Is it permissible to marry a second wife in another country if the first wife refuses to document her consent to the marriage, or is it permissible to deceive her to obtain her signature?

Polygyny is permissible for a man who is capable of bearing the financial responsibilities of marriage and of being just among his wives. He is not required to seek permission from his first wife. The condition of obtaining the first wife's consent is invalid, unless she stipulated in the marriage contract that he would not marry another. In such a case, it is permissible to disregard this condition, while still being obligated to be just among his wives.