  Aims: We study the impact of Post-Newtonian correction terms on the energetic
interaction 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 the
interactions between stars and an SMBH binary at separations of$\sim
1000\,R_{sch}$. For all of the interactions, we investigate in detail the
energy balance of the three-body systems, using both Newtonian and
Post-Newtonian expressions for the SMBH binary orbital energy, taking into
account the GW emission by the binary. Results: We find that at these
separations, purely Newtonian treatment of the binary orbital energy is
insufficient to properly account for the SMBH binary orbital evolution.
Instead, along with GW emission, even terms in the PN-corrections must be
included in order to describe the energy change of the binary during the
stellar interaction.es, 2
