Lifting General Relativity to Observer Space

Understand

The `observer space' of a Lorentzian spacetime is the space of future-timelike unit tangent vectors.

• Using Cartan geometry, we first study the structure a given spacetime induces on its observer space, then use this to define abstract observer space geometries for which no underlying spacetime is assumed.
• We propose taking observer space as fundamental in general relativity, and prove integrability conditions under which spacetime can be reconstructed as a quotient of observer space.
• Additional field equations on observer space then descend to Einstein's equations on the reconstructed spacetime.