Post-Carrollian Mechanics, Ideal Gas, and Gravity

Abstract

Energy and momentum in Newtonian mechanics have the familiar relations, ($\mathrm{E}=m{v}^2/2$) and ($\mathbf{P}=m\mathbf{v}$), 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 ($\mathbf{P}=\hat{\mathbf{v}}m{c}^3/2v^2$). 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.

20 + 12 pages, 5 figures, 2 tables; published in IJMPA

References in corpus (27)

• The BMS/GCA correspondence
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Gauging the Carroll Algebra and Ultra-Relativistic Gravity
• Carrollian Physics at the Black Hole Horizon
• Conformal Carroll groups
• Carroll versus Galilei Gravity
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• Perfect Fluids
• Carroll Expansion of General Relativity
• Tachyon Condensates, Carrollian Contraction of Lorentz Group, and Fundamental Strings
• Magic Fermions: Carroll and Flat Bands
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• Non-Lorentzian theories with and without constraints
• Higher-dimensional kinematical Lie algebras via deformation theory
• Super-Carrollian and Super-Galilean Field Theories
• Hamiltonian form of `Carroll' gravity
• Classification of Conformal Carroll Algebras
• An Approach for Modelling Tachyons with Gravitation
• Carroll-Schrödinger Equation
• Massive to Massless by Applying a Nonlocal Field Redefinition