Alain Haraux†
A toy model is proposed for the Cosmic Dipole consisting in the Shapley attractor and the so-called Dipole repeller, whose action is assimilated to an anti-gravitational force. According to this model, the local group will collapse in finite time with the Shapley attractor and, by using the available figures for distances and masses, it is shown that it will happen in less than 100 billion years. To obtain a more precise estimate, more knowledge will be necessary on the equivalent negative mass of the repeller.
Keywords: energy, mass, gravitation, differential equations, finite-time collapse.
MSC: 8508, 85A05.
DOI 10.56082/annalsarscimath.2025.2.45
† alain.haraux@sorbonne-universite.fr, Sorbonne Universit´e, Universit´e ParisDiderot SPC, CNRS, INRIA, Laboratoire Jacques-Louis Lions, LJLL, F-75005, Paris,
France
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 17 no 2, 2025
