For anyone who followed up on the excellent link posted of an article on GA laws applicable in this case, written by a practicing appellate attorney in GA,
The Ahmaud Arbery Killing and Georgia Law
here's a link to the GA Supreme case he noted.
Carter v. State, 506 S.E.2d 124, 269 Ga. 891 – CourtListener.com
The issue of citizen's arrest came up somewhat tangentially at trial.
In a nutshell: the victim in the case had once chased down someone he suspected of burglarizing his friend's house, and had beaten that person with a baseball bat when he caught up with him.
At trial, the defendant used this incident to try to justify his own use of lethal force as self-defense: that the victim was known to be violent.
The State argued that the victim had simply been making a lawful citizen's arrest when he chased after and assaulted the person he believed to be a burglar.
The GA Supreme Court ruled that no, the victim had not in fact made a lawful citizen's arrest, stating: "only force that is reasonable in the circumstances may be used to restrain the individual being arrested," and that the assault with a baseball bat was too excessive to be part of a legitimate (lawful) citizen's arrest.