The crease flow on null hypersurfaces

Autor: Cotsakis, Spiros
Rok vydání: 2023
Předmět:
Zdroj: Eur. Phys. J. C 84, 391 (2024)
Druh dokumentu: Working Paper
DOI: 10.1140/epjc/s10052-024-12743-4
Popis: The crease flow, replacing the Hamiltonian system used for the evolution of crease sets on black hole horizons, is introduced and its bifurcation properties for null hypersurfaces are discussed. We state the conditions of nondegeneracy and typicality for the crease submanifolds, and find their normal forms and versal unfoldings (codimension 3). The allowed boundary singularities are thus prescribed by the Arnold-Kazaryan-Shcherbak theorem for 3-parameter versal families, and hence identified as swallowtails and Whitney umbrellas of particular kinds. We further present the bifurcation diagrams describing crease evolution at the crossings of the bifurcation sets and elsewhere, and a typical example is studied. Some remarks on the connection of these results to the crease evolution on black hole horizons are also given.
Comment: v2: 19 pages, more explanations and results added, improvements in presentation, new scenario made clearer in Section 6, title slightly changed, matches version to appear in EPJC Letters
Databáze: arXiv
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