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The Barrow entropies in the thermodynamics of high-dimensional Gauss-Bonnet black holes

Yuxuan Shi, Hongbo Cheng

Abstract

We study the thermodynamics of $D$-dimensional Gauss-Bonnet black holes with Barrow entropy. It is found that the Gauss-Bonnet coupling and the Barrow factor revise the thermodynamic variables such as event horizon, Hawking temperature, entropy and heat capacity. It is interesting that the larger five-dimensional black holes exist stably and the smaller ones evaporate to disappear owing to the nature of heat capacities amended by the coupling and factor. The discussions exhibit that the $D$-dimensional black holes with $D=6, 7$ set free all of their energy to vanish because of the minus heat capacities as functions of Hawking temperature although the extra term and the fractal power bring about their revisions on the functions, but they cannot change the heat capacity signs, so they also cannot change the fate of six- or seven-dimensional black holes.

The Barrow entropies in the thermodynamics of high-dimensional Gauss-Bonnet black holes

Abstract

We study the thermodynamics of -dimensional Gauss-Bonnet black holes with Barrow entropy. It is found that the Gauss-Bonnet coupling and the Barrow factor revise the thermodynamic variables such as event horizon, Hawking temperature, entropy and heat capacity. It is interesting that the larger five-dimensional black holes exist stably and the smaller ones evaporate to disappear owing to the nature of heat capacities amended by the coupling and factor. The discussions exhibit that the -dimensional black holes with set free all of their energy to vanish because of the minus heat capacities as functions of Hawking temperature although the extra term and the fractal power bring about their revisions on the functions, but they cannot change the heat capacity signs, so they also cannot change the fate of six- or seven-dimensional black holes.

Paper Structure

This paper contains 9 sections, 20 equations, 15 figures.

Table of Contents

  1. Introduction
  2. Theoretical Framework and Thermodynamic Quantities
  3. Thermodynamic Stability and Phase Transitions
  4. Behavior of Hawking Temperature
  5. Entropy-Temperature Relation and Stability
  6. Local Thermodynamic Stability Analysis
  7. Conclusion and Discussion
  8. Explicit Form of Heat Capacity
  9. Thermodynamic Behaviors in D=7

Figures (15)

  • Figure 1: The Hawking temperature $T_{GBB}$ as a function of the horizon radius $r_+$ for a fixed Gauss-Bonnet coupling $\alpha=0.1$. The black curves represent $D=5$ cases, while the red curves represent $D=6$. Different line styles correspond to different Barrow parameters: $\Delta=0.0$ (solid), $\Delta=0.5$ (dashed), and $\Delta=1.0$ (dotted).
  • Figure 2: The Hawking temperature $T_{GBB}$ as a function of $r_+$ for a fixed Barrow parameter $\Delta=0.5$. The black curves ($D=5$) and red curves ($D=6$) show the effect of varying the Gauss-Bonnet coupling: $\alpha=0.1$ (solid), $\alpha=0.3$ (dashed), and $\alpha=0.5$ (dotted).
  • Figure 3: The Entropy-Temperature $S_{GBB}-T_{GBB}$ diagrams for fixed $\alpha=0.1$. The presence of a cusp in the $D=5$ curves (black) indicates a phase transition, while the $D=6$ curves (red) show monotonic instability.
  • Figure 4: The $S_{GBB}-T_{GBB}$ diagrams for fixed $\Delta=0.5$ with varying Gauss-Bonnet coupling $\alpha$. Larger $\alpha$ shifts the critical point to lower temperatures.
  • Figure 5: The heat capacity $C_{V,GBB}$ versus Hawking temperature for fixed $\alpha=0.1$. The vertical dashed lines indicate the divergence of heat capacity for $D=5$ cases, marking the phase transition point. Note that for $D=6$ (red curves), the heat capacity is always negative.
  • ...and 10 more figures