Re: cosmology and quantum gravity

[Joel Rauber <Joel_Rauber@SDSTATE.EDU>]

Jack wrote in part:
. . .
> The static gravitational effects that we can observe are
> embedded in the
> metric (more strictly, the curvature) outside of the horizon.  In the
> usual metric, the gravitational effects get larger and larger as we
> approach the black hole until they blow up at the horizon,
> where there is
> a coordinate singularity.   . . .

I wouldn't have put it that way, the gravitational effects *do not* blow up
at the event horizon; i.e. the tidal forces at that point are not infinite.
There is a coordinate singularity at the event horizon if you choose "bad"
coordinates to describe the situation there; a typical and common set of
"bad" coordinates would be spherical polar angular coordinates and the so
called "radial area coordinate"; a radial coordinate which yields for
constant *t* and constant *r* a spatial (outside of the event horizon) two
dimensional surface of area 4*pi*r^2.

There exist other coordinate systems to describe a Schwarzchild black hole
that have no coordinate singularities at the event horizon.  One oft cited
example are the Kruskal-Szekeres coordinates (named after their creators, I
assume) See the book "Gravitation" by Misner, Thorne and Wheeler (know to
many students as MTW) around page 831 for a discussion.

Joel