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Aims: We study the impact of Post-Newtonian correction terms on the energeticinteraction between a gravitational wave (GW)-emitting supermassive black hole(SMBH) binary system and incoming stars via three-body scattering experiments.Methods: We use the AR-chain code to simulate with high accuracy theinteractions between stars and an SMBH binary at separations of$\sim1000\,R_{sch}$. For all of the interactions, we investigate in detail theenergy balance of the three-body systems, using both Newtonian andPost-Newtonian expressions for the SMBH binary orbital energy, taking intoaccount the GW emission by the binary. Results: We find that at theseseparations, purely Newtonian treatment of the binary orbital energy isinsufficient to properly account for the SMBH binary orbital evolution.Instead, along with GW emission, even terms in the PN-corrections must beincluded in order to describe the energy change of the binary during thestellar interaction.es, 2

The impact of Post-Newtonian effects on massive black hole binary evolution at $\sim 1000\,R_{sch}$ separations