Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment

We review versions of the Generalized Uncertainty Principle (GUP) obtained in string theory and in gedanken experiments carried out in Quantum Gravity. We show how a GUP can be derived from a measure gedanken experiment involving micro-black holes at the Planck scale of spacetime. The model uses only Heisenberg principle and Schwarzschild radius and it is independent from particular versions of Quantum Gravity.Comment: to appear in Physics Letters B, probably in an issue of April 1999, 9 pages, 2 figures, file p

Gravity coupling from micro-black holes

Recently much work has been done in lowering the Planck threshold of quantum gravitational effects (sub-millimeter dimension(s), Horava-Witten fifth dimension, strings or branes low energy effects, etc.). Working in the framework of 4-dim gravity, with semi-classical considerations based on Hawking evaporation of planckian micro-black holes, I shall show here as quantum gravity effects could occur also near GUT energies.Comment: LaTex file, 5 pages, no figure

Horizon wave-function for single localized particles: GUP and quantum black hole decay

A localised particle in Quantum Mechanics is described by a wave packet in position space, regardless of its energy. However, from the point of view of General Relativity, if the particle's energy density exceeds a certain threshold, it should be a black hole. In order to combine these two pictures, we introduce a horizon wave-function determined by the particle wave-function in position space, which eventually yields the probability that the particle is a black hole. The existence of a minimum mass for black holes naturally follows, albeit not in the form of a sharp value around the Planck scale, but rather like a vanishing probability that a particle much lighter than the Planck mass be a black hole. We also show that our construction entails an effective Generalised Uncertainty Principle (GUP), simply obtained by adding the uncertainties coming from the two wave-functions associated to a particle. Finally, the decay of microscopic (quantum) black holes is also described in agreement with what the GUP predicts.Comment: 8 pages, 5 figures, extended version of arXiv:1305.3195 with new results about the GUP and black hole decay, clarifications about black hole decay adde

Glimpses on the micro black hole Planck phase

Mass thresholds, lifetimes, entropy and heat capacity for micro black holes close to their late Schwarzschild phase are computed using two different generalized uncertainty principles, in the framework of models with extra spatial dimensions. Emissions of both photons and gravitons (in the bulk) are taken into account. Results are discussed and compared.Comment: 17 pages, 8 figures, files latex plus eps, archive .tg

Special Relativity induced by Granular Space

We show that the special relativistic dynamics when combined with quantum mechanics and the concept of superstatistics can be interpreted as arising from two interlocked non-relativistic stochastic processes that operate at different energy scales. This interpretation leads to Feynman amplitudes that are in the Euclidean regime identical to transition probability of a Brownian particle propagating through a granular space. Some kind of spacetime granularity could be held responsible for the emergence at larger scales of various symmetries. For illustration we consider also the dynamics and the propagator of a spinless relativistic particle. Implications for doubly special relativity, quantum field theory, quantum gravity and cosmology are discussed.Comment: 6 pages, RevTeX4. Some revisions in DSR section and in Conclusions. References adde

Gravitational tests of the Generalized Uncertainty Principle

We compute the corrections to the Schwarzschild metric necessary to reproduce the Hawking temperature derived from a Generalized Uncertainty Principle (GUP), so that the GUP deformation parameter is directly linked to the deformation of the metric. Using this modified Schwarzschild metric, we compute corrections to the standard General Relativistic predictions for the light deflection and perihelion precession, both for planets in the solar system and for binary pulsars. This analysis allows us to set bounds for the GUP deformation parameter from well-known astronomical measurements.Comment: 20 pages, 2 figure