Do black holes come to mind when you think about singularities? In optics, singularities occur when one or more parameters are undefined, and are also associated with non-intuitive phenomena such as energy backflow and superoscillations. While the vast majority of optical singularities take the form of string-like lines and loops, this paper introduces a technique to engineer singularities belonging to a wider class of shapes. As a demonstration, the authors engineer sheet singularities that have heart-shaped cross-sections, then realize these light fields experimentally using...