Planar Carrollian statistical physics is well-defined thanks to central extensions and rotation, yielding logarithmic entropy scaling with disc area and two-dimensional ideal-gas pressure.
Celestial Mechanics, Conformal Structures, and Gravitational Waves
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The equations of motion for $N$ non-relativistic particles attracting according to Newton's law are shown to correspond to the equations for null geodesics in a $(3N+2)$-dimensional Lorentzian, Ricci-flat, spacetime with a covariantly constant null vector. Such a spacetime admits a Bargmann structure and corresponds physically to a generalized pp-wave. Bargmann electromagnetism in five dimensions comprises the two Galilean electro-magnetic theories (Le Bellac and L\'evy-Leblond). At the quantum level, the $N$-body Schr\"odinger equation retains the form of a massless wave equation. We exploit the conformal symmetries of such spacetimes to discuss some properties of the Newtonian $N$-body problem: homographic solutions, the virial theorem, Kepler's third law, the Lagrange-Laplace-Runge-Lenz vector arising from three conformal Killing 2-tensors, and motions under inverse square law forces with a gravitational constant $G(t)$ varying inversely as time (Dirac). The latter problem is reduced to one with time independent forces for a rescaled position vector and a new time variable; this transformation (Vinti and Lynden-Bell) arises from a conformal transformation preserving the Ricci-flatness (Brinkmann). A Ricci-flat metric representing $N$ non-relativistic gravitational dyons is also pointed out. Our results for general time-dependent $G(t)$ are applicable to the motion of point particles in an expanding universe. Finally we extend these results to the quantum regime.
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UNVERDICTED 4representative citing papers
The Bohlin variant of the Eisenhart lift embeds Lagrangian systems into timelike geodesics of conformally flat (d+2)-dimensional metrics and yields novel examples of such metrics admitting higher-rank Killing tensors.
Derives post-Newtonian equations from a scalar-extended Newtonian Lagrangian and bounds its free parameter with Solar System observations.
Analyzes TsT deformations and Penrose limits on fibered I-branes from prior work, finding preserved solvability when TsT precedes the limit and new asymptotically free or parallelizable sectors in the reverse order.
citing papers explorer
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Statistical Physics of Planar Carroll Systems
Planar Carrollian statistical physics is well-defined thanks to central extensions and rotation, yielding logarithmic entropy scaling with disc area and two-dimensional ideal-gas pressure.
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The Bohlin variant of the Eisenhart lift
The Bohlin variant of the Eisenhart lift embeds Lagrangian systems into timelike geodesics of conformally flat (d+2)-dimensional metrics and yields novel examples of such metrics admitting higher-rank Killing tensors.
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Lagrangian Extensions of Newtonian Gravity constrained by Solar System tests
Derives post-Newtonian equations from a scalar-extended Newtonian Lagrangian and bounds its free parameter with Solar System observations.
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Penrose limits and TsT for fibered $I$-branes
Analyzes TsT deformations and Penrose limits on fibered I-branes from prior work, finding preserved solvability when TsT precedes the limit and new asymptotically free or parallelizable sectors in the reverse order.