Time dilation near a horizon

node

Clocks run slow in a gravitational potential, and near a black hole the effect becomes unbounded. A static clock at radius r ticks slower than a distant one by the square root of one minus the ratio of Schwarzschild radius to r, a factor that goes to zero at the horizon. The consequence is the sharpest asymmetry in the subject: an infalling observer crosses the horizon in finite proper time and notices nothing locally, while a distant observer never sees the crossing at all. What the distant observer sees instead is the infalling object slowing, reddening and fading, its light dimming exponentially on a timescale set by the light-crossing time of the hole - about a ten-thousandth of a second for a ten-solar-mass hole and a matter of hours for M87*. The object does not hover; it becomes unobservable. The two descriptions are not in conflict, because they are answers to different questions asked by observers who can no longer exchange signals. Not a place on Earth.

A node is not a place. Drawing it on a map would assert something about the world that no stored fact supports.