https://doi.org/10.1140/epjc/s10052-024-12743-4
Letter
The crease flow on null hypersurfaces
1
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, CB3 0WA, Cambridge, UK
2
Clare Hall, University of Cambridge, Herschel Road, CB3 9AL, Cambridge, UK
3
Institute of Gravitation and Cosmology, RUDN University, ul. Miklukho-Maklaya 6, 117198, Moscow, Russia
Received:
15
December
2023
Accepted:
29
March
2024
Published online:
12
April
2024
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.
© The Author(s) 2024
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