Routing protocol

Physics

Gravitation

Cosmological constant

Event (particle physics)

Computer network

Mathematics

Mathematical physics

Black hole (networking)

Black hole thermodynamics

Link-state routing protocol

Entropy (arrow of time)

Statistics

Astronomy

Horizon

RADIUS

Event horizon

Uncertainty principle

Lambda

Theoretical physics

Computer science

de Sitter–Schwarzschild metric

Quantum mechanics

Realization (probability)

Routing (electronic design automation)

BTZ black hole

Computer security

Quantum

Physical review. D/Physical review. D.

We investigate the structure of the gravity-induced Generalized Uncertainty Principle in three dimensions. The subtleties of lower dimensional gravity, and its important differences with respect to four and higher dimensions, are duly taken into account, by considering different possible candidates for the gravitational radius, $R_g$, that is the minimal length/maximal resolution of the quantum mechanical localization process. We find that the event horizon of the $M \neq 0$ Ba\~{n}ados-Teitelboim-Zanelli micro black hole furnishes the most consistent $R_g$. This allows us to obtain a suitable formula for the Generalized Uncertainty Principle in three dimensions, and also to estimate the corrections induced by the latter on the Hawking temperature and Bekenstein entropy. We also point to the extremal $M=0$ case, and its natural unit of length introduced by the cosmological constant, $\ell = 1 / \sqrt{-\Lambda}$, as a possible alternative to $R_g$, and present a condensed matter analog realization of this scenario.

Generalized uncertainty principle in three-dimensional gravity and the BTZ black hole