Physical charges versus conformal invariance in Unimodular Gravity

Abstract

There is a formulation of unimodular gravity (UG) in which the unimodular metric is obtained out of an unrestricted one as γ µν “ | g | ´ 1 n g µν . This unrestricted metric is only defined up to a Weyl rescaling. Physical charges like ADM energy or horizon entropy, however, are not Weyl invariant in general. In this paper a Weyl invariant definition of some physical charges is given, and the results are illustrated for the Painlev´e-Gullstrand extension of Schwarzschild spacetime