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Equation of State for Finite-Density Black Holes: Addressing the Singularity Problem with a Discrete Spacetime Framework v2-unity

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Abstract

This paper presents an anisotropic equation of state (EoS) for modeling finite-density black holes, addressing the singularity problem in classical general relativity within a discrete spacetime framework. The proposed EoS relates radial, tangential, and azimuthal pressures to the energy density, incorporating adjustable parameters to represent ultra-dense matter under extreme conditions. By ensuring compliance with the Weak, Dominant, and Strong Energy Conditions, this framework establishes physical viability for finite-density cores. Quantum corrections are incorporated via a scalar field and modified Einstein field equations, providing a consistent theoretical foundation for exploring black hole interiors and their observational signatures. The framework also integrates the effects of angular momentum, using a modified Kerr metric to account for rotational dynamics and their influence on the scalar field and anisotropic pressures. Additionally, a discrete frame-based model and metatagging techniques are integrated to represent subparticles as discrete entities and encode their quantum states. This holistic approach builds on numerical validation and provides insight into both quantum and macroscopic processes.

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