A simple indicator could be the slope around your point location (there is a slope function in ArcGIS Spatial analyst). Then you can take the maximum (or the mean) of the slope around your point using the focal statistics tool.
Alternatively, you could use the difference between the minimum elevation around your point (with focal statistics) and the point itself. This looks similar to slope if you divide by the pixel spacing, but the slope function in ArcGIS uses a neighborhood of three by three centered on your pixel, while with the minimum elevation method you capture the sharpest edge.
Note that the slope is the first derivative of the elevation, and the curvature (slope of slope) is the second derivative. In a raster, because of the built-in point spacing, you should always be able to compute the derivative (if you don't have NoData pixels, of course).
Also note that the proposed methods do not take the position of the sharpest edge into account. If you know the line segment between the receptor and the emittor, then you could use some zonal stats to have a "directional" topographic characterisation.