  Recently, it was shown that two distant test masses, each prepared in a
spatially superposed quantum state, become entangled through their mutual
gravitational interaction. This entanglement, it was argued, is a signature of
the quantum nature of gravity. We extend this treatment to a many-body system
in a general setup and study the entanglement properties of the time-evolved
state. We exactly compute the time-dependent I-concurrence for every
bipartition and obtain the necessary and sufficient condition for the creation
of genuine many-body entanglement. We further show that this entanglement is of
generalised GHZ type when certain conditions are met. We also evaluate the
amount of multipartite entanglement in the system using a set of generalised
Meyer-Wallach measures.
