The diplacement of a gravity wave is only known after it reaches the observer forward in time. The displacement in space between the time extremity farthest behind along the space-time trajectory to the extremity closest is negative. The time extremity is where the singularity begins, and time slows down. My point is that radius is tied to gravity in the force of gravity equation, and a negative displacement means the gravity wave originating closer in space happened farther in the past along the space-time trajectory (farther in the time past as experienced outside by an observer that passed through the loop, but not in the time past by an observer that did not follow the same space-time trajectory loop).



[edit] Not time extremity, that is a time interval. The space interval as measured at an observation point t=2 x=4 above, is |1-4|, going forward along the space-time trajectory, but both space-time trajectories intersect, and it appears as though time just stops on the outside until the inner loop completes... Any event that happened along the loop, originating at the intersection, then, would instantaneously propagate to the intersection, and it would appear gravity waves from both space extremities happen at the same time?
Maybe the important point is not negative radius. That's an interpretation of this plot, but things don't come out of blackholes as we all know.

I make a point not to engage with crackpots (and that PDF I read this morning is off the charts) so I will just say one thing: even if the math is perfectly correct, it is absolutely worthless as the basis of a physical theory if it cannot be observed and verified experimentally by way of measurements corroborating said theory (directly or indirectly). And even then the theory may not be correct for all values that the math technically admits: the theory may only be accurate for some limited range of inputs to the theory's equations, or the accuracy of the theory may taper off into absurdity as the input values get larger and larger or smaller and smaller.

For instance, classical Newtonian mechanics makes excellent predictions for small velocities, but gets horribly inaccurate at relativistic speeds, even though the math on which Newton's formulas of motion are based have absolutely no problem with arbitrarily large speeds. More to the point, I can make a theory that gravity actually falls off proportional to 1/r^3 rather than 1/r^2, and derive from this the possible gravitational orbits that can be achieved and so on (which is a completely legitimate and mathematically valid activity and a nice exercise in differential equations), but there's a small problem with this as a physical theory: our universe doesn't work that way, as even the most cursory observation will demonstrate. Until you collect actual physical evidence that it actually works this way, all you're really doing is conjecturing.

In short, just because your math is flawless doesn't mean the assumptions from which this math originates are physically meaningful. And reinterpreting existing physical formulas to make them mean something else than they already do or by arbitrarily "extending" them in random and inexplicable ways isn't going to change that fact. You just cannot do that and expect meaningful results!

Has anybody ever tried plotting the gravitational motion along a straight path, for all acceptable values? Somebody must have already solved the Taylor series, so why am I expecting to find anything. But I want to see what I will get. So don't want to do this. I will gather the patience. Might take a few days. Help greatly appreciated.

Look at this beast!

y(x) = 0 + ( sigma n={2} to {inf} ((n-1)! * 1/n! * x^n * 1/( 2-y(n-1) )^n) )

Also, a bulb trajectory is still calculated even with absolute radius, except it is flipped upside and doesn't flow continuously.

Switch B and A and you get a positive number.

Which makes more sense to you:

A - B or B - A?

As someone coming from a slightly more mathematical background: it does not matter. Distances (and by implication radii) are based on a metric. A metric cannot be negative.
You are certainly free to define an alternative set of axioms which allow, for example, negative metrics. But the first step you have to undertake then is to see how much of what you think of as conventional math is still accessible to you.

If you don't believe what I say, prove my math wrong.

That which can be proven with no evidence can equally be disproved with no evidence. So far you've proven exactly nothing.

I am no physicist. I just had an idea. Only good things come from solving equations. Yes I guess its conjecturing not hypothesizing.

Switch B and A and you get a positive number.

Which makes more sense to you:

A - B or B - A?

As someone coming from a slightly more mathematical background: it does not matter. Distances (and by implication radii) are based on a metric. A metric cannot be negative.
You are certainly free to define an alternative set of axioms which allow, for example, negative metrics. But the first step you have to undertake then is to see how much of what you think of as conventional math is still accessible to you.

That was more or less what I was trying to get at. Thanks!

You should check out Mathur's fuzzball approach to black hole interiors.

I already wrote this somewhere else. If the curvature of space around a gravity source is proportional to the square root of distance, like the gravitational time dilation formula, then negative distance (internal space) becomes a complex number and gets an extra dimension - the real number and the imaginary. Is there any truth to that?

Is it something like this:

https://en.wikipedia.org/wiki/Imaginary_time