1202.2991 (Kristina Giesel et al.)

Gravitational dynamics for all tensorial spacetimes carrying predictive,
interpretable and quantizable matter    [PDF]

Kristina Giesel, Frederic P. Schuller, Christof Witte, Mattias N. R. Wohlfarth

Only a severely restricted class of tensor fields can provide classical
spacetime geometries, namely those that can carry matter field equations that
are predictive, interpretable and quantizable. These three conditions on matter
translate into three corresponding algebraic conditions on the underlying
tensorial geometry, namely to be hyperbolic, time-orientable and
energy-distinguishing. Lorentzian metrics, on which general relativity and the
standard model of particle physics are built, present just the simplest
tensorial spacetime geometry satisfying these conditions and, incidentally, the
only one that does not implement superluminal particles in perfectly causal
fashion. The problem of finding gravitational dynamics---for the general
tensorial spacetime geometries satisfying the above minimum requirements---is
reformulated in this paper as a system of linear partial differential
equations, in the sense that their solutions yield the actions governing the
corresponding spacetime geometry, and is thus reduced to a clear mathematical
task.

View original: http://arxiv.org/abs/1202.2991