Re: black holes and singularity

From: Tom Roberts (tjroberts_at_lucent.com)
Date: 11/11/04 

Date: Thu, 11 Nov 2004 10:38:40 -0600

xxein wrote:
> xxein: Some get the notion that because escape velocity (or such
> relative velocity) approaches c at the BH horizon, that
> science-relativity fails.
>
> Can you expound in a plain and simple everyday language why this is
> not a valid conclusion? Iow, what common sense should be applied to
> explain why events below the large and mild EH should be normal to the
> inhabitants there.

Event horizons and escape velocities are global aspects of the manifold,
in that they depend on properties of the manifold not only at the
location in question, but at other places as well (here "manifold" =
"model of the world").

But all physics is local. That is, every modern fundamental theory of
physics is expressed as a set of differential equations, and all
measurements at a given point can be determined from properties of the
model in an infinitesimal neighborhood of that point.

In GR, an observer confined to a "small" free-falling elevator cannot
determine whether or not the elevator crossed the horizon of a black
hole, as long as the black hole is large enough so the tidal forces
within the elevator are below the measurement accuracy.

Locally the horizon is nothing special. Globally it is, but the observer
confined to the small elevator can make only local measurements.

        In principle at least there could be radiation trapped on the
        horizon. Even if the observer could observe it inside the
        elevator this would not be distinguishable from an equal
        amount of radiation simply going by in flat spacetime.
        
But as soon as the observer can make a global measurement, then it can
be possible to determine when the horizon is crossed. For instance, if
the world is populated with distant "fixed stars", then by watching
their images the observer can determine where and when the horizon is
crossed.

Tom Roberts tjroberts@lucent.com

Relevant Pages

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