What would the last photon look like with time dilation near a black hole?

[Donald.T]

I’ve been trying to wrap my head around the concept of gravitational time dilation near a supermassive black hole, specifically how time would appear to pass for a distant observer watching an object approach the event horizon. I get that it would seem to slow down and essentially freeze, but I’m struggling to visualize what the last detectable photon from that object would actually look like in terms of its redshift and fading.

[Scarlett_M]

I’ve poked at this while staring at the night sky with a notebook. As the object gets closer to the horizon, the photons you see come with bigger and bigger gravitational redshift and arrive increasingly slowly. The color drifts from visible toward red, then infrared, and the overall brightness fades until it’s barely a flicker or disappears.

[Benjamin_P]

I tried a rough toy model once, just to see what a light curve might look like. You get a tail of photons that stretches out, the spectrum sliding red and the intervals between arriving photons widening. If the object is moving, Doppler shifts mix in, so some photons can appear briefly blueshifted, but that doesn’t rescue the signal for long.

[Ronald59]

Would you expect the last detectable photon to have a crisp color, or would it just be a barely measurable smear in the noise? I keep picturing it as a red smear, but I’m not sure how the telescope’s sensitivity would shape that final wink.

[Emily_G]

Analytical note: In Schwarzschild spacetime, the gravitational redshift factor goes to infinity as r approaches 2M, and the arrival rate of photons decays to zero for a distant observer. So in theory the last photon would be infinitely redshifted, but in practice a finite tail is all you’ll ever see because of instrumental limits and background.