Is it permissible to threaten a friend who has committed adultery by informing his father or by taking more severe action to deter him from his deed?

The young man should be advised and warned of Allah, and the evil of fornication should be explained to him. Indeed, it is one of the gravest major sins and immoralities, for Allah Almighty says: (And do not approach unlawful sexual intercourse. Indeed, it is ever an immorality and is evil as a way) and (And those who do not invoke with Allah another deity or kill the soul which Allah has forbidden [to be killed], except by right, and do not commit unlawful sexual intercourse. And whoever does that will meet a penalty.) The Prophet, peace and blessings be upon him, said regarding the greatest sins after polytheism and killing one's child: "That you commit adultery with your neighbor's wife." And he said: "No fornicator commits fornication while he is a believer at the time of committing fornication." If he persists in his action, threaten him with exposing his matter. Let this be merely a threat without actually informing anyone, because it falls under spreading immorality, and concealment is desired. Then abandon him and cut ties with him if advice is of no avail.