arXiv:2404.16909v1 Announce Type: new
Abstract: In this paper, we study the relativistic correction to Bekenstein-Hawking entropy in the canonical ensemble and isothermal-isobaric ensemble and apply it to the cases of non-rotating BTZ and AdS-Schwarzschild black holes. This is realized by generalizing the equations obtained using Boltzmann-Gibbs(BG) statistics with its relativistic generalization, Kaniadakis statistics, or $kappa$-statistics. The relativistic corrections are found to be logarithmic in nature and it is observed that their effect becomes appreciable in the high-temperature limit suggesting that the entropy corrections must include these relativistically corrected terms while taking the aforementioned limit. The non-relativistic corrections are recovered in the $kapparightarrow 0$ limit.
Relativistic Correction to Bekenstein-Hawking Entropy
In this study, the authors analyze the relativistic correction to the Bekenstein-Hawking entropy in the canonical ensemble and isothermal-isobaric ensemble. They specifically focus on non-rotating BTZ and AdS-Schwarzschild black holes. The relativistic corrections are obtained by generalizing the equations derived from Boltzmann-Gibbs (BG) statistics using a relativistic generalization known as Kaniadakis statistics or $kappa$-statistics.
The authors find that the relativistic corrections exhibit a logarithmic behavior and are most pronounced at high temperatures. They emphasize the importance of including these relativistically corrected terms in entropy calculations when considering the high-temperature limit. Furthermore, in the $kapparightarrow 0$ limit, the non-relativistic corrections are recovered.
Future Roadmap: Challenges and Opportunities
Further research in this field holds significant challenges and opportunities. Here is an outline for a future roadmap:
1. Quantifying the Relativistic Corrections
- One key challenge is to develop a robust framework for quantifying the relativistic corrections to the Bekenstein-Hawking entropy.
- Exploring alternative statistical ensembles and methods for incorporating these corrections will contribute to a deeper understanding of the entropy in black hole systems.
- Investigating the impact of different spacetime geometries on the relativistic corrections can provide valuable insights into the interplay between gravity and entropy.
2. Experimental Verification
- An important opportunity lies in designing experiments or observational studies to verify the existence of these relativistic corrections in black hole systems.
- Collaboration between theoretical physicists and experimentalists may help develop novel techniques for detecting and measuring the relativistic effects on entropy.
- Exploring the connection between quantum information theory and black hole entropy can provide additional avenues for experimental verification.
3. Applications and Implications
- Understanding the relativistic corrections to the Bekenstein-Hawking entropy can have implications beyond black hole physics.
- Exploring the connection between entropy and thermodynamics in other relativistic systems, such as cosmological models or condensed matter systems, can lead to novel insights.
- Investigating the role of these corrections in the context of quantum gravity theories can shed light on the fundamental nature of spacetime and information.
In conclusion, the relativistic correction to Bekenstein-Hawking entropy, as studied in this paper, opens up a wide range of research opportunities. Addressing the challenges and pursuing the outlined roadmap can deepen our understanding of black hole physics, thermodynamics, and the fundamental nature of the universe.