From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
arXiv:0712.2332 · doi:10.1088/0264-9381/25/9/093001
Abstract
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.
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
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- Conservation laws for dynamical black holes
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Cited by in corpus (21)
- The 1965 Penrose singularity theorem
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- Numerical simulations of black-hole binaries and gravitational wave emission
- An introduction to local Black Hole horizons in the 3+1 approach to General Relativity
- Killing tensor and Carter constant for Painleve-Gullstrand form of Lense-Thirring spacetime
- From Clock Synchronization to Dark Matter as a Relativistic Inertial Effect
- Gravitational waves in dynamical spacetimes with matter content in the Fully Constrained Formulation
- Excised black hole spacetimes: quasi-local horizon formalism applied to the Kerr example
- A critical appraisal of the singularity theorems
- Characteristic Formulation for Metric Gravity
- Constant- geodesics in the Painleve-Gullstrand form of Lense-Thirring spacetime
- Uniqueness of complete maximal hypersurfaces in spatially open -dimensional Robertson-Walker spacetimes with flat fiber
- On uniqueness of the foliation by comoving observers restspaces of a Generalized Robertson Walker spacetime
- Neighbourhoods of Isolated Horizons and their stationarity
- On the Hyperbolicity and Stability of Formulations of Metric Gravity
- Stable maximal hypersurfaces in Lorentzian spacetimes
- Gravitational radiation and angular momentum flux from a slow rotating dynamical black hole