Question: I want to marry a second wife. Is it allowed for me to marry in secret and not inform my [first] wife of that?
Answer: “It is allowed to marry and not inform your wife of that, however, it is necessary for the marriage to be apparent and announced because the Prophet (ﷺ) ordered that. He said:
Publicize the Marriage
[Graded Saheeh by Al-Albani in Saheeh Jami no. 1072]
And if you do what Allah and his Messenger (ﷺ) ordered of publicizing the marriage, then Allah will be pleased with you and your wife if you tell her”.
[Taken from: http://shamela.ws/browse.php/book-2300/page-5426]
Faisal Ibn Abdul Qaadir Ibn Hassan