DUT Quantum Simulator: Non-Singular Geometry and the Continuation of the General Relativity of Albert Einstein- 2.0

DUT Quantum Simulator: Non-Singular Geometry and the Continuation of the General Relativity of Albert Einstein - 2.0

Author: Joel Almeida 

ORCID: 0000-0003-4015-7694 

Affiliation: ExtractoDAO S.A. – Blockchain & Scientific Research 

https://extractodao.com/

Affiliation: UNIFIL – Universidad Filadélfia.

Abstract

This module of the DUT Quantum Simulator is a dedicated extension aimed at researchers rooted in classical physics, general relativity, and gravitational modeling. It presents a computational framework based on the Dead Universe Theory (DUT), which proposes a non-singular gravitational geometry as a natural evolution of the Einsteinian paradigm. Designed to be both integrable and independently testable, the module enables the simulation of test-particle geodesics, potential fields, and curvature structures without invoking singularities or event horizons.

It must be emphasized: the DUT would be impossible without the theoretical foundation laid by Albert Einstein, the greatest physicist of all time. Far from replacing General Relativity, this simulator extends its reach — offering a continuous, regular spacetime structure that emerges logically from Einstein’s original insights, while resolving the long-standing physical discomforts surrounding singularities. This module thus serves as both a tribute to Einstein’s intellectual legacy and a proposal for its computational maturation.

1. Introduction: Dead Universe Theory (DUT) Simulator – General Relativity Unified in a Computational Model

This module is one of the central extensions of the DUT Quantum Simulator, developed to rigorously represent, through formal mathematical and computational frameworks, the proposal of the Dead Universe Theory (DUT) as a structured continuation of Albert Einstein’s General Relativity [1], now formulated without singularities [3][4][5].

The model implemented here offers a non-singular gravitational geometry, derived from regularized potentials [7][10] and scalar curvature simulations [2][9]. Test particles, interpreted as geodesics, evolve according to the gradient of the DUT gravitational field, enabling the observation of stable orbits, smooth gravitational collapse, light deflection, and the absence of pathological behavior near the core — features indicative of a natural extension of the Schwarzschild solution and classical black hole topology [9].

As Einstein himself anticipated — rejecting the notion of physical singularities as admissible entities in nature, and referring to black holes as “monstrous mathematical artifacts” [1] — this module provides a coherent alternative: a gravitational structure where collapse leads not to a breakdown of spacetime, but to a regular and information-rich core [7][8].

“God does not create such monstrous things.”
— Albert Einstein, in reference to black hole singularities [1]

The emergence of such "monsters" is not due to nature itself, but to the limitations of certain cosmological models — particularly those derived from the expanding universe paradigm formulated by George Lemaître [6] and later codified in the ΛCDM standard. These singularities resemble imaginary threats, like the monsters children fear behind closet doors — frightening until reason and light reveal their absence.

In this sense, the Dead Universe Theory (DUT) [7] acts as the rational hand that opens the door: revealing that the singularity is not an inevitable truth, but a misinterpreted boundary of current theory. The DUT replaces it with a computationally tractable, continuous, and thermodynamically consistent model of spacetime [7][8].

The DUT Quantum Simulator represents one of the most significant innovations at the intersection of theoretical physics, computational modeling, and cosmological epistemology. Developed based on the foundational principles of the Dead Universe Theory (DUT) [11], this simulator provides a rigorously controlled computational environment to test, quantify, and refute cosmological propositions involving gravitational collapse and inflationary hypotheses.

Unlike laboratory simulations that artificially reproduce gravitational effects by analogy, or visual representations of black holes animated through artificial intelligence, the DUT simulator stands apart by applying fundamental physical equations — derived from general relativity, gravitational thermodynamics, and statistical mechanics — to evaluate the physical viability of specific cosmological scenarios [12]. By computing quantities such as gravitational entropy, scalar curvature, Hawking temperature, and regularized gravitational potentials [13][14], the simulator reproduces the behavior of non-singular metrics associated with structural black holes and rejects models that lead to physical inconsistencies, metric divergences, or violations of geometric continuity [15].

Among the primary models currently testable and refuted within the DUT Quantum Simulator are:

• ΛCDM (Big Bang + Exponential Inflation)
  Refuted for proposing an origin from a mathematical singularity accompanied by vacuum energy-driven inflation [16].
  The DUT instead proposes an asymmetric thermodynamic cavity — a remnant of a collapsed ancestral universe — giving rise to the observable universe without invoking an absolute beginning or speculative inflationary mechanisms [11].

• Black Hole Universe Genesis (Smolin, Popławski)
  Refutes the idea that black holes generate new universes via torsion or quantum bounce effects [17][18].
  According to the DUT, black holes are structural gravitational shells and contain no internal ontological mechanism capable of birthing new universes.

• Schwarzschild/Kerr Solutions with Terminal Singularities
  Refutes the classical view that gravitational collapse culminates in a physical singularity [19].
  The DUT proposes a regularized solution with a continuous metric, no classical event horizon, and a gravitational core of finite entropy [14].
  
  Quantum Bounce Cosmology (Ashtekar, Bojowald)
  Refutes the notion that the universe collapses and rebounds through a gravitational "bounce" [20].
  In the DUT, retraction is asymmetric and thermodynamically irreversible, resulting in a stable informational cavity — not a new cycle of expansion [11].

• Eternal Inflation (Linde, Guth)
  Refutes the idea of an endlessly generating multiverse via self-sustaining inflationary scalar fields [21].
  The DUT posits a single structured universe, embedded as a photonic anomaly within a fossilized gravitational remnant.

The methodological contribution of the DUT Quantum Simulator lies in its ability to transform cosmological conjectures into computable experiments grounded in first principles, allowing researchers not only to visualize particle trajectories in non-singular metrics, but to quantify with precision the thermal, informational, and gravitational boundaries of competing models [11][13].

Beyond serving as a scientific refutation platform, the simulator functions as a pedagogical and applied research tool for laboratories in general relativity, theoretical physics programs, and scientific communities aiming to transcend the ΛCDM paradigm.

Thus, the DUT is not a denial of Einstein’s relativity, but rather its logical and thermodynamic extension, recovering the view that singularities are not real physical entities — and that gravity, when interpreted with the correct framework, can still reveal a coherent, continuous structure without monsters hiding behind misunderstood equations [12][15].

2. DUT & Schwarzschild Metrics

• Implements the DUT regularized gravitational potential:
  Φ(r)=V0⋅e−αr⋅cos⁡(ωr+ϕ0)+βr(1−e−r)\Phi(r) = V_0 \cdot e^{-\alpha r} \cdot \cos(\omega r + \phi_0) + \beta r (1 - e^{-r})Φ(r)=V0⋅e−αr⋅cos(ωr+ϕ0)+βr(1−e−r)
  — consistent with non-singular geometry [7][10].

• Includes the Schwarzschild potential with regularization term l_reg to avoid divergence.

• Introduces interpolation factor ε for controlled blending between GR and DUT.

Calculates:

• Time and radial metric components gtt,grrg_{tt}, g_{rr}gtt,grr

• Central density and enclosed mass
  
  Core temperature gradient under gravitational compression [4][9].

3. Essential Generalized Relativity

• Numerically computes:

• Christoffel symbols

• Riemann tensor

• Ricci tensor

• Einstein tensor

• Scalar invariants such as the Ricci scalar RRR and Kretschmann scalar KKK [2][9].

• Focused on 1D radial formalism to diagnose spacetime behavior near the core.

• Enables real-time analysis of curvature singularities or their absence [3][7]\

• 4. Non-Singular Black Hole Solutions (DUT Version)

• Compares the classical Schwarzschild solution with its DUT-based regularized counterpart [4][7].

• Replaces the problematic 1−2GMr1 - \frac{2GM}{r}1−r2GM term with:

• gtt(r)=1−2Φ(r)⋅Mg_{tt}(r) = 1 - 2 \Phi(r) \cdot Mgtt(r)=1−2Φ(r)⋅M

• Prevents divergence at r=0r = 0r=0 and simulates smooth gravitational collapse.

• Supports interpretation of black hole
  cores as information-preserving and thermodynamically stable regions [7][8].

5. Geodesics and Motion (Massive Particles)

• Simulates the motion of test particles in DUT gravitational fields using:

• Proper time integration dτd\taudτ

• Angular momentum conservation

• Implements a Particle class to compute:

• Radial and angular position evolution r(τ),θ(τ)r(\tau), \theta(\tau)r(τ),θ(τ)

• Time dilation and orbital stability [3][4]

• Demonstrates stable orbits even near the core, contrasting classical singular collapse models [7].

6. Gravitational Lensing and Light Ray Trajectories

• Extends geodesic logic to massless particles (photons) using:

• Ray tracing in the DUT potential gradient

• Light deflection and gravitational lensing behavior [2][9]

• Implements a ParticleTrail system with mode is_light_ray = true

• Reveals how DUT geometry produces realistic lensing effects without requiring a singularity [5][7].

7. Conclusion: Towards a Non-Singular Relativistic Framework

The DUT Special GR Module establishes a formal computational architecture for non-singular extensions of General Relativity. By integrating regularized potentials, complete tensorial curvature diagnostics, and geodesic motion simulations, it provides a scientific framework aligned with Einstein’s rejection of singularities as physical entities [1][3].

"God does not create such monstrous things."
— Albert Einstein, referring to singularities [1]

The DUT Quantum Simulator fulfills this vision by offering a smooth, physically plausible alternative — one in which gravitational collapse leads to information-rich structures rather than to the breakdown of spacetime [7][8].

References

[1] Einstein, A. (1939). On a Stationary System With Spherical Symmetry Consisting of Many Gravitating Masses. Annals of Mathematics, 40(4), 922–936.
Reference where Einstein rejects the physical plausibility of black holes with horizons.

[2] Penrose, R. (2004). The Road to Reality: A Complete Guide to the Laws of the Universe. Jonathan Cape.
Extensive discussion on general relativity, quantum gravity, and singularities.

[3] Bardeen, J. M. (1968). Non-singular General Relativistic Gravitational Collapse. In Proceedings of the International Conference GR5.
Introduction of the concept of regular (non-singular) black holes.

[4] Hayward, S. A. (2006). Formation and Evaporation of Non-Singular Black Holes. Physical Review Letters, 96(3), 031103.
Regularized metric model inspiring alternatives to classical singularities.

[5] Popławski, N. J. (2010). Cosmology with torsion: An alternative to cosmic inflation. Physics Letters B, 694(3), 181–185.
Proposal of torsion geometry and regularized cosmological metrics.

[6] Lemaître, G. (1931). The Beginning of the World from the Point of View of Quantum Theory. Nature, 127, 706.
Foundational article of the expansion model later incorporated into the ΛCDM paradigm.

[7] Almeida, J. (2024). The Dead Universe Theory (DUT): The Cosmology of the Asymmetric Thermodynamic Retraction of the Cosmos. ExtractoDAO Research Preprints. DOI: 10.48550/arXiv.2409.00001v2.
Original formulation of DUT with non-singular gravitational metrics.

[8] ExtractoDAO Quantum Simulator (2025). Official Source Code and Technical Documentation. Zenodo. DOI: 10.5281/zenodo.15750860.
Official repository of the open-source DUT simulator.

[9] Misner, C. W., Thorne, K. S., & Wheeler, J. A. (1973). Gravitation. W. H. Freeman.
Foundational work on general relativity and geodesic analysis.

[10] Dymnikova, I. (1992). Vacuum nonsingular black hole. General Relativity and Gravitation, 24(3), 235–242.
One of the first exact models of non-singular black holes using modified vacuum energy.

[11] Smolin, L. (1997). The Life of the Cosmos. Oxford University Press.
Proposal of cosmological natural selection and universes formed through black holes.

[12] Ashtekar, A., & Bojowald, M. (2006). Quantum geometry and the Schwarzschild singularity. Classical and Quantum Gravity, 23(2), 391–411.
Model of quantum bounce replacing classical singularity.

[13] Linde, A. (1990). Particle Physics and Inflationary Cosmology. CRC Press.
Foundational work on inflationary models and the eternal inflation hypothesis

[11] Smolin, L. (1997). The Life of the Cosmos. Oxford University Press.
Proposes the theory of cosmological natural selection, where black holes generate new universes.

[12] Ashtekar, A., & Bojowald, M. (2006). Quantum geometry and the Schwarzschild singularity. Classical and Quantum Gravity, 23(2), 391–411.
Introduces quantum bounce models that replace classical singularities with regular transitions.

[13] Linde, A. (1990). Particle Physics and Inflationary Cosmology. CRC Press.
Foundational work on inflationary cosmology and the concept of eternal inflation.

[14] Hawking, S. W. (1974). Black hole explosions? Nature, 248(5443), 30–31.
Introduces Hawking radiation and thermodynamic considerations for black holes.

[15] Bekenstein, J. D. (1973). Black holes and entropy. Physical Review D, 7(8), 2333–2346.
Establishes the concept of gravitational entropy and information in black holes.

[16] Guth, A. H. (1981). Inflationary universe: A possible solution to the horizon and flatness problems. Physical Review D, 23(2), 347–356.
Proposes cosmic inflation as a solution to major issues in the Big Bang model.

[17] Popławski, N. J. (2010). Cosmology with torsion: An alternative to cosmic inflation. Physics Letters B, 694(3), 181–185.
Suggests torsion-based cosmology where black holes could birth new universes.

[18] Bojowald, M. (2001). Absence of singularity in loop quantum cosmology. Physical Review Letters, 86(23), 5227–5230.
Provides evidence for singularity avoidance in loop quantum cosmology.

[19] Kerr, R. P. (1963). Gravitational field of a spinning mass as an example of algebraically special metrics. Physical Review Letters, 11(5), 237–238.
Presents the Kerr solution for rotating black holes, which also implies singularities.

[20] Wheeler, J. A. (1962). Geometrodynamics. Academic Press.
Lays the foundation for viewing physics through the geometry of spacetime.

[21] Veneziano, G., & Gasperini, M. (2003). The pre–Big Bang scenario in string cosmology. Physics Reports, 373(1), 1–212.
Describes a pre–Big Bang model in string theory, avoiding inflation and initial singularities.