A time-like window into tensionless worldsheets

Abstract: Rindler worldsheets are known to acquire a Carrollian structure at infinite acceleration, marking their tensionless limit. This work extends the same paradigm to time-evolving worldsheets in the background target spacetime spanning the Kasner wedges. Specifically, we demonstrate that approaching the null horizons of the Kasner worldsheet induces a Carrollian structure, necessitating an infinite limit on the time-evolution parameter. We further examine how the associated Bogoliubov transformations on the usual tensile Kasner worldsheets -- encompassing quantum modes, vacuum states, and oscillators -- provide insights into their yet-unexplored tensionless regime. Intriguingly, phenomena such as null string complementarity (i.e., the emergence of open string physics from closed strings) and Hagedorn physics naturally arise in the quantum vacuum of tensionless worldsheets. These findings validate that time-like entanglement in Kasner worldsheets is not merely analogous to, but exactly equivalent to, space-like entanglement in Rindler worldsheets, viewed in distinct causally-disconnected regions.