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The center of our Galaxy is known to host a massive compact object, SgrA$^*$, which is commonly considered as a super-massive black hole of $\sim4\times 10^6$ M$_\odot$. It is surrounded by a dense and massive nuclear starcluster, with a half mass radius about $5$~pc and a mass larger than $10^{7}$M$_\odot$.  In this paper we studied the evolutionary fate of a very dense cluster ofintermediate mass black holes, possible remnants of the dissipative orbitalevolution of massive globular cluster hosts. We performed a set of highprecision $N$-body simulations taking into account deviations from pureNewtonian gravitational interaction via a Post Newtonian development up to$2.5$ order, which is the one accounting for energy release by gravitationalwave emission. The violent dynamics of the system leads to various successivemerger events such to grow a single object containing $\sim 25$ per cent of thetotal cluster mass before partial dispersal of the cluster, and such togenerate, in different bursts, a significant quantity of gravitational wavesemission. If generalized, the present results suggest a mechanism of massgrowth up to the scale of a super massive black hole.

Dynamics of a Superdense Cluster of Black Holes and the Formation of the Galactic SMBH