The fate of black holes

General relativity predicts that at the heart of a black hole, all matter collapses into a point of infinite density: the "singularity". But this prediction is mathematically absurd — and everybody knows it. TQNT proposes something else.

The embarrassment of general relativity

In 1915, Einstein published general relativity. It describes gravity no longer as a force, but as the curvature of spacetime. The theory is so elegant, so well verified by experiment, that it has become an absolute reference. But it has a flaw, and it is a very awkward one.

When applied to a black hole, the equation predicts that at the centre, the curvature of spacetime becomes infinite. All the matter that falls in concentrates into a dimensionless point: the singularity. Yet infinities, in physics, are almost always a sign that the theory has stepped outside its domain of validity.

Stephen Hawking proved in the 1960s that, according to general relativity, these singularities are inevitable as soon as a black hole forms. He made a theorem out of it, which bears his name. And he then spent thirty years trying to figure out how to get rid of them.

The information paradox

On top of the singularity comes a second, even more disturbing mystery: the information paradox.

When you throw a book into a fire, the information of the book (its text, its structure) is not really lost: the ash molecules, the heat photons, all of it carries a trace. If you could observe the smoke and ashes in their entirety with perfect precision, you could theoretically reconstruct the book. This is the principle of unitarity in quantum mechanics: information never disappears.

But Hawking showed, in 1974, that black holes evaporate by emitting thermal radiation (Hawking radiation). This radiation is purely thermal — it carries no information about what has been swallowed. So when a black hole evaporates completely, all the information it had swallowed disappears. A head-on contradiction with quantum mechanics.

This contradiction is unresolved to this day in the standard framework. It is one of the greatest open questions in theoretical physics.

The TQNT picture: the frozen-knot star

TQNT proposes a radically different answer: there is no singularity at all. And information is perfectly preserved.

Here is the idea. Remember (lesson 1) that in TQNT, spacetime is not a pre-existing stage: it emerges from the density of the wavefunctions of knot-particles. Where knots are abundant (concentrated), space curves and time slows down. Where there are none, space is flat.

Now consider what happens at the heart of a gravitational collapse: a huge number of knots are compressed into a small volume. The knot density becomes enormous. The emergent metric, which depends on this density, does something remarkable: it decays exponentially instead of dropping to zero.

And this difference changes everything. In general relativity, the metric vanishes at the centre, hence the singularity. In TQNT, the metric tends to a very small but non-zero value. The result is that, inside, space becomes tremendously dilated, and time slows down gigantically, but everything remains well defined.

Information is preserved

Since the knots still exist inside — frozen, but really there — the topological information they carry is preserved. The number of crossings, the Jones polynomial, the linking of each component: all of it is encoded in the structure of the knots, and never disappears.

The emitted radiation (Hawking) is no longer purely thermal in TQNT: it carries subtle correlations that progressively transport, over time, the topological information of the swallowed knots. When the black hole evaporates completely, all the information comes back, distributed across the final radiation. Quantum mechanics is saved.

E = mc²: the cost of deconfinement

Everyone knows this equation. It is the most famous in physics. But what does it mean, at heart? Why can mass be converted into energy?

TQNT proposes a very simple interpretation: mass is energy confined inside a knot. To release this energy, you need to undo the knot, that is, cut it. Cutting it costs precisely the topological cohesion energy, and the energy that comes out is the energy that was stored in the shape.

So E = mc² is, in TQNT, the cost of deconfining a knot. Mass is not a mysterious substance: it is just energy in the act of being confined by topology.

Hawking and Schwinger: two regimes of the same mechanism

Hawking showed that black holes emit a quantum radiation. Schwinger, in the 1950s, had shown that an extreme electric field can spontaneously produce particle pairs (Schwinger effect). These are very different phenomena — one cosmological, the other microscopic.

TQNT proposes that they are the same mechanism, seen at two different scales: at the boundary between a strongly curved zone and a flat zone, knots nucleate spontaneously.

• At the baryonic boundary (ordinary atoms / vacuum), this mechanism produces Schwinger;
• At the event horizon of a black hole, the same mechanism produces Hawking;
• In deep vacuum, it produces the residual contribution to dark energy.

Three apparently disconnected phenomena are in fact three regimes of a single postulate: this is the so-called postulate P22 of TQNT (boundary nucleation).

Can a particle escape from a black hole?

In TQNT, the answer is yes, provided you wait long enough. The knots frozen inside are preserved, but they communicate with the outside through the boundary (the event horizon). Hawking radiation progressively transports the topological information outward. After a colossal time (of the order of 10⁶⁷ years for a solar-mass black hole), everything is returned.

But — and this matters — a knot cannot escape as a knot. It comes out as diffuse radiation, which carries its trace. Like a book whose ashes would be carefully collected and preserved intact: the book itself is undone, but it can be reconstructed.