The Generalized Uncertainty Principle and higher dimensions: Linking black holes and elementary particles

Black holes play an important role in linking microphysics with macrophysics, those of the Planck mass ($M_P \sim10^{-5}$g) featuring any theory quantum gravity. In particular, Compton-Schwarzschild correspondence posits a smooth transition between Compton wavelength ($R_C \propto 1/M$) below and Schwarzschild radius ($R_{\rm S} M$) above it. The duality $R_{\rm C}$ S}$ implies form Generalized Uncertainty Principle (GUP) suggests that elementary particles may be sub-Planckian black holes. simplest possibility is ADM has $M + \beta M_P^2/M$ for some constant $\beta$ this model can extended to charged rotating holes, clearly relevant particles. Another arise loop gravity explicitly links Higher dimensions modify both proposals. If there are $n$ extra dimensions, all same compactification scale, one expects M^{1/(1+n)}$ scale but depends on higher-dimensional wave-function. it spherically symmetric, then C} M^{-1}$, so broken reduced, allowing TeV wave-function pancaked M^{-1/(1+n)}$ preserved unchanged.