3 research outputs found
From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
This article reviews some aspects in the current relationship between
mathematical and numerical General Relativity. Focus is placed on the
description of isolated systems, with a particular emphasis on recent
developments in the study of black holes. Ideas concerning asymptotic flatness,
the initial value problem, the constraint equations, evolution formalisms,
geometric inequalities and quasi-local black hole horizons are discussed on the
light of the interaction between numerical and mathematical relativists.Comment: Topical review commissioned by Classical and Quantum Gravity.
Discussion inspired by the workshop "From Geometry to Numerics" (Paris, 20-24
November, 2006), part of the "General Relativity Trimester" at the Institut
Henri Poincare (Fall 2006). Comments and references added. Typos corrected.
Submitted to Classical and Quantum Gravit
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