*Dr. Christian Pfeifer (ZARM, University of Bremen)*

The gravitational field of a kinetic gas is usually obtained by the Einstein-Vlasov equations. The dynamics of the gas are described by a so called 1-particle distribution function (1PDF) on the tangent bundle, and the energy momentum tensor sourcing the Einstein equations is obtained by the second moment of the 1PDF. The drawback in this approach is that the contribution of the velocity distribution of the gas to its gravitational field is only taken into account on average.

In this talk I will present how the gravitational field of the kinetic gas can be determined from the 1PDF without the need of velocity averaging, by coupling the 1PDF of the gas to the geometry of spacetime directly on the tangent bundle.

To achieve this goal I will use Finsler spacetime geometry, a geometric framework, whose dual formulation, in terms of momenta instead of velocities, is also employed to study deformed relativistic kinematics and modified dispersion relations in quantum gravity phenomenology on curved spacetimes.

I will discuss how action based field theories on Finsler spacetimes are formulated and use the Lagrangian formulation of the coupling of the kinetic gas to the Finslerian geometry of spacetime to determine the gravitational field equation on the tangent bundle as well as a covariant conservation law in terms of an energy-momentum distribution tensor.

These equations generalise the Einstein-Vlasov system, and determine the gravitational field of a kinetic gas from its 1PDF, taking the full information on the velocity distribution of the gas particles into account.