1208.5570 (Michael Maziashvili)

Hilbert space representation of higher-dimensional minimum-length
deformed uncertainty relation and some of its implications for ADD model    [PDF]

Michael Maziashvili

We construct a Hilbert space representation of minimum-length deformed uncertainty relation in presence of extra dimensions. Following this construction, we study corrections to the gravitational potential (back reaction on gravity) with the use of correspondingly modified propagator in presence of two (spatial) extra dimensions. Interestingly enough, for $r \rightarrow 0$ the gravitational force approaches zero and the horizon for modified Schwarzschild-Tangherlini space-time disappears when the mass approaches quantum-gravity energy scale. This result points out to the existence of zero-temperature black hole remnants in ADD brane-world model.

View original: http://arxiv.org/abs/1208.5570