i am aware that it is biblically permitted to have relations with a gentile as long as it is not for marriage. since they are permitted, is it more lenient to look at a gentile women naked? if not, what is the transgression? is it rabinic or a biblical transgression? Thank you very much for your service
Having relations with a gentile while technically only rabbinic, this is only if it a onetime story, however if it is a relationship, there would be four different prohibitions, (see Rambam Isurei BIah 12-2). Even this one time story, it is still a serious transgression, and in certain instances, can be punishable by what is called “kanoim bogim bo”. (This is what happened with Pinchas and Zimri in the desert; that Pinchas was allowed to kill Zimri for what he did).
Regarding your specific question, looking at women that are undressed is not permitted whether she is a Jew or a gentile, and the transgression would be a biblical one, and not merely rabbinic. Looking at a naked woman, whether Jew or gentile, is included in the biblical commandment of “V’nishmartem m’kol savar ra” (Deutoronomy 23-10). This is because it brings a person to lose seed, (if not at the time, then it can cause it later because it will cause him to fantasize about it later). This prohibition applies is even if one has no intention of even having a relationship with the woman. It causes improper thoughts can cause loss of seed. The second prohibition is “V’lo tasusu acharei einiechem”, not to think immoral thoughts, which bring a person to immoral relations. The idea of all of this is because G-d wants us to lead a morally elevated life, and therefore we are to distance ourselves from lust and anything that brings us to immorality.
Igros Moshe E:H 1-59.