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Unimodularity can be implemented in different ways. In this paper we consideronly the formulation of Unimodular Gravity in which the unimodular metric isobtained out of an unrestricted one as $\g_{\m\n}=|g|^{-{1\over n}} g_{\m\n}$.This procedure induces an extra Weyl symmetry. Some physical implications ofthis symmetry on the conserved currents are discussed. Finally the results areillustrated for the Painlev\'e-Gullstrand extension of Schwarzschild spacetime.

Physical charges versus conformal invariance in unimodular gravity