  Observing spatial entanglement in the Bose-Marletto-Vedral (BMV) experiment
would demonstrate the existence of non-classical properties of the
gravitational field. We show that the special relativistic invariance of the
linear regime of general relativity implies that all the components of the
gravitational potential must be non-classical. This is simply necessary in
order to describe the BMV entanglement consistently across different inertial
frames of reference. On the other hand, we show that the entanglement in
accelerated frames could differ from that in stationary frames.
