What is the ruling on a husband lying to his first wife about his marriage to another woman, justifying his absence with new work, and claiming that Islam permits a man to lie to his wife? Is this true?

It is permissible to lie to one's wife to please her and maintain her affection, as well as to lie in war and for reconciling people. It is also permissible for a man to conceal his marriage to another woman from his first wife, if there is a benefit in doing so for the sake of harmony. He may use equivocation (ma'arid) or even lie explicitly if equivocation does not suffice, in order to avoid harm.