Interplay of Null Energy Condition Violations and Thermodynamics in Kiselev Black Hole Evaporation

Abstract

The evaporation of black holes with two horizons presents a rich thermodynamic landscape that departs fundamentally from the Schwarzschild paradigm. In this work, we analyze the Hawking temperature dynamics of the Kiselev black hole under varying mass $M$ and anisotropic fluid parameter $N$, explicitly connecting temperature behavior to phase transitions and violations of the null energy condition (NEC). We find that the temperature does not necessarily diverge during evaporation; instead, it typically falls to zero as the black hole evaporates. This cooling behavior is preceded, in certain parameter regimes, by a phase transition marked by a peak in temperature and a divergence in heat capacity. Crucially, the presence and nature of these phase transitions are dictated by the spacetime regions where the NEC is violated: global NEC violation leads to horizon merger and temperature suppression, while partial or absent violation can restore the standard evaporation picture. Our results establish a direct correspondence between thermodynamic stability, horizon dynamics, and energy condition structure in anisotropic black hole spacetimes.