What is the ruling on slandering one's wife when her adultery is confirmed but no child is attributable to the adulterer, or when the paternity of an existing child is unknown?

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It is permissible for a husband to slander his wife if he witnesses her adultery, or if her adultery is established by other means, provided there is no child whose lineage can be attributed to the adulterer. This permission also extends if a trustworthy person informs him of her adultery and he believes them, or if public rumor ('ish'ah) spreads regarding her fornication with a specific man, and he observes him entering or leaving her dwelling, or if his strong assumption ('ghalabat Dhann') is that she is committing fornication. This permissibility is evidenced by the report that a man approached the Prophet, peace be upon him, regarding finding another man with his wife, and the Prophet did not prohibit him from speaking or remaining silent in such a situation. Remaining silent and divorcing her is preferable, as it serves to conceal the matter from both spouses.