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

Quantization of fermions on Kerr space-time

We study a quantum fermion field on a background nonextremal Kerr black hole. We discuss the definition of the standard black hole quantum states (Boulware, Unruh, and Hartle-Hawking), focussing particularly on the differences between fermionic and bosonic quantum field theory. Since all fermion modes (both particle and antiparticle) have positive norm, there is much greater flexibility in how quantum states are defined compared with the bosonic case. In particular, we are able to define a candidate Boulware-like state, empty at both past and future null infinity, and a candidate Hartle-Hawking-like equilibrium state, representing a thermal bath of fermions surrounding the black hole. Neither of these states have analogues for bosons on a nonextremal Kerr black hole and both have physically attractive regularity properties. We also define a number of other quantum states, numerically compute differences in expectation values of the fermion current and stress-energy tensor between two states, and discuss their physical properties

Black hole determinants and quasinormal modes

We derive an expression for functional determinants in thermal spacetimes as a product over the corresponding quasinormal modes. As simple applications we give efficient computations of scalar determinants in thermal AdS, BTZ black hole and de Sitter spacetimes. We emphasize the conceptual utility of our formula for discussing `1/N' corrections to strongly coupled field theories via the holographic correspondence.Comment: 28 pages. v2: slightly improved exposition, references adde

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