Private property is, indeed, private property. Entering without permission is trespassing. Whether or not it's
criminal trespass depends on the wording of the state's laws on trespass.
According to the
National Review, Georgia's state law on citizen's arrest is:
A private person may arrest an offender if the offense is committed in his presence or within his immediate knowledge. If the offense is a felony and the offender is escaping or attempting to escape, a private person may arrest him upon reasonable and probable grounds of suspicion.
Apparently the two defendants are claiming that they witnessed Arbery committing a burglary, giving them the right to arrest him. But he didn't take anything from the construction site, so he didn't commit a "burglary," even though he was trespassing. So their claim that they had justification to arrest him is open to debate. More to the point -- the law on citizen's arrest (if the citation from the NR is correct and complete) doesn't seem to authorize the use of deadly force in effecting a citizen's arrest.
Stay tuned.
[Edit to add] Found an article by a Georgia attorney about Georgia's law on criminal trespass:
https://bixonlaw.com/georgia-trespassing-101/It doesn't appear that Arbery's entry into the construction site qualifies as criminal trespass -- unless he had intentions of stealing, but if he was out for a jog that's unlikely. In any event, it looks like even criminal trespass in Georgia is only a misdemeanor, not a felony.
Another recital of the law, from an unbiased source:
https://law.justia.com/codes/georgia/2010/title-16/chapter-7/article-2/part-1/16-7-21/