Re: More on the controversy about the Schwarzschild radius and black

Daryl McCullough wrote:
Eric Gisse says...
stevendaryl3...@xxxxxxxxx (Daryl McCullough) wrote:
I think that LEJ Brouwer may be
thinking of the "event horizon" and the "Schwarzschild radius" as synonymous.
Aren't they, in _this specific case_ ?

Definitely not. In the case we are talking about, we have a
converging shell of matter. Inside the shell, there is no
matter to speak of. So the total mass involved in the
scenario is constant, M = the mass of the shell. The
corresponding Schwarzschild radius is also constant,
R = 2GM/c^2. But the event horizon is expanding outwards
at speed c. So they're not the same thing. The event
horizon is not expanding because the Schwarzshchild
radius is expanding. The relationship between them is
just this: the radius of the event horizon approaches
the Schwarzschild radius as t --> infinity.

That t is the coordinate of a distant observer. To any observer inside r=2GM/c^2, who will be directly affected by this, the horizon races past him at the (local) speed of light, in a finite time after any specified point on his worldline. This happens before the stars reach him, and no local measurement by him can determine when the horizon races past. But as soon as the stars reach him, a finite time after the horizon passes, he will be inevitably dragged down with them and annihilated at the singularity which forms.

Relating this to closed trapped surfaces, throughout the region inside the incoming stars there is no closed trapped surface, even though there is a horizon present when the stars are close enough to r<2GM/c^2. A closed trapped surface implies both a singularity inside and a horizon outside, but a horizon does not imply either a c.t.s or a singularity.


Tom Roberts
.

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