What is the legitimate ruling on a second marriage without the first wife's knowledge, with a promise of justice between the two wives once the first one finds out?

Allah has permitted a man to marry more than one woman if he is able to be just between them. If one of the wives relinquishes her right to a share [of his time and provision] or part of it, there is no harm in that. However, if she demands her right, then justice becomes obligatory. Thus, there is no sin in marrying another woman and not being just between her and the first one, with her consent. But if her consent is conditional upon the first wife not knowing, then justice becomes obligatory when the first wife learns about it. Indeed, she has the right to demand justice even if the first wife does not know.