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GR: Fachverband Gravitation und Relativitätstheorie

GR 12: Alternative Allgemeine Relativitätstheorie II

GR 12.3: Talk

Thursday, March 1, 2012, 09:10–09:30, ZHG 002

Gravity underlying matter beyond the standard model — •Frederic P. Schuller — Max-Planck-Institut für Gravitationsphysik, Golm, Deutschland

Superluminal neutrinos, if indeed observed, force one to forsake Lorentzian geometry as the spacetime structure. But only a severely restricted class of tensor fields can provide an alternative classical spacetime geometry. Their precise structure and kinemantics are determined already by the requirements that the geometry be able to carry predictive matter field equations, be time-orientable and allow for an observer-independent distinction of positive and negative particle energies. Lorentzian metrics, on which general relativity and the standard model of particle physics are built, present just the simplest such tensorial spacetime geometry, and incidentally the only one that does not implement superluminal particles in perfectly causal fashion.

The problem to find the gravitational dynamics for general tensorial spacetime geometries satisfying the above minimum requirements can be reformulated as a system of linear partial differential equations, in the sense their solutions present the actions for the corresponding spacetime geometry. This opens the possibility to formulate the search for alternative classical theories of gravity in general---and in particular for gravity compatible with superluminal matter---as a well posed mathematical task.