## Phase Transitions in Dyonic AdS Black Holes with QTE in EGB Background

arXiv:2403.14730v1 Announce Type: new

Abstract: In this study, we employ the thermodynamic topological method to classify critical points for the dyonic AdS black holes with QTE in the EGB background. To this end, we find that there is a small/large BH phase transition in any space-time dimension, a conventional critical point exists with the total topological charge of $Q_t=-1$. The existence of the coupling constant $alpha$ gives rise to a more intricate phase structure of the black hole, with the emergence of a triple points requires $alphageq0.5$ and $d=6$. Interestingly, the condition for the simultaneous occurrence of small/intermediate and intermediate/large phase transition is that the coupling constant a takes a special value ($alpha=0.5$), the two conventional critical points $(CP_{1},CP_{2})$ of the black hole are (physical) critical point, and the novel critical point that lacks the capability to minimize the Gibbs free energy. The critical point ($Q_{CP_1}=Q_{CP_2}=-1$) is observed to occur at the maximum extreme points of temperature in the isobaric curve, while the critical point $(Q_{CP_3}=1)$, emerges at the minimum extreme points of temperature. Furthermore, the number of phases at the novel critical point exhibits an upward trend, followed by a subsequent decline at the conventional critical points. With the increase of the coupling constant $(alpha = 1 )$, although the system has three critical points, only $CP_{1}$ is a (physical) critical point, and the $CP_{2}$ serves as the phase annihilation point. This means that the coupling constant $alpha$ has a non-negligible effect on the phase structure of the black hole.

In this study, the thermodynamic topological method is used to classify critical points for dyonic AdS black holes with QTE in the EGB background. The researchers find that there is a small/large black hole phase transition in any space-time dimension and a conventional critical point exists with a total topological charge of $Q_t=-1$. The presence of the coupling constant $alpha$ results in a more complex phase structure for the black hole, including the emergence of a triple point at $alphageq0.5$ and $d=6$. Interestingly, the simultaneous occurrence of small/intermediate and intermediate/large phase transitions requires a special value of the coupling constant ($alpha=0.5$). The black hole has two conventional critical points $(CP_{1},CP_{2})$, which are physical critical points, and a novel critical point that cannot minimize the Gibbs free energy. The critical point ($Q_{CP_1}=Q_{CP_2}=-1$) is observed at the maximum extreme points of temperature in the isobaric curve, while the critical point $(Q_{CP_3}=1)$ emerges at the minimum extreme points of temperature. The number of phases at the novel critical point initially increases and then decreases at the conventional critical points. Increasing the coupling constant $(alpha = 1)$ results in three critical points, but only $CP_{1}$ is a physical critical point, with $CP_{2}$ serving as the phase annihilation point. Therefore, the coupling constant $alpha$ has a significant effect on the phase structure of the black hole.

## Future Roadmap

### Challenges

- Further research is needed to understand the implications and consequences of the small/large black hole phase transition in different space-time dimensions.
- Exploring the intricate phase structure of black holes with the presence of the coupling constant $alpha$ in various scenarios and dimensions.
- Determining the physical significance and potential applications of the triple point at $alphageq0.5$ and $d=6$ in the phase structure of black holes.
- Investigating the nature and properties of the novel critical point that lacks the capability to minimize the Gibbs free energy.
- Understanding the reasons behind the upward trend followed by a subsequent decline in the number of phases at the novel critical point and conventional critical points.

### Opportunities

- Exploring the role of the coupling constant $alpha$ in modifying the phase structure of black holes and its implications in other areas of physics.
- Investigating the connections between the presence of critical points and the thermodynamic properties of black holes.
- Expanding the thermodynamic topological method to study other types of black holes and their phase transitions.
- Exploring potential applications of the novel critical point with unique properties in thermodynamics and related fields.
- Utilizing the knowledge gained from this study to develop new theoretical frameworks and models for understanding black holes and their behavior.