Finite Density Black Holes in a Quantum Gravity Framework

We propose a theoretical framework to address the singularity problem in black holes by introducing the concept of finite-density cores composed of ultra-dense crystalline matter formed under extreme pressure. By modifying the Einstein field equations to incorporate a scalar field representing quantum corrections and defining an anisotropic equation of state (EoS) for this exotic matter, we aim to unify classical and quantum descriptions without introducing singularities. Our model explores the possibility that subatomic particles, when subjected to pressures beyond those in neutron stars, form a crystalline lattice at scales approaching the Planck length. We present the modified field equations, the proposed EoS, and discuss the implications for black hole physics, quantum gravity, and potential observational signatures. The EoS is contained in a separate file in this project

The classical description of black holes in general relativity predicts singularities—points of infinite density and curvature—which pose significant challenges to our understanding of physics. Resolving these singularities is a crucial step toward unifying general relativity with quantum mechanics. In this work, we explore a novel approach by proposing that black holes have finite-density cores composed of ultra-dense crystalline matter formed under extreme pressure.

Analogous to neutron stars, where matter is compressed to nuclear densities, we hypothesize that black holes compress matter even further. At these extreme conditions, subatomic particles form a crystalline lattice, possibly involving new states of matter where even electrons are broken down into smaller constituents. This exotic matter would only exist under specific temperatures and pressures near the Planck scale.