Numerical Development of the TQTU-HEPS- Framework From a 70-Trial Minimal Scalar Existence Scan to an Enthalpy-Based Scalar Polytropic Plasma Mode

The TQTU–HEPS Numerical Development Program A Staged, Falsifiable Search for Regular Compact Objects Beyond the Singularity Paradigm The High-Energy Plasma Stabilizer (HEPS) sector of the Tanfarid Quantum Thermodynamic Universe (TQTU) represents a systematic attempt to replace the classical gravitational singularity—a point of infinite density—with a finite, regular compact-object configuration. This article documents the staged numerical development of that program, from a minimal scalar-field model to an enthalpy-based scalar–polytropic plasma framework. Why This Research Matters General relativity predicts that gravitational collapse inevitably leads to a singularity—a breakdown of classical physics. But singularities are mathematical artifacts, not physical realities. They signal that our theory is incomplete. The TQTU–HEPS program asks a fundamental question: Can gravitational collapse terminate in a finite-density, horizonless, regular configuration rather than a singularity? If such configurations exist, they would resolve long-standing paradoxes in black-hole physics: the information loss problem, the violation of the second law of thermodynamics, and the incompatibility between general relativity and quantum mechanics. How the Numerical Program Works The program proceeds in controlled stages. Each stage tests a specific set of equations, predeclares acceptance criteria, and allows the solver to reject the model when necessary. This approach ensures that any eventual positive result is a genuine discovery rather than a programmed artifact. Stage A: Minimal Static Canonical-Scalar Model The first realization was deliberately minimal: a static, spherically symmetric spacetime with a canonical scalar field, no plasma, no anisotropic stress, and no rotation. A scan of 70 physical trials produced: 55 near-horizon terminations — the configuration collapsed before forming a regular core. 15 no-vacuum outcomes — the scalar field did not approach the exterior vacuum. 0 accepted candidates — no trial satisfied all regularity, mass, and horizonless criteria. Conclusion: The minimal scalar-field model is insufficient. New physics is required. Stage B1a: Constant-ww Isotropic Plasma The first fluid extension used a constant equation of state p=wρp=wρ. However, an analytical analysis revealed a localization limitation: in an asymptotically flat spacetime, a constant-ww fluid cannot naturally vanish at infinity. This is not a numerical failure—it is a structural property of the equations. Conclusion: The constant-ww fluid cannot support a finite compact core. Stage B1a-prime: Scalar + Polytropic Isotropic Plasma The current framework replaces the constant-ww fluid with a polytropic equation of state p=KρΓp=KρΓ, evolved through a relativistic enthalpy variable. This formulation: Allows the plasma surface to emerge dynamically (H=0H=0) rather than being imposed. Avoids numerical singularities near the plasma boundary. Supports causal sound-speed filtering (0≤cs2≤10≤cs2≤1). Defines a clear hierarchy from existence to convergence to stability to observational testing. The Scientific Hierarchy Any numerical solution must pass successive levels of validation: Level Meaning Regular, causal candidate Horizonless, finite surface, positive mass, causal plasma. Asymptotically converged Solution stable under domain extension and numerical refinement. Perturbatively stable Passes radial stability analysis (ω02>0ω02>0). Predictive compact-object model Produces predeclared observable quantities (photon sphere, shadow, echoes).