Effective source approach to self-force calculations

Numerical evaluation of the self-force on a point particle is made difficult by the use of delta functions as sources. Recent methods for self-force calculations avoid delta functions altogether, using instead a finite and extended "effective source" for a point particle. We provide a review of the general principles underlying this strategy, using the specific example of a scalar point charge moving in a black hole spacetime. We also report on two new developments: (i) the construction and evaluation of an effective source for a scalar charge moving along a generic orbit of an arbitrary spacetime, and (ii) the successful implementation of hyperboloidal slicing that significantly improves on previous treatments of boundary conditions used for effective-source-based self-force calculations. Finally, we identify some of the key issues related to the effective source approach that will need to be addressed by future work.Comment: Invited review for NRDA/Capra 2010 (Theory Meets Data Analysis at Comparable and Extreme Mass Ratios), Perimeter Institute, June 2010, CQG special issue - 22 pages, 8 figure

Self-force: Computational Strategies

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.Comment: Synchronized with final published version. Review to appear in "Equations of Motion in Relativistic Gravity", published as part of the Springer "Fundamental Theories of Physics" series. D. Puetzfeld et al. (eds.), Equations of Motion in Relativistic Gravity, Fundamental Theories of Physics 179, Springer, 201

Spin–orbit precession for eccentric black hole binaries at first order in the mass ratio

We consider spin–orbit ('geodetic') precession for a compact binary in strong-field gravity. Specifically, we compute ψ, the ratio of the accumulated spin-precession and orbital angles over one radial period, for a spinning compact body of mass m 1 and spin s 1, with ${{s}_{1}}\ll Gm_{1}^{2}/c$ , orbiting a non-rotating black hole. We show that ψ can be computed for eccentric orbits in both the gravitational self-force and post-Newtonian frameworks, and that the results appear to be consistent. We present a post-Newtonian expansion for ψ at next-to-next-to-leading order, and a Lorenz-gauge gravitational self-force calculation for ψ at first order in the mass ratio. The latter provides new numerical data in the strong-field regime to inform the effective one-body model of the gravitational two-body problem. We conclude that ψ complements the Detweiler redshift z as a key invariant quantity characterizing eccentric orbits in the gravitational two-body problem

Research Update on Extreme-Mass-Ratio Inspirals

The inspirals of stellar-mass mass compact objects into massive black holes in the centres of galaxies are one of the most important sources of gravitational radiation for space-based detectors like LISA or eLISA. These extreme-mass-ratio inspirals (EMRIs) will enable an ambitious research program with implications for astrophysics, cosmology, and fundamental physics. This article is a summary of the talks delivered at the plenary session on EMRIs at the 10th International LISA Symposium. It contains research updates on the following topics: astrophysics of EMRIs; EMRI science potential; and EMRI modeling.Comment: 17 pages, no figures. Proceedings of the LISA Symposium X, to be published at the Journal of Physic