image The stress-energy tensor is decomposed as image or, equivalently, image, image, and image where image denotes the operation of projection onto the spatial hypersurface and it acts on all free indices. Note that the matter terms in Eqs. (12Popup Equation), (14Popup Equation), and (15Popup Equation) are defined with respect to a normal observer. This is in contrast to the usual definition of image with respect to the rest frame of the fluid in hydrodynamics.