Post-Carrollian mechanics, ideal gas and gravity

Energy and momentum in Newtonian mechanics have the familiar relations, ([Formula: see text]) and ([Formula: see text]), derived from the nonrelativistic limit of special relativity. In this study, we find the corresponding relations to formulate the so-called “post-Carrollian mechanics” by applying the ultra-relativistic limit to tachyon theory, resulting in ([Formula: see text]) and ([Formula: see text]). Using these, we determine the energy-momentum relation and investigate the thermodynamics of an ideal gas composed of post-Carroll particles. Moreover, by applying the ultra-relativistic limit to Einstein’s equations coupled to tachyon dust, we find the post-Carrollian gravitational potential. Finally, utilizing the geodesic equation, we determine the post-Carrollian gravitational field, which unlike the Newtonian case is found to be radially outward.