New Construction of Black Hole Solution in Non-Commutative Geometry and Their Thermodynamic Properties

Abstract

In this work, we present a new construction of black hole solutions in non-commutative gauge theory by applying the Seiberg-Witten map directly to interaction potentials before solving Einstein's equations. This approach provides a dynamical effect of spacetime non-commutativity that preserves gauge covariance. We obtain both NC Schwarzschild and charged Reissner-Nordstrom-like black hole solutions, showing that the charged sector exhibits a novel branch dependence between attractive and repulsive electric interactions absent in the commutative limit. We analyze the geometrical properties, energy conditions, and thermodynamic properties of these spacetimes. Our results reveal that non-commutativity eliminates the temperature divergence at the final evaporation stage, inducing a second-order phase transition, or a Hawking-Page-like phase transition in the presence of pressure. Additionally, linear response analysis indicates high sensitivity to the NC parameter for small black holes. Finally, quantum tunneling investigations for both thermal and non-thermal radiation demonstrate that the NC deformation suppresses the particle-number density and weakens correlations between successive emissions, acting as a barrier to particle escape and supports the formation of a cold finite remnant. From a cosmological standpoint, since these stable remnant possess a fixed Planck-scale mass ($M^{\text{min}}\simeq2.73 M_{P}$), they provide a dynamically generated, purely gravitational cold dark matter candidate that aligns with dark universe phenomenology while simultaneously resolving the black hole information loss paradox.