On the Nested Causal Structure of Iterated Event Horizons: A "Matryoshka" Model of Spacetime

 J. Rogers, SE Ohio

Abstract:

We explore a theoretical model wherein the interchange of temporal and spatial coordinates, a known consequence of crossing a black hole's event horizon, is treated as an iterative physical principle. This paper posits that a black hole formed within the interior of a parent black hole would experience a second, reciprocal coordinate interchange, resulting in a nested region of spacetime where the temporal direction is restored to alignment with that of the external universe. This leads to a "Matryoshka" model of causality, with nested domains of forward and reversed time, each causally isolated. This framework offers a potential resolution to the singularity problem and suggests that the arrow of time is a local, frame-dependent property. We argue that this model provides a more coherent explanation for certain cosmological observations, such as the maturity of early galaxies, by re-contextualizing them within a vastly older parent universe.

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1. Introduction: The Event Horizon as a Causal Transformer

General Relativity describes a non-trivial transformation of spacetime coordinates at the event horizon of a black hole. For an external observer using Schwarzschild coordinates (t, r, θ, φ), the time coordinate t is timelike and the radial coordinate r is spacelike. However, for an infalling observer, upon crossing the event horizon, the character of these coordinates inverts: r becomes a timelike coordinate, compelling all matter towards the singularity at r=0, while t becomes a spacelike coordinate.

This paper elevates this transformation from a one-time curiosity to a fundamental, iterative principle. The central thesis is: The formation of an event horizon acts as a local operator that inverts the roles of the prevailing temporal and spatial coordinates. If this principle is universal, it should apply not only to our universe but also to any sufficiently dense region of spacetime, including one already within an event horizon.

2. The Iterated Transformation: Nested Causal Domains

Let us define a hierarchy of spacetime domains, denoted as U_n.

• Domain 
  This is our observable universe. The arrow of time, T₀, is aligned with the coordinate t. Causality proceeds forward in t. The radial coordinate R₀ is aligned with r.

• Domain 
  An object from U₀ crosses the primary event horizon, EH₁. The coordinate transformation occurs:

  • The local time arrow, T₁, is now aligned with -r. The future is a destination (r=0), not a duration.

  • The local spatial coordinate, R₁, is now aligned with t.
    From the perspective of U₀, causality within U₁ is inverted. Time appears to run backward.

• Domain 
  Assume a sufficient concentration of matter within U₁ collapses to form a secondary black hole with its own event horizon, EH₂. An object from U₁ crossing EH₂ would experience a second coordinate inversion, relative to the prevailing coordinates of .

  • The new time arrow, T₂, inverts with the local time arrow T₁. Thus, T₂ is aligned with the local spatial coordinate of , which is t.

  • The new spatial coordinate, R₂, inverts with the local spatial coordinate R₁. Thus, R₂ is aligned with the local time coordinate of , which is -r.

The result is that within Domain  An observer in U₂ would experience a locally stable, "forward-moving" time, identical in character to that of U₀. They would be causally disconnected from U₁, which is itself disconnected from U₀.

This structure can, in principle, be iterated indefinitely, creating a nested series of universes with alternating temporal causality: U₀ (forward) → U₁ (backward) → U₂ (forward) → U₃ (backward) → ...

3. Physical Implications

3.1 Resolution of the Singularity Problem
The classical singularity at r=0 is a point of infinite density where the laws of physics break down. In the nested model, the gravitational collapse of matter within a black hole does not terminate at a singularity. Instead, the collapse is arrested by the formation of a secondary event horizon, EH₂, which creates a new, stable U₂ domain. The singularity is thus perpetually "cloaked" by the next iteration of horizon formation, preventing its physical realization. This could be described as an infinite cascade of gravitational collapse, creating a fractal-like spacetime structure.

3.2 The Arrow of Time as an Environmental Property
This model demotes the arrow of time from a universal constant to a local, frame-dependent property. The "direction" of time is determined solely by which side of an event horizon an observer occupies. This suggests that causality is not a globally consistent feature of the cosmos, but rather a property of isolated, nested domains.

3.3 A New Cosmological Framework
The Matryoshka model offers a compelling alternative to the standard Big Bang cosmology. Our observable universe, U₀, may not be the ultimate reality, but merely a U_n domain within a much larger, older parent structure. The "Big Bang" could be reinterpreted as the formation event of our parent black hole, EH_(n-1).

This framework provides a natural explanation for the observed maturity of early galaxies (e.g., via JWST). These galaxies would have formed in U_(n-1), a domain with its own vast history, before the event that created our U_n domain. They are not "impossibly mature"; they are simply ancient relics from a parent universe, observed from the perspective of its comparatively young offspring universe.

4. Conclusion and Falsifiable Predictions

The concept of nested causal domains presents a radical but internally consistent model of spacetime. It resolves the classical singularity problem and provides a new lens through which to view foundational cosmological questions.

While direct observation of nested horizons is beyond current capabilities, the model offers a distinct cosmological prediction:

• The absence of a "Dark Age": Standard cosmology predicts a period after the CMB where no luminous objects existed. This model, reinterpreting the CMB as a time-rate horizon within a larger structure, predicts that more sensitive instruments looking to lower frequencies will continue to find structured, mature galaxies "behind" the CMB, as they are simply older objects from the parent domain.

The discovery of such objects would serve as strong evidence against the standard cosmological model and would necessitate consideration of alternative frameworks, such as the nested causal structure proposed herein. This model, born from the simple iterative application of a core principle of General Relativity, suggests that the universe may be infinitely more complex and ancient than our current perspective allows.