Threshold of Singularity Formation in the Semilinear Wave Equation

Details Threshold of Singularity Formation in the Semilinear Wave Equation Threshold of Singularity Formation in the Semilinear Wave Equation

2005-02-11

arxiv.org/abs/gr-qc/0502056v1

Phys.Rev. D71 (2005) 044019

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages, 7 figures

Scientific paper

10.1103/PhysRevD.71.044019

Solutions of the semilinear wave equation are found numerically in three spatial dimensions with no assumed symmetry using distributed adaptive mesh refinement. The threshold of singularity formation is studied for the two cases in which the exponent of the nonlinear term is either $p=5$ or $p=7$. Near the threshold of singularity formation, numerical solutions suggest an approach to self-similarity for the $p=7$ case and an approach to a scale evolving static solution for $p=5$.

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