A semi-classical analogue of the relation between the chiral and the gluon QCD condensates

We present a semi-classical analogue of the relation between chiral and gluon QCD condensates, in which a condensation of a massless scalar field is provided by a classical field, instead of a quantum Yang–Mills field. For the classical field, we choose a gravitational field of a spherically symmetric object. The size of such an object becomes then a classical-physics analogue of the QCD vacuum correlation length, whereas the squared curvature of the gravitational field plays the role of the gluon condensate. Finally, by iterating the emerging contribution to the trace of the energy–momentum tensor, we prove that the energy density of the object remains of the same order of magnitude, i.e. no instability of the system occurs.