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We report on the successful numerical evolution of the compactified hyperboloidal initial value problem in general relativity using generalized harmonic gauge.
1903
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1909
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1911
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R. M. Wald, General relativity (The University of Chicago Press, Chicago, 1984)
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C. R. Evans, A Method for Numerical Relativity: Simulation of Axisymmetric Gravitational Collapse and Gravitational Radiation Generation , Ph.D. thesis, University of Texas at Austin (1984)
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L. Hörmander, The lifespan of classical solutions of non-linear hyperbolic equations, in Pseudo-Differential Operators: Proceedings of a Conference held in Oberwolfach, February 2–8, 1986 (Springer Berlin Heidelberg, Berlin, Heidelberg, 1987) pp. 214–280
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H. Lindblad and I. Rodnianski, The weak null condition for Einstein’s equations, Comptes Rendus Mathematique 336
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J. Frauendiener, Conformal infinity, Living Rev. Relativity 7
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H. Friedrich, On the non-linearity of the subsidiary systems, Class. Quant. Grav. 22
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G. Calabrese, C. Gundlach, and D. Hilditch, Asymptotically null slices in numerical relativity: Mathematical analysis and spherical wave equation tests, Class.Quant.Grav. 23
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L. Lindblom, M. A. Scheel, L. E. Kidder, R. Owen, and O. Rinne, A new generalized harmonic evolution system, Class. Quant. Grav. 23
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A. Zenginoglu, Hyperboloidal evolution with the Einstein equations, Class. Quant. Grav. 25
2008
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M. Alcubierre, Introduction to 3+1 Numerical Relativity (Oxford University Press, Oxford, 2008)
2008
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2009
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2010
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2021
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J. Frauendiener and C. Stevens, The non-linear perturbation of a black hole by gravitational waves. i. the bondi–sachs mass loss, Classical and Quantum Gravity 38
2021
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2011
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2011
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J. Winicour, Characteristic evolution and matching, Living Rev. Relativity 15
2012
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2022
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R. P. Macedo, B. Leather, N. Warburton, B. Wardell, and A. Zenginoğlu, Hyperboloidal method for frequency-domain self-force calculations, Physical Review D 105
2022
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2022
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2022
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2023
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2023
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J. Frauendiener and C. Stevens, The non-linear perturbation of a black hole by gravitational waves. ii. quasinormal modes and the compactification problem, Classical and Quantum Gravity 40
2023
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2024
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J. Frauendiener, A. Goodenbour, and C. Stevens, The non-linear perturbation of a black hole by gravitational waves. iii. newman–penrose constants, Classical and Quantum Gravity 41
2024
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