Probing tachyon kinks in Newton-Cartan background

In this paper, we perform a systematic analysis of tachyon condensation over string Newton-Cartan (NC) geometry by probing the background with non BPS $Dp$ brane. We construct the \textit{finite} tachyon effective action for NC geometry and explore the dynamics associated with the tachyon kink on the world-volume of the non BPS $Dp$ brane. We show that under certain specific assumptions, the spatial dependent tachyon condensation leads to an emerging BPS $D(p-1)$ brane dynamics over NC background. We further compute the strees energy tensor and show the equivalence between two different $Dp$ brane configurations in the NC limit.