TOPICAL REVIEW: From geometry to numerics: interdisciplinary aspects in mathematical and numerical relativity
Abstract
This paper 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 in light of the interaction between numerical and mathematical relativists.
- Publication:
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Classical and Quantum Gravity
- Pub Date:
- May 2008
- DOI:
- 10.1088/0264-9381/25/9/093001
- arXiv:
- arXiv:0712.2332
- Bibcode:
- 2008CQGra..25i3001J
- Keywords:
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- General Relativity and Quantum Cosmology
- E-Print:
- 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 Gravity