Chapter 4

Rigorous Derivation of the Cosmic Field

Section: Foundations

General Relativity works perfectly and remains valid locally up to the TOV limit. But what happens beyond? Observation tells us something fundamental: the event horizon grows. And this changes everything.

The Phases of Gravitational Collapse

Before getting into the details, here is the complete sequence that Common Relativity describes:

1 GR Valid Locally

General Relativity works perfectly up to the TOV limit. No correction needed in this regime.

2 TOV Limit (~3.4 M)

The gravitational boundary beyond which photons can no longer overcome gravity. The neutron star goes dark but does not disappear.

3 Continuous Accretion

The darkened star continues to aggregate matter. The event horizon grows - proof that matter is not in a point.

4 Reaching ξ (~3×1054 kg)

The maximum limit of aggregation. Requires contribution from multiple universes. When ξ is reached: bounce and birth of a new universe.

The Truth: A Darkened Neutron Star

ξ ≈ 3×10⁵⁴ "What you call a black hole is a neutron star. This is the maximum value of aggregation it can reach." Central darkened star (improperly: "black hole") CORRECT SEQUENCE: GR valid → TOV (darkening) → Accretion → ξ → Bounce From TOV to ξ: eons of multi-universal cosmic accretion

At the center of galaxies there is no "hole" in spacetime fabric, but a darkened neutron star that continues to aggregate matter up to the limit ξ.

The TOV Limit: Where Light Surrenders

The Tolman-Oppenheimer-Volkoff (TOV) limit marks a precise threshold: about 3.4 solar masses. Beyond this limit, gravity overcomes neutron degeneracy pressure and photons can no longer escape.

The neutron star goes dark. It doesn't disappear, it doesn't collapse into a point: light simply can no longer exit. The event horizon is exactly this: the boundary beyond which photons can no longer overcome gravity.

What we call a "black hole" is a darkened neutron star, not a hole in spacetime fabric.

The Proof of the Growing Horizon

Here is the crucial point that standard physics doesn't adequately explain:

If General Relativity were complete...

...all matter should collapse instantaneously into a point of zero volume and infinite density (the singularity). In that case, the event horizon could not grow, because there would be no more matter to aggregate: it would all already be in the singular point.

Instead we observe the opposite: black holes grow. We see them accreting matter, we observe them with Hubble and the Event Horizon Telescope, we measure their masses increasing over time. The event horizon expands as mass increases.

The Proof of the Growing Horizon

IF GR WERE COMPLETE WHAT WE OBSERVE (Impossible scenario) Collapse to singularity FIXED Horizon (cannot grow) NO ACCRETION Matter already in point t₁ t₂ t₃ HORIZON GROWS The darkened star continues to accrete The growing horizon PROVES that matter is not in a point

If matter collapsed into a singularity, the horizon could not grow. Observation proves the opposite.

From TOV to ξ: The Long Journey

The TOV limit (~3.4 M) marks darkening. But the aggregation limit ξ (~3×1054 kg) is enormously larger. From TOV to ξ, eons of cosmic accretion pass.

The Path from TOV to ξ

TOV ~3.4 M ~10³¹ kg Stellar 10-100 M ~10³² kg Intermediate 10³-10⁵ M ~10³⁵ kg Supermassive 10⁶-10¹⁰ M ~10⁴⁰ kg Ultramassive ? ~10⁴⁵ kg ξ LIMIT 3×10⁵⁴ kg Observable zone (Hubble, EHT, LIGO) Requires multi- universal contribution EONS of cosmic accretion Darkening Bounce

Logarithmic mass scale: from the TOV limit (~10³¹ kg) to the ξ limit (~10⁵⁴ kg) there are 23 orders of magnitude

Why ξ Cannot Be Reached by a Single Universe

Here is the fundamental point: a single universe cannot generate a new universe on its own.

Why? Because while matter tries to aggregate gravitationally, the universe expands. Cosmic expansion moves matter apart faster than gravity can aggregate it on sufficiently large scales.

To reach ξ would require all the matter of a universe concentrated in a point, but expansion prevents it. The solution comes from the Cosmos: the contribution of multiple universes.

A universe is never the child of a single universe. It is the contribution of cosmic matter from multiple expanding bubble-universes.

The Cosmic Lake: Colliding Waves

Imagine the Cosmos as the surface of an infinite lake. Each Big Bang is a pebble falling into the water, generating concentric expanding waves: a bubble-universe.

Now imagine multiple pebbles. The waves they generate, at a certain point, collide. It is there, in the zones of gravitational intersection between multiple expanding universes, that the combined contribution can reach ξ.

The Cosmic Lake: Multi-Universal Contribution

BB₁ Universe 1 (expanding) BB₂ Universe 2 BB₃ Universe 3 ξ COLLISION ZONE LEGEND = Big Bang (pebble) = Waves (expansion) = Intersection zone = New universe (ξ)

Like waves on a lake: each Big Bang generates an expanding universe. Where waves meet, the combined gravitational contribution can reach ξ and generate a new universe.

No Going Down: The STOP to Singularity

Common Relativity places an impassable physical limit. Fermionic matter, governed by the Pauli Exclusion Principle, cannot be compressed beyond a certain point. The singularity does not exist: there is a darkened neutron star that can grow up to ξ, and then bounces generating a new universe.

Spacetime Curvature: No Going Down

STOP C "If you observe the event horizon, you'll see the black hole growing" TOV at 3.4 solar masses I turn off the light P "It's not a hole, idiots." "Sorry, no going down" BOUNCE when M = ξ ξ ≈ 3×10⁵⁴ Maximum limit of aggregation Pauli Limit • TOV = Darkening (light can't escape) • STOP = Singularity impossible (Pauli) • ξ = Limit, then bounce → New universe

The spacetime curvature shows the gravitational funnel. But there's a bottom: the Pauli Principle prevents collapse into a point. You can't go down infinitely.

Summary

The derivation of the cosmic field in Common Relativity is based on concrete observations:

  • GR is valid locally up to the TOV limit (~3.4 M)
  • Beyond TOV, the star goes dark but doesn't disappear - the event horizon is proof
  • The horizon grows - impossible if matter were in a singularity
  • From TOV to ξ eons of cosmic accretion pass
  • ξ requires multi-universal contribution - like colliding waves on the cosmic lake
  • The singularity does not exist - the Pauli Principle sets a physical limit
  • When ξ is reached the bounce occurs and a new universe is born

What you call a black hole is a darkened neutron star. It's not a hole: it's real matter, which grows, and which one day - with the Cosmos's contribution - will generate a new universe.