Momentum and velocity-dependent spacetime geometries: Traces of quantum gravity, fields in media and the gravitational field of kinetic gases

• Applicant: Dr. Christian Pfeifer
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 420243324

Despite all of its successes, general relativity cannot be the final answer to our understanding of gravity. On the observational side, its predictions are not consistent with the accelerated expansion of the universe and the rotation curves of galaxies. These led to the conclusion that the universe is filled with dark energy and dark matter, and only a small part is made out of the constituents of the standard model of particle physics. On the theoretical side, general relativity can still not be extended to a quantum theory of gravity in a self consistent way and moreover, it predicts singularities. Due to the absence of a fundamental theory of quantum gravity, I will employ momentum-dependent spacetime geometry as an effective model, which realises the following intuitive picture: Elementary particles, such as photons and neutrinos, probe the structure of spacetime, i.e. gravity, at scales inversely proportional to their energy. Thus, higher energetic particles interact more strongly with the quantum nature of gravity than lower energetic ones. A fundamental theory of quantum gravity should describe this effect in terms of the scattering matrices between the probe particles and gravitons. The aim is, on the one hand, to predict qualitatively and quantitatively observable effects, like energy-dependent (1) time of arrivals of photons, (2) black hole shadows, (3) gravitational lensing images as well as (4) products of particle collisions near black holes, and to identify them in data taken from telescopes like HESS, Veritas, MAGIC or the EHT. On the other hand, the mathematical relation between momentum-dependent spacetime geometry and curved non-commutative spacetimes will be investigated and extensions of the Einstein equations, which determine the momentum-dependent spacetime geometry, will be derived. An additional application of momentum-dependent spacetime geometry is the effective description of classical and quantum fields in media. A new approach to understand dark energy and dark matter is to consider physical systems in the universe which are usually modelled as fluids (the universe as a whole, ordinary and neutron stars, accretion discs) as kinetic gases. The advantage of this viewpoint is that the gravitational field of the gas can be described by a velocity-dependent Finsler spacetime geometry, which includes the contribution of the kinetic energy and the velocity distribution of the gas particles. Usually, in the Einstein-Vlasov equations, only the average over the velocity distribution of the gas particles is taken into account. This procedure enables us to construct a cosmological model which incorporates that the constituents of the cosmological fluid/gas have a velocity distribution, they move relatively to each and only propagate in the cosmological time direction on average. This may be the source of dark matter.

• DFG Programme: Research Grants