Is it permissible to look at one's beloved without lust, and does this fall under the category of the adultery of the eyes or ears?

All incidents originate from the gaze; therefore, Allah commanded believers to lower their gaze, as it is a means to fall into what displeases Him. The Hadith clarifies that the adultery of the eyes is looking, the adultery of the tongue is speaking, and the soul wishes and desires. The prohibition of looking is a measure of "sadd al-dhara'i'" (blocking the means), which is preventing something permissible if it leads to or results in something forbidden. If a woman's heart develops love for a man due to his knowledge or virtue, and she lowers her gaze and keeps her matter concealed, there is no sin upon her. However, if she lets her eyes and ears roam freely and enjoys looking and listening, she has fallen into the forbidden.