Entanglement inequalities for timelike intervals within dynamical holography

This paper extends our previous work (arXiv:2504.14313) of a single timelike subregion to two, in the framework of AdS$_3$-Vaidya holography. We confirm the positivity of timelike mutual information and the statement of weak monotonicity when the subregions are non-overlapping. We also study entanglement inequalities such as Araki-Lieb inequality and strong subadditivity when the intervals start to overlap. In line with the recent findings in the literature, we provide explicit working examples showing that the timelike version of the strong subadditivity is generally violated in these setups, even though the statements of subadditivity and Araki-Lieb inequality hold true.