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

TL;DR

This paper investigates how violations of the null energy condition influence the thermodynamics and evaporation process of Kiselev black holes with two horizons, revealing complex phase transitions and horizon behaviors.

Contribution

It provides a detailed analysis of the connection between NEC violations, phase transitions, and thermodynamic properties in anisotropic black hole spacetimes, highlighting new effects on evaporation dynamics.

Findings

Temperature typically decreases to zero during evaporation.

Phase transitions occur with temperature peaks and heat capacity divergence.

NEC violations influence horizon merger and evaporation behavior.

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.