Unstable D-brane in Torsional Newton-Cartan Background

This paper is devoted to the construction of unstable D-brane action in torsional Newton-Cartan background through T-duality along null direction. We determine corresponding equations of motion and analyze their solution that corresponds to lower dimensional non-relativistic D(p-1)-brane. We also find Hamiltonian for unstable Dp-brane and study tachyon vacuum solutions that can be interpreted as gas of non-relativistic strings.