Is it permissible for a man in Islam to marry secretly without the knowledge of his wife and family?

A man is not obligated to inform his wife or family of his desire to marry [another woman], even though it is preferable for him to do so. If he does not inform them, there is no sin upon him, provided that the marriage fulfills the legal conditions and pillars. However, if he marries a second wife, he is obligated to be just between his wives in terms of lodging, dwelling, and rights. In this case, it becomes impossible to conceal the matter from his [first] wife, and doing so could lead to lying and injustice.