9 pags. As expressed in terms of classical coordinates, the inertial spacetime metric that contains quantum corrections deriving from a quantum potential defined from the quantum probability amplitude is obtained to be given as an elliptic integral of the second kind that does not satisfy Lorentz transformations but a generalised invariance quantum group. Based on this result, we introduce a new, alternative procedure to quantise Einstein general relativity where the metric is also given in terms of elliptic integrals and is free from the customary problems of the current quantum models. We apply the procedure to Schwarzschild black holes and briefly analyse the results. ARF gratefully acknowledges financial support by the Fundacao para a Ciencia e a Tecnologia (FCT) (Portugal) through the postdoctoral fellowship SFRH/BPD /96981/2013 and by Ministerio de Economía y Competitividad (Spain) through project number FIS2012-38816. Peer Reviewed