Fixing the dynamical evolution of self-interacting vector fields

• Published in: arXiv.org
• Main Authors: Rubio, Marcelo E, Lara, Guillermo, Bezares, Miguel, Crisostomi, Marco, Barausse, Enrico
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 29.08.2024
• Subjects: Breakdown; Cauchy problems; Fields (mathematics); Fixing; Gravitational collapse; Physics - General Relativity and Quantum Cosmology; Tensors; Well posed problems
• DOI: 10.48550/arxiv.2407.08774

Numerical simulations of the Cauchy problem for self-interacting massive vector fields often face instabilities and apparent pathologies. We explicitly demonstrate that these issues, previously reported in the literature, are actually due to the breakdown of the well-posedness of the initial-value problem. This is akin to shortcomings observed in scalar-tensor theories when derivative self-interactions are included. Building on previous work done for k-essence, we characterize the well-posedness breakdowns, differentiating between Tricomi and Keldysh-like behaviors. We show that these issues can be avoided by ``fixing the equations'', enabling stable numerical evolutions in spherical symmetry. Additionally, we show that for a class of vector self-interactions, no Tricomi-type breakdown takes place. Finally, we investigate initial configurations for the massive vector field which lead to gravitational collapse and the formation of black holes.