## On Maximal Proper Force, Black Hole Horizons and Matter as Curvature in Momentum Space

**Authors:** Carlos Castro

Starting with the study of the geometry on the cotangent bundle (phase space), it is shown that the maximal proper force condition, in the case of a uniformly accelerated observer of mass $m$ along the $x$ axis, leads to a minimum value of $x$ lying $inside$ the Rindler wedge and given by the black hole horizon radius $ 2Gm$. Whereas in the uniform circular motion case, we find that the maximal proper force condition implies that the radius of the circle cannot exceed the value of the horizon radius $2Gm$. A correspondence is found between the black hole horizon radius and a singularity in the curvature of momentum space. The fact that the geometry (metric) in phase spaces is observer dependent (on the momentum of the massive particle/observer) indicates further that the matter stress energy tensor and vacuum energy in the underlying spacetime may admit an interpretation in terms of the curvature in momentum spaces. Consequently, phase space geometry seems to be the proper arena for a space-time-matter unification.

**Comments:** 14 Pages. Submitted to the IJGMMP.

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### Submission history

[v1] 2017-01-16 06:25:21

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