Post-Carrollian Mechanics, Ideal Gas, and Gravity

arXiv:2509.14330v1 Announce Type: new
Abstract: Energy and momentum in Newtonian mechanics have the familiar relations, ($mathrm{E}=mv^2/2$) and ($mathbf{P}=mmathbf{v}$), derived from the non-relativistic 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 ($mathrm{E}={m,c^{,3}}/{v}$) and ($mathbf{P}=mathbf{hat{v}},{m,c^{,3}}/{2,v^{,2}}$). 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.