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The (twice-contracted) second Bianchi identity is a differential curvature identity that holds on any smooth manifold with a metric. In the case when such a metric is Lorentzian and solves Einstein's equations with an (in this case inevitably smooth) energy-momentum-stress tensor of a 'matter field' as the source of spacetime curvature, this identity implies the physical laws of energy and momentum conservation for the 'matter field'. The present work inquires into whether such a Bianchidoi:10.1088/1361-6382/ac1853 fatcat:j4q3apyxxbfwlhqnq7cl6kiole