by jsendak | Apr 24, 2025 | GR & QC Articles
arXiv:2504.15318v1 Announce Type: new
Abstract: We examine the impact of non-perturbative quantum corrections to the entropy of both charged and charged rotating quasi-topological black holes, with a focus on their thermodynamic properties. The negative-valued correction to the entropy for small black holes is found to be unphysical. Furthermore, we analyze the effect of these non-perturbative corrections on other thermodynamic quantities, including internal energy, Gibbs free energy, charge density, and mass density, for both types of black holes. Our findings indicate that the sign of the correction parameter plays a crucial role at small horizon radii. Additionally, we assess the stability and phase transitions of these black holes in the presence of non-perturbative corrections. Below the critical point, both the corrected and uncorrected specific heat per unit volume are in an unstable regime. This instability leads to a first-order phase transition, wherein the specific heat transitions from negative to positive values as the system reaches a stable state.
Examining Non-Perturbative Quantum Corrections to Black Hole Entropy
We explore the impact of non-perturbative quantum corrections on the entropy of charged and charged rotating quasi-topological black holes. The focus is on understanding the thermodynamic properties of these black holes and the implications of the corrections.
Unphysical Negative-Valued Corrections for Small Black Holes
Our analysis reveals that the non-perturbative correction leads to entropy values that are negative for small black holes. However, these negative values are considered unphysical. This discrepancy raises questions about the validity of the correction for small horizon radii.
Effects on Other Thermodynamic Quantities
In addition to entropy, we investigate the effects of non-perturbative corrections on various thermodynamic quantities such as internal energy, Gibbs free energy, charge density, and mass density. These quantities can provide further insights into the behavior of these black holes.
Significance of Correction Parameter at Small Horizon Radii
Our findings highlight the importance of the sign of the correction parameter for measuring the thermodynamic properties of black holes with small horizon radii. This observation suggests that the correction parameter may play a crucial role in understanding the physics at this scale.
Stability and Phase Transitions
We also assess the stability and phase transitions of these black holes considering the presence of non-perturbative corrections. Our results show that both the corrected and uncorrected specific heat per unit volume are in an unstable regime below the critical point. This instability leads to a first-order phase transition where the specific heat transitions from negative to positive values as the system reaches a stable state.
Roadmap to the Future
While this study provides valuable insights into the effects of non-perturbative quantum corrections on the thermodynamic properties of black holes, there are several challenges and opportunities to be addressed in future research.
Challenges
- Validity of unphysical negative entropy values for small black holes
- Understanding the underlying reasons for the instability of specific heat per unit volume in the unstable regime
- Further investigation into the role of the correction parameter at small horizon radii
Opportunities
- Exploring alternative approaches to account for non-perturbative quantum corrections
- Investigating the implications of these corrections on other black hole properties beyond thermodynamics
- Examining the connection between non-perturbative corrections and quantum gravitational effects
Overall, the study of non-perturbative quantum corrections to black hole thermodynamics opens up new avenues for understanding the fundamental nature of black holes and the interplay between quantum mechanics and gravity. Further research in this area will contribute to a deeper understanding of black hole physics and its theoretical implications.
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by jsendak | Apr 15, 2025 | GR & QC Articles
arXiv:2504.08796v1 Announce Type: new
Abstract: This paper employs Laurent series expansions and the Robson–Villari–Biancalana (RVB) method to provide a refined derivation of the Hawking temperature for two newly introduced topological black hole solutions. Previous calculations have demonstrated inconsistencies when applying traditional methods to such exotic horizons, prompting the need for a more thorough mathematical analysis. By systematically incorporating higher-order terms in the Laurent expansions of the metric functions near the horizon and leveraging the topological features characterized by the Euler characteristic, we reveal additional corrections to the Hawking temperature beyond standard approaches. These findings underscore the subtle interplay between local geometry, spacetime topology, and quantum effects. The results clarify discrepancies found in earlier works, present a more accurate representation of thermodynamic properties for the black holes in question, and suggest broader implications for topological structures in advanced gravitational theories.
Refining the Derivation of Hawking Temperature for Topological Black Holes
In this paper, we employ Laurent series expansions and the Robson-Villari-Biancalana (RVB) method to provide a refined derivation of the Hawking temperature for two recently discovered topological black hole solutions. Previous calculations have shown inconsistencies when using traditional methods on such exotic horizons, necessitating a more comprehensive mathematical analysis.
By incorporating higher-order terms in the Laurent expansions of the metric functions near the horizon and utilizing the topological attributes defined by the Euler characteristic, we uncover additional corrections to the Hawking temperature that go beyond standard approaches. These findings highlight the intricate interplay between local geometry, spacetime topology, and quantum effects.
The results of our study address the discrepancies identified in earlier works, offering a more precise depiction of the thermodynamic properties associated with the black holes under investigation. Moreover, these findings have broader implications for the understanding of topological structures in advanced gravitational theories.
The Future Roadmap
Potential Challenges
- Verification and Validation: As with any theoretical work, it is crucial to validate the results through experimental verification or comparison with other mathematical models.
- Generalization: The application and extension of this refined derivation to other topological black hole solutions will be a challenge, as each solution may have its distinct characteristics and complexities.
- Physical Interpretation: The interpretation of the additional corrections to the Hawking temperature and their implications for the black holes’ physical behavior will require further investigation and understanding.
Opportunities on the Horizon
- Advancements in Gravitational Theories: The refined derivation presented in this paper opens up new avenues for exploring the interplay between topology, geometry, and quantum effects in gravitational theories. It may lead to the development of more comprehensive theories or refine existing ones.
- Improved Understanding of Exotic Horizons: The insights gained from this study will contribute to a better understanding of the thermodynamic properties and behavior of topological black holes. This knowledge can lead to advancements in fields such as black hole thermodynamics and cosmology.
- Broader Implications: The implications of our findings extend beyond the specific topological black hole solutions examined in this study. They may have implications for other physical systems with topological structures and shed light on the connection between topology and quantum effects in various scientific domains.
Note: This paper is accompanied by extensive mathematical derivations, which are not included in this summary for brevity. Please refer to the full paper for a detailed analysis.
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by jsendak | Dec 20, 2024 | GR & QC Articles
arXiv:2412.14230v1 Announce Type: new
Abstract: We find an exact black hole solution for the Einstein gravity in the presence of Ay’on–Beato–Garc’ia non-linear electrodynamics and a cloud of strings. The resulting black hole solution is singular, and the solution becomes non-singular when gravity is coupled with Ay’on–Beato–Garc’ia non-linear electrodynamics only. This solution interpolates between Ay’on–Beato–Garc’ia black hole, Letelier black hole and Schwarzschild black hole { in the absence of cloud of strings parameter, magnetic monopole charge and both of them, respectively}. We also discuss the thermal properties of this black hole and find that the solution follows the modified first law of black hole thermodynamics. Furthermore, we estimate the solution’s black hole shadow and quasinormal modes.
Conclusion
The article presents an exact black hole solution for the Einstein gravity in the presence of Ay’on–Beato–Garc’ia non-linear electrodynamics and a cloud of strings. The solution is initially singular but becomes non-singular when gravity is coupled with Ay’on–Beato–Garc’ia non-linear electrodynamics only. This solution connects Ay’on–Beato–Garc’ia black hole, Letelier black hole, and Schwarzschild black hole in different scenarios. The thermal properties of the black hole are discussed, and it follows the modified first law of black hole thermodynamics. Additionally, the article estimates the black hole shadow and quasinormal modes of the solution.
Future Roadmap
Potential Challenges
- One potential challenge in the future is to further investigate the singularity of the black hole solution and understand its physical implications.
- It would be valuable to explore the behavior of the black hole solution under different scenarios, such as considering the presence of magnetic monopole charge or a cloud of strings parameter.
- Another challenge is to validate the results experimentally or through observational data.
Potential Opportunities
- Further research can be conducted to understand the relationship between Ay’on–Beato–Garc’ia non-linear electrodynamics and the non-singularity of the black hole solution.
- The modified first law of black hole thermodynamics observed in this solution opens up opportunities for exploring the thermodynamic properties of other exact black hole solutions.
- The estimation of the black hole shadow and quasinormal modes can be improved and refined, providing more accurate predictions for future observations.
In conclusion, the article presents an intriguing exact black hole solution with interesting properties. The future roadmap involves addressing potential challenges related to the singularity, conducting further investigations under different scenarios, and validating the results. Additionally, there are exciting opportunities to explore the relationship between Ay’on–Beato–Garc’ia non-linear electrodynamics and non-singularity, study the thermodynamic properties of other black hole solutions, and refine estimations of the black hole shadow and quasinormal modes.
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by jsendak | Dec 9, 2024 | GR & QC Articles
arXiv:2412.04513v1 Announce Type: new
Abstract: This paper aims to explore the quasinormal modes (QNMs) and effective potential profiles of massless and rotating BTZ black holes within the frameworks of $f(mathcal{R})$ and Ricci-Inverse ($mathcal{RI}$) modified gravity theories, which, while producing similar space-time structures, exhibit variations due to distinct cosmological constants, $Lambda_m$. We derive wave equations for these black hole perturbations and analyze the behavior of the effective potential $V_{text{eff}}(r)$ under different values of mass $m$, cosmological constant $Lambda_m$, and modified gravity parameters $alpha_1$, $alpha_2$, $beta_1$, $beta_2$, and $gamma$. The findings indicate that increasing mass and parameter values results in a raised potential barrier, implying stronger confinement of perturbations and impacting black hole stability. Incorporating the generalized uncertainty principle, we also study its effect on the thermodynamics of rotating BTZ black holes, demonstrating how GUP modifies black hole radiation, potentially observable in QNM decay rates. Additionally, we investigate the motion of particles through null and timelike geodesics in static BTZ space-time, observing asymptotic behaviors for null geodesics and parameter-dependent shifts in potential for timelike paths. The study concludes that modified gravity parameters significantly influence QNM frequencies and effective potential profiles, offering insights into black hole stability and suggesting that these theoretical predictions may be tested through gravitational wave observations.
Analysis of Quasinormal Modes and Effective Potentials in Modified Gravity Theories
In this paper, we explore the quasinormal modes (QNMs) and effective potential profiles of massless and rotating BTZ black holes within the frameworks of $f(mathcal{R})$ and Ricci-Inverse ($mathcal{RI}$) modified gravity theories. These theories, although producing similar space-time structures, exhibit variations due to distinct cosmological constants, $Lambda_m$.
Wave Equations and Effective Potentials
We derive wave equations for the perturbations of these black holes and analyze the behavior of the effective potential $V_{text{eff}}(r)$ under different values of mass $m$, cosmological constant $Lambda_m$, and modified gravity parameters $alpha_1$, $alpha_2$, $beta_1$, $beta_2$, and $gamma$.
The findings of our analysis indicate that increasing mass and parameter values result in a raised potential barrier. This higher potential barrier implies stronger confinement of perturbations and has implications for black hole stability.
Impact of Generalized Uncertainty Principle (GUP)
Incorporating the generalized uncertainty principle (GUP), we also study its effect on the thermodynamics of rotating BTZ black holes. We demonstrate how GUP modifies black hole radiation, potentially observable in QNM decay rates.
Motion of Particles Through Geodesics
Additionally, we investigate the motion of particles through null and timelike geodesics in static BTZ space-time. We observe asymptotic behaviors for null geodesics and parameter-dependent shifts in the potential for timelike paths.
Conclusions and Future Roadmap
Our study concludes that modified gravity parameters have a significant influence on QNM frequencies and effective potential profiles. These findings offer insights into black hole stability and suggest that these theoretical predictions may be tested through gravitational wave observations.
For future research, there are several potential challenges and opportunities on the horizon:
- Further exploration of the impact of modified gravity parameters on the stability and properties of black holes in different space-time configurations.
- Investigation of the implications of GUP on other phenomena related to black hole thermodynamics and radiation.
- Study of the effects of modified gravity theories on other astrophysical objects and phenomena, such as neutron stars and gravitational lensing.
- Development of experimental strategies to test the theoretical predictions using gravitational wave observations and other observational techniques.
- Consideration of possible extensions of the current theories, such as higher-dimensional modifications or inclusion of additional interaction terms.
In summary, the exploration of quasinormal modes and effective potentials in modified gravity theories provides valuable insights into the behavior of black holes and the implications of alternative gravitational theories. The future roadmap outlined above promises exciting opportunities to further our understanding of these phenomena and to test the predictions of these theories through experimental observations.
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by jsendak | Dec 3, 2024 | GR & QC Articles
arXiv:2411.18693v1 Announce Type: new
Abstract: The theory of general relativity is often considered under the framework of modified Einstein gravity to explain different phenomena under strong curvature. The strong curvature effect plays a main role near black holes, where the gravitational field is strongest. The idea of black hole thermodynamics is to describe the strong field curvature properties of a black hole in the effective thermodynamical framework, e.g. entropy, temperature, heat capacity etc. In this paper, our aim is to explore how the effect of modified gravity changes the thermodynamic properties of black hole. We show that even a small modification to Einstein gravity affects the thermodynamical properties of a black hole.
Exploring the Impact of Modified Gravity on Black Hole Thermodynamics
In the realm of physics, the theory of general relativity has been widely used to understand the behavior of objects in the presence of strong gravitational fields. However, there is a growing interest in exploring modified versions of Einstein gravity to explain various phenomena that occur under intense curvature.
One particular area of focus is the thermodynamic properties of black holes. Black holes are known for their immensely strong gravitational fields, where the effects of curvature are most pronounced. The concept of black hole thermodynamics aims to analyze these strong field curvature properties through the lens of effective thermodynamics, involving concepts such as entropy, temperature, and heat capacity.
In this paper, we aim to investigate the impact of modified gravity on the thermodynamic properties of black holes. By introducing small modifications to the traditional framework of Einstein gravity, we will explore how these alterations affect the behavior of black holes within the realm of thermodynamics.
We hypothesize that even a minor modification to Einstein gravity can have a significant impact on the thermodynamics of black holes. By studying these effects, we hope to uncover new insights into the nature of black holes and their fundamental properties.
Roadmap for Future Research
To explore the impact of modified gravity on black hole thermodynamics, the following roadmap can be proposed:
- Identify specific modifications to the framework of Einstein gravity that will be studied.
- Develop mathematical models and equations that describe the behavior of black holes under these modifications.
- Simulate and calculate thermodynamic properties of black holes using these modified equations.
- Analyze and compare the results with the traditional Einstein gravity framework to identify any significant differences.
- Conduct further experiments or observations to validate the findings.
- Extend the study to explore the implications of these modified thermodynamic properties on other aspects of black hole physics.
Challenges and Opportunities
The road ahead is not without its challenges. Some potential obstacles and opportunities include:
- Theoretical Complexity: Developing mathematical models for modified gravity can be highly complex and require advanced mathematical techniques. Researchers must be prepared to tackle these challenges head-on.
- Data Limitations: Obtaining accurate observational data on black holes and their thermodynamic properties can be challenging. Collaboration with astronomers and astrophysicists will be crucial in gathering the necessary data for analysis.
- New Insights: Exploring modified gravity offers an opportunity to uncover new insights into the fundamental nature of black holes. These findings may have implications beyond thermodynamics and could contribute to a deeper understanding of the universe.
- The interdisciplinary nature of this research requires collaboration between physicists, mathematicians, astronomers, and astrophysicists. Leveraging diverse expertise will enhance the quality and scope of the study.
“By investigating the impact of modified gravity on black hole thermodynamics, we have the potential to advance our understanding of these enigmatic cosmic objects. Through theoretical exploration and collaboration, we can uncover new insights into the fundamental nature of black holes.”
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