[evan_au]

a) Positive mass attracts negative mass.

I am not aware of any proven examples of negative gravitational mass for an object in a vacuum.
- Although some weird quantum things can occur for charge carriers in semiconductors

CERN's ALPHA experiment is trying to measure the gravitational attraction of antimatter.
- Because it is antimatter does not necessarily mean that it is anti-mass.
- But their final conclusion has not yet been published.

See: https://en.wikipedia.org/wiki/Gravitational_interaction_of_antimatter

Newton's shell theorem addresses the field strength inside the boundary.

Newton's Shell Theorem also addresses the gravitational field outside the shell: It behaves as if there is a point mass at the center of the shell.
See: https://en.wikipedia.org/wiki/Shell_theorem

[puppypower]

It is well known that the speed of light goes to zero at the event horizon of a Schwarzschild black hole. You can prove this to yourself by solving the metric for a radially in-falling photon, for which proper time is identical to zero. The result is:
c=c_o(1-r_s/r)
The Shapiro effect exemplifies this phenomenon.
What happens to an in-falling mass is less obvious because the speed of proper time is a function of velocity:
dT/dt=sqrt((1-r_s/r)(1-(v/c)²))

The mass density of a back hole defines the local space-time profile. This profile is not defined by the observer,  any more than the gravity of the sun and the pressures it exerts is dependent on the observer. Mass is an invariant. It defines local space-time, via GR, to be a local invariant. Confusion appears because we measure this with second hand data, stemming from energy output signals. This second hand data can is reference dependent.

The analogy is judging a book by the cover, but never opening the book. The cover or second hand data is where sale pitch rules. A smile does not always mean friendly, but this is how relative reference seeks to interpret it. An acceleration will exert pressure; g-force. This pressure will impact matter but may not show up in the energy profile used by relative reference. Energy does not accelerate.

Gravity can exert pressure, which physically moves mass together and then alters the phases of matter. This has nothing to do with the observer, I might be able to find a reference that appears to alter the space-time profile of the sun to it appears lighter based on its apparent profile. However, this relative reference will not make the sun stop fusion, since the fusion has nothing to do with me or my reference illusion.

For example, if hydrogen atoms were in motion, we might see the emission spectrum red shifted. This does not mean a new type of hydrogen has formed. The hydrogen atom and its spectrum is invariant. We know enough to tell that this is due to motion. But what becomes of exotic phases where data is scarce? Relative reference will use its imagination to make up the plot, based on the book cover and sales pitch on the cover. 

If you fell into a black hole, the pressures would kill you long before we could run any test. All your tools would get squished and stop transmitting. Space-time is only half the story. Drop a space probe on Venus and see if spacetime leads. If you fell into a black hole you would become squished and then all your molecules and atoms would undergo phases changes until you become elementary particles and beyond.

One problem this creates, in terms of reference, is although space-time will appear to slow the process, the matter transitions speed up as pressure increases. Matter time is running opposite to space-time. The sun does the same thing. On the surface we have plasma speed transition in matter, but the core is gamma speed transitions which are faster, even though space-time should show slowed time.  An acceleration is d/t/t or in this case is expresses as two components; space-time plus time due to matter phases.

[Mike Gale (OP)]

Negative mass experiment: https://en.wikipedia.org/wiki/Negative_mass#Experimentation

[Mike Gale (OP)]

Interaction between positive and negative masses: https://en.wikipedia.org/wiki/Negative_mass#Runaway_motion

[jeffreyH]

You could define a negative energy, but only for kinetic energy and if the energy were expressed as a vector rather than a scalar. Negative rest energy would be a very bizarre concept indeed.

[Mike Gale (OP)]

The mass density of a back hole defines the local space-time profile. This profile is not defined by the observer,  any more than the gravity of the sun and the pressures it exerts is dependent on the observer. Mass is an invariant.

Only rest mass is invariant. The effective mass of a gravitating body is zero for an observer in free-fall.

If you fell into a black hole, the pressures would kill you long before we could run any test.

The (radial) pressure gradient is irrelevant if the observer is arbitrarily small. The point is that the observer reaches the horizon in coordinate space at the end of coordinate time.

[jeffreyH]

Eventually all this can end up in group theory. Especially considering the Lorentz and Poincare groups. Group theory isn't my favourite pastime.
https://en.m.wikipedia.org/wiki/Fundamental_group

[Mike Gale (OP)]

You could define a negative energy, but only for kinetic energy and if the energy were expressed as a vector rather than a scalar. Negative rest energy would be a very bizarre concept indeed.

Absolutely, but it is allowed by the equations and we've been burned many times by our prejudices in that regard. Best to keep an open mind on the subject.

[Mike Gale (OP)]

Here's a pretty good explanation for black hole growth: http://mathpages.com/rr/s7-02/7-02.htm

In a nutshell, the Schwarzschild solution cannot accommodate black hole growth because it only addresses the one-body problem. Lacking an exact solution for the two-body problem, we can only speculate about the process.

[Mike Gale (OP)]

Eventually all this can end up in group theory. Especially considering the Lorentz and Poincare groups. Group theory isn't my favourite pastime.
https://en.m.wikipedia.org/wiki/Fundamental_group

Yikes.

[yor_on]

You wrote "The best I can do is appeal to causality. A reference frame in which mass can out pace light doesn't make any sense." Mike. Not sure what you're thinking of there?

A red shifted light should pass into oblivion from the far away observers point of view. We don't see the 'mass', we see the (reflected/excited) light of the infalling object, right?
 
As far as I get it any 'caught' light, inside a 'real event horizon' still has a geodesic it follows, although it's a closed one leading only one way, into some 'center' unless we assume that there also is a possibility of the geodesic to be in some sort of equilibrium relative that center.