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EoS for Finite Density Black Holes in a Quantum Gravity Framework

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Version 2 2024-11-17, 23:39
Version 1 2024-11-17, 20:51
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posted on 2024-11-17, 23:39 authored by Jesse Daniel BrownJesse Daniel Brown, Mccade Smith

In this paper, we develop an anisotropic equation of state (EoS) to model ultra-dense crystalline matter within the cores of finite-density black holes. Traditional general relativity predicts singularities at the centers of black holes, characterized by infinite density and curvature, which pose significant challenges for a unified theory of physics. By introducing a novel EoS that accounts for anisotropic pressures resulting from a crystalline structure at extreme densities, we aim to provide a framework that avoids such singularities.

Our model proposes that matter, when subjected to pressures beyond those found in neutron stars, forms a crystalline lattice approaching the Planck scale. In this state, the energy density reaches a maximum finite value at the core, ensuring that densities remain finite throughout the black hole. The anisotropic pressures—radial and tangential—reflect the directional dependencies inherent in a crystalline lattice. These pressures are formulated to remain finite as the energy density approaches its maximum, naturally introducing anisotropy into the system.

We incorporate this anisotropic EoS into the modified Einstein field equations, which include a scalar field representing quantum corrections. The scalar field contributes to the stress-energy tensor and helps stabilize the solution against singularities. By solving the coupled differential equations for a static, spherically symmetric spacetime, we explore the implications of our EoS on the internal structure of black holes.

Our findings suggest that the inclusion of ultra-dense crystalline matter with an anisotropic EoS provides a viable pathway to model finite-density black holes without singularities. This approach bridges classical and quantum descriptions of gravity and has potential implications for quantum gravity theories. We discuss the physical consistency of the model, methods for solving the equations—possibly through numerical techniques—and potential observational signatures that could arise from this framework.

Keywords: Equation of State, Ultra-Dense Crystalline Matter, Anisotropic Pressure, Finite-Density Black Holes, Quantum Gravity, Scalar Field, Singularity Avoidance

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