At the horizon, the Schwarzschild surface
At exactly \(1\) Schwarzschild radius,
the horizon, the Schwarzschild surface.
The point of no return.
An observer outside the black hole cannot see us beyond this point -
we would appear to take an infinite amount of time to pass through,
becoming slower and more redshifted as time goes by.
But from our own point of view space and time continue normally.
The small white dot indicates our point of entry through the horizon.
Remarkably,
the Schwarzschild surface, the red grid, still appears to
stand off at some distance ahead of us.
The white dot is actually a line which extends from us to the Schwarzschild
surface still ahead, though we only ever see it as a dot, not as a line.
The dot-line marks the formation of the Schwarzschild bubble
(see below), and our entry into that bubble.
Persons who fell through the Schwarzschild surface at this precise point
before us would lie arrayed along this dot-line.
At this instant, as we pass through the horizon into the Schwarzschild bubble,
we see all the other persons who passed through this location before us
also pass through the horizon into the bubble.
The tidal force between head and toes is now \(1\) million gees,
for this \(30\) solar mass black hole.
But the tides wouldn’t be so bad for a very massive black hole.
The tide at \(1\) Schwarzschild radius would be less than \(1\) gee
if the black hole exceeded \(30{,}000\) solar masses.
From here to the central singularity will take \(0.0001\) seconds in free fall,
for this \(30\) solar mass black hole.
The infall time is proportional to the mass of the black hole.
Relative to an observer stationary in the Schwarzschild metric,
our velocity has now reached the speed of light.
Relative to an observer freely falling radially from rest at infinity,
our velocity is
\(\sqrt{8/9} \, c = 0.94 \, c\).
Answer to the
quiz question 2:
No, the horizon is not the place where you are suddenly torn apart.
In a stellar-sized black hole like this one,
the tidal force would already have torn you apart well outside the horizon.
In a supermassive black hole the tidal forces are weaker,
and you could survive well inside the horizon of the black hole
before being torn apart.
Answer to the
quiz question 3:
To remain at rest just above the horizon,
you would have to accelerate like crazy just to stay put.
Radial distances measured in your frame are greatly
stretched compared to radial distances measured by observers who
go with the flow,
so you’d have to pay out your fishing line a long way before it
hit the horizon.
The acceleration goes to infinity for something that attempts to
remain at rest at the horizon,
so the fishing line that passed the horizon would either break,
or drag you in.
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