2013/10/21 by R. Casadio, Roberto Casadio, Casadio, R. · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Physics (quant-ph) #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.48550/arxiv.1310.5452
6 pages, 2 figures. Prepared for the Proceedings of the Karl Schwarzschild meeting 2013
arxiv created 2013/10/21 · openalex publication_date 2013/10/21 · arxiv updated 2013/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 position wave-function, which yields the probability that the particle is a black hole. The existence of a (fuzzy) minimum mass for black holes naturally follows, and we also show that our construction entails an effective Generalised Uncertainty Principle simply obtained by adding the uncertainties coming from the two wave-functions.