  A binary stellar system that ventures too close to a supermassive black hole
can become tidally separated. In this article, we investigate the role of
relativistic effects in these encounters through 3-body simulations. We use the
Hybrid Relativistic-Newtonian Approximation (HRNA), which combines the exact
relativistic acceleration from a Schwarzschild black hole with a Newtonian
description of the binary's self-gravity. This method is compared against
Newtonian and Post-Newtonian (1PN) simulations. Our findings show good
agreement between HRNA and 1PN results, both of which exhibit substantial
differences from Newtonian simulations. This discrepancy is particularly
pronounced in retrograde encounters, where relativistic simulations predict up
to $30\%$ more separation events and an earlier onset of binary separation
($\beta=2$ compared to $2.5$ in Newtonian simulations, with $\beta$ the impact
parameter). Additionally, the HRNA model predicts about 15$\%$ more potential
extreme mass ratio inspirals and generate a higher number of hypervelocity star
candidates, with velocities up to 2,000 km/s faster than those predicted from
Newtonian simulations. Furthermore, compared to Newtonian cases, relativistic
encounters are more likely to result in direct stellar collisions and binary
mergers.
