SMuK 2021 – scientific programme

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GR: Fachverband Gravitation und Relativitätstheorie

GR 3: Classical GR-2

GR 3.7: Talk

Tuesday, August 31, 2021, 15:30–15:45, H6

The gravitating kinetic gas - Lifting the Einstein Vlasov system to the tangent bundle — •Christian Pfeifer — ZARM, University of Bremen, Bremen, Germany

In this talk I will present a new model for the description of a gravitating kinetic gas, by coupling the 1-particle distribution function (1PDF) of the gas directly to the gravitational field, described directly by the geometry of the tangent bundle of spacetime. This procedure takes the influence of the velocity distribution of the kinetic gas particles on their gravitational field fully into account, instead of only on average, as it is the case for the Einstein-Vlasov system.

By using Finsler spacetime geometry I construct an action for the kinetic gas on the tangent bundle, which is added as matter action to a canonical Finslerian generalisation of the Einstein-Hilbert action. The invariance of the kinetic gas action under coordinate changes gives rise to a new notion of energy-momentum conservation of a kinetic gas in terms of an energy-momentum distribution tensor. The variation of the total action with respect to the spacetime geometry defining Finsler Lagrangian yields the gravitational field equation, which determines the geometry of spacetime directly from the full non-averaged 1PDF.