The Gravitational Field of Kinetic Gases and their Dynamics

Many astrophysical systems, such as accretion discs, stars, galaxies, and even the cosmological evolution of the universe as a whole, can more fundamentally be described as kinetic gases, instead of as a perfect fluid. In relativistic kinetic theory, the state of matter is encoded in the one-particle distribution function (1PDF) on phase space, whose evolution is governed by the Boltzmann or, in the collision-less case, Vlasov equation. Fluid models arise only as limiting descriptions, reflecting the spirit of Hilbert’s sixth problem of deriving continuum physics from microscopic dynamics. When coupled to gravity, the resulting Einstein–Vlasov system has proven mathematically robust and physically successful.

Yet, in the standard coupling to general relativity, only the second velocity moment of the 1PDF, the energy–momentum tensor, acts as the gravitational source. This averaging procedure suppresses the rich statistical structure of Boltzmann or Vlasov matter encoded in the full 1PDF. This observation immediately raises the questions: Why should only the second moment gravitate? Do the neglected degrees of freedom contribute to the gravitational field? Could they account for dark energy or dark matter?

To answer these questions, this seminar brings together scientists working on kinetic gas theory and the theoretical description of gravity through pseudo-Riemannian geometry, as for example in general relativity, or generalisations thereof. A particularly promising generalised geometry, that will be discussed, is Finsler spacetime geometry, as it allows a direct coupling between gravity and the full 1PDF of the gas, without averaging. Moreover, through the application of Finsler gravity not cosmology it has recently been demonstrated that it predicts an accelerated expansion without the need of a cosmological constant from the Finsler–Friedmann equation.

The conference language will be English. The Wilhelm and Else Heraeus-Foundation bears the cost of full-board accommodation for all participants.