Powerful new LEDs provide enough luminosity for a single one to illuminate a transparent EXIT sign, but efficient injection means are required, with luminance-uniformity a prime goal. We present a totally-internally-reflecting `Black Hole' indentation on the waveguide surface. This cuspated configuration deflects the light from an immersed LED, aimed perpendicular to the plane of the waveguide, into guided light trapped within the slab, to be extracted by the sign's alphabetic features. In spherical coordinates, a +/- 60 degree(s) output cone (for example) is deflected into the 360 degree(s)-azimuth guided range of +/- 47 degree(s). That is, this reflector transforms a polar cone into an equatorial swath, a symmetry that is useful whenever the total horizon must be dealt with, just as a lighthouse, or better yet a marker buoy, must send warning light to all the quarters of the compass. In its circularly symmetric configurations, this device offers a removable disc, optically bonded to the LED source, that completely hides the source from view above the indentation. Non-waveguide, stand-alone illumination applications include aircraft-warning beacons, alarm flashers, and near-field illuminators.