Generalized uncertainty principle and burning stars

Abstract

Gamow’s theory of the implications of quantum tunneling for star burning has two cornerstones: quantum mechanics and the equipartition theorem. It has been proposed that both of these foundations are affected by the existence of a non-zero minimum length, which usually appears in quantum gravity scenarios and leads to the generalized uncertainty principle (GUP). Mathematically, in the framework of quantum mechanics, the effects of the GUP are considered as perturbation terms. Here, generalizing the de Broglie wavelength relation in the presence of a minimal length, GUP corrections to the Gamow temperature are calculated, and in parallel, an upper bound for the GUP parameter is estimated.