AN INVARIANT CRITERION OF PROXIMITY TO THE HORIZON OF A BLACK-HOLE

Let a probe dive into a free fall from a mother craft hovering over a black hole. Let the mother craft regularly send standard signals to the probe. The net frequency shift due to both the gravitational and Doppler effects is calculated for the signals received by the probe. The shift is found to be a red one and it assumes a universal value z = 1/2 as the probe approaches the horizon.