Positive mass theorems for manifolds with asymptotically locally hyperbolic toroidal ends

In [Classical Quantum Gravity 35, 115015 (2018)], P. Chruściel, L. Nguyen, T.-T. Paetz, and the first-named author obtained a positive mass theorem for asymptotically locally hyperbolic manifolds with boundary, having a toroidal end. The proof made use of properties of marginally outer trapped surfaces (MOTS). Here we present some new positive mass results for such manifolds, but without boundary, which allow for other more general ends. The proofs, while still MOTS-based, involve a more elaborate technique (related to μ-bubbles) introduced in work of D. A. Lee, M. Lesourd, and R. Unger [Calculus Var. Part. Differ. Equations 62(7), 194 (2023)] for manifolds with an asymptotically flat end, and further developed by the second-named author in [arXiv:2604.26978 (2026)] for manifolds with an asymptotically hyperbolic end.