arXiv:2503.07679v1 Announce Type: new
Abstract: This paper investigates the thermodynamic properties of the coexistence region of two horizons in the charged 4-dimensional Einstein-Gauss-Bonnet (4D-EGB) spacetime. Initially, we apply the universal first law of thermodynamics to derive the corresponding thermodynamic quantities for the coexistence region between the black hole event horizon and the cosmological event horizon, subject to the relevant boundary conditions. Next we examine the thermal properties of the thermodynamic system described by these equivalent quantities. Our analysis reveals that the peak of the heat capacity as a function of temperature exhibits characteristics similar to those observed in a paramagnetic system under specific conditions. We further conclude that, under certain conditions, the heat capacity mirrors that of a two-level system formed by two horizons with distinct temperatures. By comparing the heat capacity of the 4D-EGB spacetime’s equivalent thermodynamic system with that of a two-level system defined by the two horizons in the spacetime, we can estimate the number of microscopic degrees of freedom at the two horizons. This findings sheds light on the quantum properties of de Sitter (dS) spacetime with two horizon interfaces and offers a novel approach to exploring the quantum properties of black holes and dS spacetime.
The Thermodynamic Properties of the Coexistence Region of Two Horizons in the Charged 4D-EGB Spacetime
This paper investigates the thermodynamic properties of the coexistence region between the black hole event horizon and the cosmological event horizon in the charged 4-dimensional Einstein-Gauss-Bonnet (4D-EGB) spacetime. By applying the universal first law of thermodynamics and considering the relevant boundary conditions, we derive the corresponding thermodynamic quantities for this coexistence region.
Thermal Properties of the Thermodynamic System
After obtaining the thermodynamic quantities, we examine the thermal properties of the system described by these equivalent quantities. Our analysis reveals that the heat capacity as a function of temperature exhibits characteristics similar to those observed in a paramagnetic system under specific conditions.
Heat Capacity Mirroring a Two-Level System
Furthermore, we conclude that, under certain conditions, the heat capacity mirrors that of a two-level system formed by the two horizons with distinct temperatures. This comparison of the heat capacity between the 4D-EGB spacetime’s equivalent thermodynamic system and the two-level system defined by the two horizons allows us to estimate the number of microscopic degrees of freedom at these horizons.
Roadmap for Future Investigations
The findings in this study shed light on the quantum properties of de Sitter (dS) spacetime with two horizon interfaces. Moving forward, there are several opportunities for further exploration:
- Quantum Properties of Black Holes: This research opens up a novel approach to exploring the quantum properties of black holes using the relation between heat capacity and two-level systems.
- Quantum Properties of dS Spacetime: The quantum properties of dS spacetime, especially with regards to the two horizon interfaces, offer interesting avenues for future investigations.
- Microscopic Degrees of Freedom: By estimating the number of microscopic degrees of freedom at the horizons, we can gain a better understanding of the underlying quantum nature of spacetime.
Potential Challenges
Despite the promising findings and opportunities, there are also challenges to address in future research:
- Validity of Assumptions: The conclusions of this study rely on certain assumptions and conditions. Further investigations should verify the validity of these assumptions and explore the robustness of the results.
- Quantum Gravity: Understanding the quantum properties of spacetime, including black holes and dS spacetime, requires a deeper understanding of quantum gravity. Integration with quantum gravity theories will be crucial for further progress.
- Experimental Verification: The findings in this study are theoretical in nature. Experimental verification or observational evidence will be necessary to validate the theoretical predictions.
In summary, this study explores the thermodynamic properties of the coexistence region between the black hole event horizon and the cosmological event horizon in the charged 4D-EGB spacetime. The analysis reveals similarities to paramagnetic systems and suggests that the thermodynamic system can be modeled as a two-level system. This opens up new avenues for investigating the quantum properties of black holes and dS spacetime. However, challenges such as verifying assumptions, integrating with quantum gravity, and experimental validation remain to be addressed in future research.