Year: 2026
Type: preprint
Abstract: We prove the existence of solutions to the Lorentzian Monge problem on synthetic Lorentzian spacetimes that satisfy the forward timelike measure contraction property $TMCP^+(K,N)$. The cost for this problem is the time separation function $\ell(x,y)$ (the Lorentz distance), which represents the maximum amount a particle can age when traveling from $x$ to $y$. The solution is based on the needle decomposition technique, and amounts to a reduction of the full problem to its one-dimensional counterparts. As an application of needle decomposition, we introduce the blended $TMCP$ condition, and obtain a quantitative refinement of the synthetic Hawking singularity theorem. We additionally prove a timelike nonbranching reversibility theorem for $TCD_p(K,N)$ spacetimes, showing that forward $p$-essentially nonbranching spacetimes are backward $p$-essentially nonbranching.
Source: arXiv (Cornell University)
Author: Akdemir, Afiny
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213513146