DUT - Refutation of Gravitational Collapse as Universe Genesis

This module explores why gravitational collapse, particularly within black holes, cannot originate new universes, as defined by the Dead Universe Theory (DUT). It replaces singularities with regular, thermodynamically consistent cores.

Symbolic Functions for Gravitational Collapse Refutation in DUT

These functions define the core principles of DUT's non-singular gravitational collapse:

1. Regularized Gravitational Potential of DUT ($V(r)$)

This potential describes the gravitational influence within the DUT structure, remaining finite at the origin.

$$ V(r) = \beta \cdot e^{-\alpha r} \cdot \cos(\kappa r) $$

Where:

  • $V(r)$: Regularized gravitational potential at radial distance $r$.
  • $\beta$: Amplitude factor, related to the strength of the central potential.
  • $\alpha$: Decay rate, controlling how fast the potential decreases with distance.
  • $\kappa$: Oscillatory frequency, introducing a wave-like behavior in the potential, preventing infinite collapse.

2. Effective Temporal Metric Component ($g_{tt}(r)$)

This component of the DUT metric directly reflects the gravitational potential and is crucial for time dilation.

$$ g_{tt}(r) = 1 + \frac{2 \cdot V(r)}{c^2} $$

Where:

  • $g_{tt}(r)$: The temporal component of the metric, indicating how proper time relates to coordinate time.
  • $V(r)$: The regularized gravitational potential.
  • $c$: The speed of light.

3. Energy Density Function (Effective) ($\rho_{eff}(r)$)

This function describes the effective energy density of matter and field sources that generate the DUT potential, remaining well-behaved at the center.

$$ \rho_{eff}(r) = \frac{\beta(\alpha \cos(\kappa r) + \kappa \sin(\kappa r)) \cdot e^{-\alpha r}}{4\pi G r^2} $$

Where:

  • $\rho_{eff}(r)$: The effective energy density at radial distance $r$.
  • $G$: The gravitational constant.
  • $\pi$: Pi.
  • Note: For $r \to 0$, the $r^2$ in the denominator must be considered with the numerator's behavior, which should lead to a finite limit in a proper DUT derivation.

4. Scalar Curvature (Approximate Ricci) ($R(r)$)

This scalar invariant provides a measure of spacetime curvature within DUT, demonstrating the absence of point singularities.

$$ R(r) = \frac{\beta(-\alpha^2 \cos(\kappa r) - 2\alpha\kappa \sin(\kappa r) + \kappa^2 \cos(\kappa r)) \cdot e^{-\alpha r}}{c^2 r} $$

Where:

  • $R(r)$: The scalar curvature (e.g., Ricci scalar) at radial distance $r$.
  • This function remains finite and oscillatory as $r \to 0$.

Scientific Summary

  1. The DUT gravitational potential $V(r)$ is regular at $r = 0$ and decays smoothly, preventing infinite density.
  2. The effective metric component $g_{tt}(r)$ neither vanishes nor diverges as $r \to 0$: $\lim_{r\to0} g_{tt}(r) = 1 + 2\beta / c^2$. This implies that time remains finite and well-defined even at the core.
  3. No event horizon is formed; gravitational collapse halts at a stable, finite core, rather than forming a point singularity.
  4. The scalar curvature $R(r)$ remains finite and oscillatory throughout spacetime, unlike the diverging singularities found in Schwarzschild or Kerr solutions.
  5. Therefore, the DUT framework mathematically excludes the creation of new universes within classical black holes.

Philosophical and Physical Conclusion

The Dead Universe Theory replaces singular cosmic "monstrosities" with structured entropy fields, maintaining the general structure of General Relativity geometry, but crucially correcting its physical limits. Unlike entropy-agnostic models or those relying on unphysical infinities, DUT posits an intrinsic thermodynamic and topological barrier to cosmic genesis from gravitational collapse. This means the universe fundamentally cannot "reset" or generate new iterations from its own decaying structures. It is a universe designed for an ultimate informational and energetic finality within its own cycle.