor-harmonic mode-sum regularization parameters that improve the efficiency of the traditional mode-sum procedure. To demonstrate the method, we calculate the first-order-in-the-mass-ratio self-force and redshift invariant for a point mass on a circular orbit in Schwarzschild spacetime.

Update: The paper has now been published as  Phys. Rev. D92, 084019 (2015).

The preprint of my latest paper with Patrick Nolan, Chris Kavanagh, Sam R Dolan, Adrian C Ottewill, and Niels Warburton is now available on the arXiv. The abstract for the article is below:

We extend the gravitational self-force methodology to identify and compute new tidal invariants for a compact body of mass on a quasi-circular orbit about a black hole of mass . In the octupolar sector we find seven new degrees of freedom, made up of 3+3 conservative/dissipative `electric’ invariants and 3+1 `magnetic’ invariants, satisfying 1+1 and 1+0 trace conditions. After formulating for equatorial circular orbits on Kerr spacetime, we calculate explicitly for Schwarzschild spacetime. We employ both Lorenz gauge and Regge-Wheeler gauge numerical codes, and the functional series method of Mano, Suzuki and Takasugi. We present (i) highly-accurate numerical data and (ii) high-order analytical post-Newtonian expansions. We demonstrate consistency between numerical and analytic results, and prior work. We explore the application of these invariants in effective one-body models, and binary black hole initial-data formulations, and conclude with a discussion of future work.

Update: The paper has now been published as Phys. Rev. D 92, 123008 (2015).

The preprint of my latest paper with Chris Kavanagh and Adrian Ottewill is now available on the arXiv. The abstract for the article is below:

We present analytic computations of gauge invariant quantities for a point mass in a circular orbit around a Schwarzschild black hole, giving results up to 15.5 post-Newtonian order in this paper and up to 21.5 post-Newtonian order in an online repository. Our calculation is based on the functional series method of Mano, Suzuki and Takasugi (MST) and a recent series of results by Bini and Damour. We develop an optimised method for generating post-Newtonian expansions of the MST series, enabling significantly faster computations. We also clarify the structure of the expansions for large values of  , and in doing so develop an efficient new method for generating the MST renormalised angular momentum,  .

Update: The paper has now been published as Phys. Rev. D 92, 084025 (2015).

I have recently finished a review paper which is due to be published by Springer in Fundamental Theories of Physics Vol. 179, as part of the book Equations of Motion in Relativistic Gravity. A preprint of the article is available on the arXiv. The abstract for the article is below:

Building on substantial foundational progress in understanding the effect of a small body’s self-field on its own motion, the past 15 years has seen the emergence of several strategies for explicitly computing self-field corrections to the equations of motion of a small, point-like charge. These approaches broadly fall into three categories: (i) mode-sum regularization, (ii) effective source approaches and (iii) worldline convolution methods. This paper reviews the various approaches and gives details of how each one is implemented in practice, highlighting some of the key features in each case.