Three models of non-perturbative quantum-gravitational binding
arXiv:2101.01028
Abstract
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.
arXiv commentImproved presentation with additional references and special attention to the dynamical triangulation (DT) part; extended and refined analysis of the early DT results; 53 pages of which 20 in appendices and references
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