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You ( Tom Roberts ) replied to me:
You (Tom) are wrong about conditions at:

· The cosmological horizon ( i.e. the start of the big bang ).

· The event horizon of a supermassive black hole.

All horizons are "apparent", subjective, not objective.
The horizon depends on where/when you are.

This is just plain not true.
Some types of horizons are so dependent,
but most types are not.

For concreteness, I'll discuss
the Schwarzschild manifold of GR.

According to Wikipedia, the Schwarzschild metric assumes
"a stationary clock located infinitely far from the massive body".
https://en.wikipedia.org/wiki/Schwar...zschild_metric

In other words, it does ·not· describe
what local obserers see, beyond our horizon.

[ ..... ]
the locations of the horizons do NOT depend on
where you are located or what coordinates you use.

They are objective properties of the manifold:
on one side it is possible to reach spatial infinity,
and on the other side it is not.

Yes, but ·only· for:
"a stationary clock located infinitely far from the massive body".

The start of the "big bang",
indeed the ·apparent· start of space and time ( the timescape ),
depends on where/when you are.

[ ..... ]
The "cosmological horizon" of a given observer in these models does depend on
the observer's location. This is the locus beyond which the observer can never
observe any portion of a non-spacelike geodesic path, and that obviously depends
on where/when the observer is located. Perhaps this is what you are thinking of
-- but it is NOT a general property of horizons.

Yes, the start of the timescape ( i.e. the cosmological horizon )
depends on where/when you are.

Local observers see a ·much· lower energy density there/then,
beyond our horizon.

A local observer, at what appears (to us) to be a horizon,
would see no such horizon ( i.e. no redshift ).

Not true for the event horizon of a black hole, or for the big bang.
But it is true for an observer's cosmological horizon.

What ? ! Per General Relativity,
the redshift depends on when/where the observer is.

Locally, the energy density within these horizons is quite low.

Hmmm. The entire visible universe is within the cosmological horizon
of an observer on earth ( that's what these words mean ).

No, I'm saying:

Local observers, outside of our horizon, measure
a ·much· lower energy density ( vs. what we see ).

[ ..... ]
in the limit as one approaches the limit point of a
past-directed non-spacelike geodesic
(i.e. approaching the big bang from the future),
the energy density increases without bound.
[ ..... ]

Yes, but ONLY for:
"a stationary clock located infinitely far from the massive body".