Spacetime Foam Effects on Charged AdS Black Hole Thermodynamics

Abstract: In this paper, we investigate the emergent thermodynamic phenomena arising from spacetime foam and its impact on black hole behavior. Within this framework, we adopt the Barrow model, where the structure of spacetime at small scales is modeled by analogy with the Koch snowflake, implying that black hole surfaces acquire a quasi-fractal structure due to quantum deformations induced by quantum gravity effects. Our analysis, conducted within the extended phase-space formalism, reveals that the quasi-fractal correction to black hole entropy significantly modifies the equation of state, critical parameters, and phase-transition behavior of charged AdS black holes. An increase in the Barrow parameter leads to higher critical pressure and temperature, which diverge at maximal deformation. Moreover, while the quasi-fractal structure has a negligible effect on small black holes with low entropy, it clearly influences the thermal evolution of medium and large event horizon black holes. Additionally, we study the impact of quasi-fractal corrections on the Joule-Thomson expansion and the phase transition between cooling and heating regimes. We also examine the effects of spacetime structure on black hole microstate density, lifetimes, and temperature detection by different observers, including local, asymptotic, and Unruh detectors. We find that spacetime foam increases microstate density and prolongs evaporation lifetimes, thus acting as a resistance to black hole evaporation, while local observers experience that the expected Tolman blueshift and Unruh temperatures remain unmodified.