Dirichlet walls and the end of time
arXiv:2606.05505
The paper investigates how imposing Dirichlet boundary conditions on a finite surface in Einstein-Hilbert gravity can cause evolutions to end in finite time due to singularities reaching the boundary, with examples in cosmology, BTZ black holes, and higher dimensions.
Abstract
We study evolution in Einstein-Hilbert gravity with Dirichlet boundary conditions imposed on a finite surface. We argue that there are open sets of initial data where such evolutions terminate at finite times due to singularities that reach the boundary. In any dimension, the simplest such examples occur in cosmologies. However, in 2+1 dimensions we also show that Dirichlet walls initially outside a BTZ black hole can fall through the horizon, and that this also leads to generic singularities. A similar construction in higher dimensions leads to trapped surfaces that reach the wall, though the end result of such evolutions is more difficult to study.
29 pages, 7 figures; replaced figure 5 and some related discussion, added reference in section 5, typos corrected