Re: rest mass/relativistic mass question -- and other adjustments to the FAQ

Pmb wrote:
If a object is not a black hole in one frame of reference then it won't be a
black hole in any other frame even though the grazvitational field will
increase with speed.

There are subtleties involved here that are not covered in any FAQ; in
large measure because of the vagueness of comments like those above.

As no less than Hawking, himself, has pointed out, the occurrence and
existence of causal horizons is *frame*-dependent [1] and there is, in
fact, no trapped region associated with a black hole -- that is, no
"black hole" in the usual classical sense of the term. Instead, there
is only a causal horizon, and one which is observer-dependent. Even the
event horizon associated with a black hole is frame-dependent.

So the question needs to be closely reexamined, since the FAQ and the
conventional wisdom of the previous century are both a little naive
with respect to the general issue.

This is, of course, not the only place there conventional wisdom will
go wrong and where the FAQ needs to be reexamined. Another good example
concerns the visual appearance of a moving sphere, where there is
actually a double-take end-run on conventional wisdom. The naive
assessment is that such an object appears flattened out. A closer
examination of the optics involved shows that the object would appear
spherical -- which is also naive.

The double-take occurs here in that this, too, is wrong. It actually
appears circular, since the optics is respect to *one* eye.

The actual 3-dimensional *stereographic* view of the moving object
(i.e., that obtained by receiving images in two eyes in real-time) need
not be spherical at all.

Note:
[1] "Frame" when used in the context of quantum theory in curved
spacetime does *not* mean coordinate grid, but global timelike flow.
We're not talking about coordinate dependence above, but dependence on
the selection of a timelike field.

.

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