# GEM-v: Horizon argument

The **horizon argument for GEM-v effects** is based on a consideration of the geometry of a moving black hole.

Consider a stationary black hole. Outward-aimed light-rays originating at the event horizon surface, r=2M, remain frozen into the horizon, and cannot leave. if we take a two-dimensional slice through the black hole and plot these outward-aimed rays over time, we find that rays generated inside r=2M move inwards, rays generated outside r=2M move outwards, and 2M itself is the critical surface where rays don;t move at all in space, and their progress points exactly in the direction of the time axis.

Now consider how the situation appears for a different observer for whom the hole is "moving". if the hole is moving directly away form us, then the critical rays have to now be receding from us, at (at least) the same rate as the hole. This means that in our modified diagram for a moving hole, the critical rays point at an angle that corresponds to the moving hole's worldline.

For an observer behind the hole, the rays now point away form them. if the ray-angle is a continuous function of distance, then there will be a new critical surface some way outside r=2M behind the hole where originating rays are again vertical. This is an effective (observer-dependent) horizon.

Since the rearward observer sees the receding hole to have an effective horizon that is further form the hole centre than 2M, it appears to them as if the hole is pulling more strongly - the hole's gravitational pull on nearby light seems stronger if the hole is receding than if it is approaching – its gravitational field appears to have a velocity-dependent component (GEM-v).