A time-like window into tensionless worldsheets

Rindler worldsheets are well known to transition into a tensionless regime in the infinite acceleration limit, acquiring an emergent Carrollian structure. In this work, we uncover an entirely new manifestation of such tensionless dynamics by constructing a time-evolving Milne worldsheet within the future (expanding) and past (contracting) regions of the background target spacetime. We show that as the Milne worldsheet approaches its null horizons, it reveals a deep and previously unexplored interplay between tensionless string dynamics and an emergent Carrollian structure, governed by an ultra-high frequency limit in time evolution. Our results demonstrate that non-inertial string dynamics can emerge in two structurally independent yet complementary settings—governed either by worldsheet acceleration (Rindler) or by the frequency of its intrinsic time evolution (Milne). Remarkably, we uncover a non-trivial duality-like correspondence between Rindler and Milne worldsheets near their respective null horizons, both exhibiting identical tensionless physics despite their distinct causal and dynamical origins. This discovery positions the Milne construction as a genuine time-like counterpart to the ultra-relativistic (Carrollian) or infinite-boost limit, offering new foundational insights into the deep structure of non-inertial string theory.