...of our response, I imagine we are done here. 3/3

...odd when you've not pointed to a single step where the proof goes wrong, you've never explained how you imagine zero invariant separation to mean anything other than coincident, and you've merely offered a suspicion that I must be confused about what that means. Anyway, given the tone...2/

I'm sorry. You told me you didn't understand the formal paper and I should have taken you at your word. Obviously, an explainer article is not a formal proof.
I don't think I've given you any reason to assume I'm "simply convinced I'm right and everyone else is wrong." That feels unfair and...1/

What, exactly, is a black hole? Headline: What, exactly, is a black hole? Black holes are the most enigmatic, intriguing, captivating, confusing and confounding objects in all of physics. In fact, despite decades of focused researc...

@gregegansf.bsky.social @johncarlosbaez.bsky.social this is the scenario I was talking about yesterday. I ended up writing this today. Cool, isn’t it? Thats an incredibly important feature of the geometry to have just missed all this time! And so simple and profound.

docs.google.com/document/d/1...

It's a fact, forced by the causal structure of the geometry. The very causal structure that defines what the event horizon is. It's a geometric identity. And it is formally proven in the paper I linked above.

An updated figure for this thought experiment. 🧮 ⚛️ ☄️ 🎢 🧪

The thick blue line is the flash of light shone towards the black hole from Earth. The thick red lines are photons reflected back at beam splitters. The collapsing star's surface, flash of light and astronaut all arrive coincidentally at r_h.

It’s like discussing the physical nature of planetary epicycles and the problems their existence creates: there are no epicycles to begin with, so there are no associated problems either. 3/3

…approach that involves “existing horizons within the global extension of the geometry” simply goes away because the thing those problems are all based on just isn’t a thing. They’re furnishings for a room that doesn’t exist. 2/3

Not at all. The paper is just simple Lorentzian geometry, and the essence of the proof is that horizons are not things that form in the universe. The event horizon is a metrically singular EVENT that happens at the end of the universe. Forewalls, Hawking radiation, holography—every semi-classical…1/

@gregegansf.bsky.social @johncarlosbaez.bsky.social this right here might be the most incredible variant of the null temporal degeneracy theorem. Catching up with a ray of photons emitted a million years earlier while travelling < c throughout 🤯

Anyway, so for now at least the proofs will exist just where they exist and we’ll see if anyone’s willing to accept a straightforward proof without institutional endorsement. Maybe someone like @johncarlosbaez.bsky.social who knows the theory perfectly well will look at it? 3/3

…culmination of 17 years of thinking beginning with my PhD thesis and wrapping in the paper I shared with you and this other one: cosmicave.org/wp-content/u...
You’re right lots of people won’t like the conclusions they draw. But you don’t have to like the truth for it to be true. 2/

Thanks for reading the paper, Greg. I suspect you understood it far better than you’re giving yourself credit for. In any case, I owe you a book and will get on that in a morning.
Fwiw, I don’t think either of these papers will ever hit traditional peer review, for personal reasons. They’re the…1/

…a million years before the astronaut decided to dive in. And yet the astronaut, the light ray, and the collapsing star all reach the horizon with zero metrical separation between them. They’re all coincident events.
Read the formal proof here: cosmicave.org/wp-content/u... 5/5

…shone IN to the black hole, travelling at the speed of light. The astronaut just catches up to that light ray, all while travelling there slower than the speed of light. And the surface of the star too. The star might’ve collapsed a billion years ago. The light ray might’ve been shone in…4/

That gap becomes identically zero by the time the astronaut reaches the horizon. At the horizon, the photons reflected back out when the ingoing null ray hit the horizon travels a radial distance dr=0 to reach the astronaut. In other words: the astronaut reaches the same light ray they earlier…3/

As the astronaut approaches the horizon radius, the radius at which the beam splitter reflected those observed photons back gets closer and closer in r. The gap between the infalling astronaut and the place where the observed photons were reflected back shrinks the whole way down. 2/

Black hole geometry is wild. 🧮 ⚛️ 🎢 ☄️ 🧪
Take the blue ingoing null line just before the astronaut dives in to be a ray of photons that encounters beam splitters the whole way down, at regular intervals that reflect some photons directly back out along the outgoing red null lines. 1/

Astronomy of Planets Course Overview In 2015, I was assigned to develop an online planetary astronomy course at the University of Saskatchewan, which provided an opportunity to correct an issue that had been nagging at…

Oh please. I teach science. The scientific method. I’ve written a stinking online course on the history of it. I understand all the nuanced distinctions. Here’s a course I wrote on the subject: cosmicave.org/course/astro...

cosmicave.org/wp-content/u...

Here’s a link to the first paper for convenience. Second one below.

cosmicave.org/wp-content/u...

It goes without saying obviously that no one has said the opposite, that there’s an issue with the proof. But that would be weird since there isn’t, and the whole thing uses very standard tools, so anyone with a GR background could follow it. It is a beautiful proof. But the tools used are standard.

It’s actually really surprising that still no one has been willing to say “I know GR/Lorentzian geometry and topological spaces and the proof in these papers is valid.”

Because it is. And it’s incredible. 🧮 🧪 ⚛️ ☄️ 🎢

Most importantly though: I asked a specific question and you supplied a page as your answer. But that page doesn’t ask the question, doesn’t answer it, and doesn’t even implicitly address it. So I’ll just refer back to the question I asked above.

When black holes happen When a star collapses to a black hole, from the outside it never quite gets there. Everything that ever falls in reaches the horizon together, at the end of time. What follows isn’t destructi…

Or an equivalent proof with conceptual logic if you prefer that to pure mathematics: cosmicave.org/2026/04/14/w...

cosmicave.org/wp-content/u...

@gregegansf.bsky.social maybe you’d care to comment?

I’d be happy to explain any point you’d like to discuss further from the article itself. I don’t think you understand it or its purpose. This is an explainer following conceptual logic (which is a form of proof in itself, though that’s irrelevant), of the results of a formal mathematical proof…1/

You should have responded like this to Greg Egan: when the star’s surface reaches the horizon, what is the metrical distance of that event from every “future” event when every future infaller reaches the horizon? How far apart are those two events? What’s the proper distance between them?” 1/2

…even though the separation between them is null. They are coincident events. It’s a metrical singularity. Not a curvature singularity but still a physically significant. It’s an event-of-events, singular in the sense that there is null separation between them. They’re coincident at that event. 3/3