2021/01/04 by Jan Smit, Smit, Jan
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 - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies
paper · pdf · doi:10.48550/arxiv.2101.01028
openalex publication_date 2021/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Known quantum and classical perturbative long-distance corrections to the Newton potential are extended into the short-distance regime using evolution equations for a `running' gravitational coupling, which is used to construct examples non-perturbative potentials for the gravitational binding of two particles. Model-I is based on the complete set of the relevant Feynman diagrams. Its potential has a singularity at a distance below which it becomes complex and the system gets black hole-like features. Model-II is based on a reduced set of diagrams and its coupling approaches a non-Gaussian fixed point as the distance is reduced. Energies and eigenfunctions are obtained and used in a study of time-dependent collapse (model-I) and bouncing (both models) of a spherical wave packet. The motivation for such non-perturbative `toy' models stems from a desire to elucidate the mass dependence of binding energies found 25 years ago in an explorative numerical simulation within the dynamical triangulation approach to quantum gravity. Models I & II suggest indeed an explanation of this mass dependence, in which the Schwarzschild scale plays a role. An estimate of the renormalized Newton coupling is made by matching with the small-mass region. Comparison of the dynamical triangulation results for mass renormalization with `renormalized perturbation theory' in the continuum leads to an independent estimate of this coupling, which is used in an improved analysis of the binding energy data.