arXiv:2506.09086v1 Announce Type: new
Abstract: We investigate the thermodynamic behavior of $(2+1)$ dimensional BTZ black holes using York’s cavity formalism, in which the black hole is enclosed within a finite-radius boundary held at a fixed temperature. This canonical ensemble construction enables the precise derivation of thermodynamic quantities such as temperature, energy, entropy, pressure, and heat capacity via the integral Euclidean path approach. Extending this analysis, we incorporate quantum corrections through Barrow entropy, a modified entropy law motivated by possible quantum-gravitational effects. The Barrow entropy is given by $S_B = (A_+/4)^{1+Delta}$, where $Delta in [0,1]$ represents the degree of fractalization of the horizon. For $Delta > 0$, we derive the corresponding generalized free energy $F_B$, which reveals that the thermodynamic phase structure changes with increasing $Delta$.The modified heat capacity of Barrow $C_B$ is also computed, which decreases with larger $Delta$, indicating suppressed thermal stability. Moreover, we study the influence of quantum effects on the thermal response, by calculating the corrected Joule Thomson coefficient $mu_B$ . We identify a well defined range $r_+ leq r leq 1.154,r_+$ within which a stable black hole configuration can spontaneously nucleate from a background of hot flat space. Together, our results highlight York’s cavity method as a robust tool to investigate black hole thermodynamics in lower dimensional gravity and show that Barrow’s entropy introduces physically significant corrections that could signal the influence of quantum gravity near the horizon.
Conclusions:
We have explored the thermodynamic properties of (2+1) dimensional BTZ black holes using York’s cavity formalism and incorporated quantum corrections through Barrow entropy. Our findings indicate a modification in the phase structure and decreased thermal stability with increasing fractalization of the horizon. The calculated Joule Thomson coefficient reveals a stable range for black hole nucleation in hot flat space, emphasizing the influence of quantum effects on black hole thermodynamics.
Future Roadmap:
- Further research into the implications of Barrow’s entropy on other black hole solutions in different dimensions could provide insights into the universality of these effects.
- Exploration of the applicability of York’s cavity formalism to higher dimensional black holes may shed light on the broader implications of quantum corrections in gravitational systems.
- Investigation into the observational signatures of these quantum-gravitational effects near black hole horizons could open new avenues for testing theories of quantum gravity.
Potential Challenges:
- Obtaining experimental data to validate the theoretical predictions of quantum corrections in black hole thermodynamics may pose a significant challenge.
- Theoretical consistency and compatibility with existing frameworks in quantum gravity need to be addressed to ensure the robustness of the proposed modifications.
Opportunities on the Horizon:
- Exploring the potential connection between quantum corrections near black hole horizons and emergent properties of spacetime could unveil novel insights into the nature of gravity.
- The development of new observational techniques and tools to detect signatures of quantum gravity effects in black hole thermodynamics may pave the way for experimental verification of these phenomena.