Year: 2023
Type: article
Abstract: We study the asymptotic behavior of the solution curves of the dynamics of spacetimes of the topological type Σp×R, p > 1, where Σp is a closed Riemann surface of genus p, in the regime of 2 + 1 dimensional classical general relativity. The configuration space of the gauge fixed dynamics is identified with the Teichmüller space (TΣp≈R6p−6) of Σp. Utilizing the properties of the Dirichlet energy of certain harmonic maps, estimates derived from the associated elliptic equations in conjunction with a few standard results of the theory of the compact Riemann surfaces, we prove that every non-trivial solution curve runs off the edge of the Teichmüller space at the limit of the big bang singularity and approaches the space of projective measured laminations/foliations (PMLPMF), the Thurston boundary of the Teichmüller space.
Source: Journal of Mathematical Physics
DOI: 10.1063/5.0136631
Author: Puskar Mondal
Institution: Harvard University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4388224858