Note that Noether's second theorem still applies, so any timelike vector field will yield a conservation law due to diffeomorphism invariance. In that sense, en

Note that Noether's second theorem still applies, so any timelike vector field will yield a conservation law due to diffeomorphism invariance. In that sense, energy conservation still holds even in the absence of Killing fields, though some people argue this doesn't count as a 'proper' law of energy conservation as it includes contributions by the gravitational field, for which an energy-momentum tensor cannot be defined...