Maximal proper force, black hole horizons and matter as curvature in momentum space

Abstract:

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 space-time may admit an interpretation in terms of the curvature in momentum spaces. Some final comments are made pertaining to the Asymptotic Safety program in gravity and why phase space geometry seems to be a proper arena for a space-time-matter unification.

Año de publicación:

2018

Keywords:

• Maximal acceleration
• Finsler Geometry
• Gravity
• Born Reciprocity
• Phase spaces

Fuente:

scopus