How can we observe gravitational time dilation near a black hole with a telescope?

[JosephTM]

I’ve been trying to wrap my head around the concept of gravitational time dilation near a supermassive black hole, specifically how an outside observer would see a clock essentially freeze at the event horizon. My confusion is whether this is a literal visual effect we could, in theory, see with a telescope, or if it's more about the mathematical coordinate singularity.

[IsabellaYT]

From far away the clock seems to slow as the hole grows larger in the sky you see it all the way to the edge but never cross in visible light the light from near the edge gets red shifted and dimmer and the signals take longer to arrive So in practice you see a clock drift toward the horizon and then fade away rather than a sharp freeze

[Olivia91]

I am a bit unsure about the visual part The horizon functions as a limit in the math not a real barrier so what you actually see is a clock that slows its ticks more and more and with each tick the light climbs deeper into the gravity well so the signal becomes slower and fainter

[Dennis_W]

I tried to model this once with a simple toy sim using a static clock far away and another clock near the edge and light rays The result was clear in the math that the far observer never sees the crossing and the near clock appears to tick slower and slower as it approaches the edge and then its light vanishes into the redshift

[Emma2]

Do you think the problem is mainly the signal delay or is there a real surface hiding the horizon?