Is it permissible to marry a second wife without the first one knowing?
It is allowed without the permission of the first wife. The Permanent Committee mentioned that:
The second question of Fatwa no. 6948
Q 2: A married man traveled to another country then married in that country without informing his first wife. Is this permissible in the Islamic Shari`ah? Please substantiate your answer with evidence.
A: It is permissible for a man to marry a second wife without taking the consent of the first wife and without informing her as long as this serves a purpose and as long as he is able to afford marriage and be just to his two or more wives. Allah (Exalted be He) says, “And if you fear that you shall not be able to deal justly with the orphan-girls then marry (other) women of your choice, two or three, or four; but if you fear that you shall not be able to deal justly (with them), then only one or (the slaves) that your right hands possess. That is nearer to prevent you from doing injustice.”
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.
Shaikh Bin Baz rahimahullah mentioned some detail. He said:
“In this [issue is] some detail. It is allowed for him to marry a second or third wife without the knowledge of the previous wives. There is no harm in that. If, for example, he traveled to another land from the lands and married there and he engages in martial relations with her there, there is no harm in that. As for in one land, then it is necessary that he informs her so that he can divide between them and have justice between them. It is not for him to delude her that he does not have a wife. Rather he informs her and obliges her that he has a wife because this is deception [otherwise]. It is necessary that he tells her that he has a wife if they are in one land. He says yes and he divides between them, has justice between them, gives them both their right, and there is no deception and plotting. As for in another land, like he traveled to study, traveled as an ambassador for a country from the countries, then he can marry in that land so that he can be chaste. Even if he did not consult his wife and even if she does not know. That does not harm as long as he marries the permissible number of wives [in Islam] which is four…if he has an opportunity. If he has one wife, then he can take a second. If he has a second wife, he can take a third, if he has a third wife he can take a fourth. There is no harm. He does not increase above four. The intent is if he needs that and he wants to marry. It is not a condition that his wife knows if she is in another land. However, this is along with observing the obligatory purpose, justice in provisions, and other than this from the obligations of the husband in terms of justice”
Faisal Ibn Abdul Qaadir Ibn Hassan