by jsendak | Apr 25, 2025 | GR & QC Articles
arXiv:2504.16156v1 Announce Type: new
Abstract: We study a point scalar charge in circular orbit around a topological star, a regular, horizonless soliton emerging from dimensional compactification of Einstein-Maxwell theory in five dimensions, which could describe qualitative properties of microstate geometries for astrophysical black holes. This is the first step towards studying extreme mass-ratio inspirals around these objects. We show that when the particle probes the spacetime close to the object, the scalar-wave flux deviates significantly from the corresponding black hole case. Furthermore, as the topological star approaches the black-hole limit, the inspiral can resonantly excite its long-lived modes, resulting in sharp features in the emitted flux. Although such resonances are too narrow to produce detectable dephasing, we estimate that a year-long inspiral down to the innermost stable circular orbit could accumulate a significant dephasing for most configurations relative to the black hole case. While a full parameter-estimation analysis is needed, the generically large deviations are likely to be within the sensitivity reach of future space-based gravitational-wave detectors.
Future Roadmap: Challenges and Opportunities
Introduction
In this article, we examine the conclusions of a study that investigates a point scalar charge in circular orbit around a topological star. This star is a regular, horizonless soliton that emerges from the dimensional compactification of Einstein-Maxwell theory in five dimensions. The findings of this study have implications for understanding astrophysical black holes and the possibility of extreme mass-ratio inspirals (EMRIs) around them. In this roadmap, we outline potential challenges and opportunities that lie ahead in this field of research.
Challenges
- Resonant Excitations: One significant challenge identified in the study is the resonant excitation of long-lived modes in the topological star as it approaches the black hole limit. This resonance leads to sharp features in the emitted flux, which deviates significantly from the flux in a black hole case. Understanding the dynamics and behavior of these resonances will require further investigation.
- Dephasing Analysis: To fully quantify the impact of the resonances on the emitted flux, a comprehensive parameter-estimation analysis is needed. This analysis will help determine the extent of dephasing that occurs during an inspiral down to the innermost stable circular orbit. Conducting such an analysis is a challenging task that requires a detailed understanding of the underlying physics and computational techniques.
Opportunities
- Detectability: Despite the challenges, the study suggests that the deviations caused by the resonant excitation and dephasing are likely to be within the sensitivity reach of future space-based gravitational-wave detectors. This presents an exciting opportunity to observe and analyze these effects, potentially providing insights into the nature of microstate geometries for astrophysical black holes.
- Parameter Variation: Extending the study to explore a wide range of parameter configurations is an opportunity for future research. By varying different parameters, such as the mass and charge of the scalar particle, and the properties of the topological star, a more comprehensive understanding of the system’s behavior can be gained.
Conclusion
In conclusion, the study of a point scalar charge in circular orbit around a topological star has highlighted both challenges and opportunities for future research in the field of extreme mass-ratio inspirals around astrophysical black holes. Overcoming challenges such as understanding resonant excitations and conducting dephasing analysis will pave the way for further investigation. The potential to detect and analyze these effects using future space-based gravitational-wave detectors provides an exciting opportunity to deepen our understanding of black hole microstate geometries. Exploring a broader parameter space will also contribute to a more comprehensive understanding of the system’s behavior. The road ahead holds great potential for uncovering new insights into the nature of black holes in our universe.
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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 23, 2025 | GR & QC Articles
arXiv:2504.14159v1 Announce Type: new
Abstract: This article focuses on different anisotropic models within the framework of a specific modified $f(mathcal{R},mathcal{T},mathcal{R}_{zetagamma}mathcal{T}^{zetagamma})$ gravity theory. The study adopts a static spherically symmetric spacetime to determine the field equations for two different modified models: (i) $f(mathcal{R},mathcal{T},mathcal{R}_{zetagamma}mathcal{T}^{zetagamma})=mathcal{R}+etamathcal{R}_{zetagamma}mathcal{T}^{zetagamma}$, and (ii) $f(mathcal{R},mathcal{T},mathcal{R}_{zetagamma}mathcal{T}^{zetagamma})=mathcal{R}(1+etamathcal{R}_{zetagamma}mathcal{T}^{zetagamma})$, where $eta$ is a constant parameter. To address the additional degrees of freedom in the field equations and obtain their corresponding unique solution, the Durgapal-Fuloria spacetime geometry and MIT bag model are utilized. Matching conditions are applied to determine unknown constants within the chosen spacetime geometry. We adopt a certain range of model parameters to analyze the physical characteristics of the developed models in the interior distribution of a particular compact star candidate 4U 1820-30. Energy conditions and some other tests are also implemented to ensure their viability and stability. Additionally, the disappearing radial pressure constraint is employed to find the values of the model parameter, aligning with the observed information of an array of stars. The study concludes that both of our models are well-behaved and satisfy all necessary conditions, and thus we observe them suitable for the modeling of astrophysical objects.
The study focuses on different anisotropic models within the framework of a modified $f(mathcal{R},mathcal{T},mathcal{R}_{zetagamma}mathcal{T}^{zetagamma})$ gravity theory. It examines two specific modified models and applies them to the Durgapal-Fuloria spacetime geometry and MIT bag model to determine unique solutions for the field equations. Matching conditions are used to determine unknown constants, and various tests and constraints are applied for viability and stability.
The study finds that both models are well-behaved and satisfy necessary conditions, making them suitable for modeling astrophysical objects. Based on these conclusions, a future roadmap for readers could include the following:
1. Further Exploration of Anisotropic Models
- Readers can delve deeper into the concept of anisotropic models within the modified $f(mathcal{R},mathcal{T},mathcal{R}_{zetagamma}mathcal{T}^{zetagamma})$ gravity theory.
- They can explore other modifications or variations of the theory to investigate different aspects of anisotropy.
- Further research can be conducted to understand the implications and applications of anisotropic models in astrophysics.
2. Study of Different Spacetime Geometries
- Readers can explore other spacetime geometries and analyze their compatibility with the modified models.
- Investigation into the behavior of the field equations and unique solutions in various spacetime geometries can provide further insights into the models’ applicability.
3. Validation and Comparison with Observational Data
- The study demonstrates the viability and stability of the models; however, readers can engage in the validation process by comparing the models’ predictions with observational data.
- Exploring the behavior of the models in different astrophysical environments and comparing their results with existing knowledge can provide a better understanding of their accuracy.
Challenges and Opportunities
While the study presents promising results, there are potential challenges and opportunities on the horizon:
- Complexity of Field Equations: The modifications in the gravity theory lead to additional degrees of freedom in the field equations. Further research is needed to understand the implications and consequences of these additional degrees of freedom.
- Availability of Observational Data: Comparing the models with observational data requires access to relevant and accurate information. The availability and quality of such data may vary, presenting challenges in validating the models.
- Extensions and Generalizations: Researchers can explore further extensions or generalizations of the modified models to incorporate other physical phenomena or address specific astrophysical scenarios. These extensions may open up new avenues for investigation and application.
- Collaboration and Interdisciplinary Research: Given the complexity and interdisciplinary nature of astrophysics and theoretical physics, collaboration between researchers from different disciplines can enhance the understanding and development of anisotropic models.
Overall, the conclusions of the study provide a foundation for readers to explore anisotropic models within the modified gravity theory framework. By further investigating different spacetime geometries, validating the models with observational data, addressing challenges, and exploring opportunities, readers can contribute to the advancement of astrophysics and theoretical physics.
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by jsendak | Apr 21, 2025 | GR & QC Articles
arXiv:2504.13222v1 Announce Type: new
Abstract: Einstein’s perihelion advance formula can be given a geometric interpretation in terms of the curvature of the ellipse. The formula can be obtained by splitting the constant term of an auxiliary polar equation for an elliptical orbit into two parts that, when combined, lead to the expression of this relativistic effect. Using this idea, we develop a general method for dealing with orbital precession in the presence of central perturbing forces, and apply the method to the determination of the total (relativistic plus Newtonian) secular perihelion advance of the planet Mercury.
Einstein’s Perihelion Advance Formula: A Geometric Interpretation
In a recent study, researchers have found a geometric interpretation for Einstein’s perihelion advance formula, shedding new light on this relativistic effect. The formula, which describes the precession of a planet’s orbit around the sun, can now be understood in terms of the curvature of the ellipse.
The Geometric Interpretation
The researchers propose a method for obtaining the perihelion advance formula by splitting the constant term of an auxiliary polar equation for an elliptical orbit into two parts. These two parts, when combined, give rise to the expression of the relativistic effect. This geometric interpretation not only provides a deeper understanding of the formula but also opens up new possibilities for studying orbital precession in the presence of central perturbing forces.
A General Method for Orbital Precession
Building on this geometric interpretation, the researchers develop a general method for dealing with orbital precession in the presence of central perturbing forces. This method can be applied to a wide range of astronomical systems, allowing for a comprehensive understanding of the dynamics involved. By considering both the relativistic and Newtonian contributions, the researchers aim to determine the total secular perihelion advance of planets.
Potential Challenges
While the geometric interpretation of the perihelion advance formula offers exciting possibilities, there are also challenges that need to be addressed. One potential challenge is the complexity of the calculations involved, as dealing with central perturbing forces can be mathematically intricate. Additionally, the applicability of this method to other astronomical systems needs to be carefully examined to ensure its validity.
Opportunities on the Horizon
The research presents a significant opportunity to further our understanding of orbital dynamics and advance our knowledge of celestial mechanics. With a more comprehensive method for dealing with orbital precession, scientists can explore the behavior of various astronomical objects and uncover new insights into the nature of the universe. Moreover, this geometric interpretation may inspire further research in related areas and lead to the development of novel approaches for studying gravitational effects in celestial systems.
Conclusion
By providing a geometric interpretation for Einstein’s perihelion advance formula, this research offers a fresh perspective on orbital precession. The general method developed for dealing with central perturbing forces opens up new avenues for exploring the dynamics of astronomical systems. Although challenges and uncertainties remain, there is great potential for further advancement in our understanding of celestial mechanics and the fundamental laws of physics.
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by jsendak | Apr 18, 2025 | GR & QC Articles
arXiv:2504.12370v1 Announce Type: new
Abstract: In our previous work [Van de Moortel, The breakdown of weak null singularities, Duke Mathematical Journal 172 (15), 2957-3012, 2023], we showed that dynamical black holes formed in charged spherical collapse generically feature both a null weakly singular Cauchy horizon and a stronger (presumably spacelike) singularity, confirming a longstanding conjecture in the physics literature. However, this previous result, based on a contradiction argument, did not provide quantitative estimates on the stronger singularity.
In this study, we adopt a new approach by analyzing local initial data inside the black hole that are consistent with a breakdown of the Cauchy horizon. We prove that the remaining portion is spacelike and obtain sharp spacetime estimates near the null-spacelike transition. Notably, we show that the Kasner exponents of the spacelike portion are positive, in contrast to the well-known Oppenheimer-Snyder model of gravitational collapse. Moreover, these exponents degenerate to (1,0,0) towards the null-spacelike transition.
Our result provides the first quantitative instances of a null-spacelike singularity transition inside a black hole. In our companion paper, we moreover apply our analysis to carry out the construction of a large class of asymptotically flat one or two-ended black holes featuring coexisting null and spacelike singularities.
Future Roadmap
Challenges
- Quantitative estimation of the stronger singularity: The previous work did not provide quantitative estimates on the stronger singularity. This poses a challenge in understanding the nature and properties of this singularity.
- Analysis of local initial data: The new approach requires analyzing local initial data inside the black hole that are consistent with a breakdown of the Cauchy horizon. This may require advanced mathematical techniques and computational simulations.
- Construction of a large class of black holes: The companion paper aims to construct a large class of asymptotically flat one or two-ended black holes with coexisting null and spacelike singularities. This task may involve complex mathematical calculations and modeling.
Opportunities
- Confirmation of a longstanding conjecture: The study confirms a longstanding conjecture in the physics literature regarding the presence of both null weakly singular Cauchy horizons and stronger (presumably spacelike) singularities in dynamical black holes formed in charged spherical collapse. This provides an opportunity to further probe the nature of black holes and test existing theories.
- Understanding spacetime estimates near the null-spacelike transition: The new analysis provides sharp spacetime estimates near the null-spacelike transition. This opens up opportunities to investigate the behavior and characteristics of spacetime in the vicinity of this transition.
- Exploring the Kasner exponents: The discovery that the Kasner exponents of the spacelike portion are positive, in contrast to the Oppenheimer-Snyder model, presents an opportunity to study and understand the role of these exponents in black hole formation and evolution.
Conclusion: The future roadmap for readers of this study involves addressing the challenges of quantitatively estimating the stronger singularity, analyzing local initial data, and constructing a large class of black holes with coexisting singularities. These efforts present opportunities to confirm a longstanding conjecture, gain insights into spacetime estimates near the null-spacelike transition, and explore the significance of Kasner exponents in black hole dynamics.
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by jsendak | Apr 17, 2025 | GR & QC Articles
arXiv:2504.11471v1 Announce Type: new
Abstract: We develop an analytic model that extends classical white hole geometry by incorporating both radiative dynamics and electric charge. Starting from a maximal analytic extension of the Schwarzschild white hole via Kruskal Szekeres coordinates, we introduce a time dependent mass function, representative of outgoing null dust to model evaporation. Building on this foundation, the study then integrates the Reissner-Nordstr”om framework to obtain a dynamic, charged white hole solution in double null coordinates. In the resulting Vaidya Reissner Nordstr”om metric, both the Bondi mass and the associated charge decrease monotonically with retarded time, capturing the interplay of radiation and electromagnetic effects. Detailed analysis of horizon behavior reveals how mass loss and charge shedding modify the causal structure, ensuring that energy conditions are preserved and cosmic censorship is maintained.
Analyzing the Conclusions of the Text
The text introduces an analytic model that extends classical white hole geometry by incorporating radiative dynamics and electric charge. The model starts with a maximal analytic extension of the Schwarzschild white hole using Kruskal-Szekeres coordinates. It then introduces a time-dependent mass function to model evaporation. By integrating the Reissner-Nordstr”om framework, a dynamic, charged white hole solution in double null coordinates is obtained. The resulting Vaidya Reissner-Nordstr”om metric shows that both the Bondi mass and the associated charge decrease with retarded time, capturing the interplay of radiation and electromagnetic effects. Additionally, the analysis of the horizon behavior shows how mass loss and charge shedding modify the causal structure while preserving energy conditions and maintaining cosmic censorship.
Future Roadmap
1. Further Exploration of the Model
- Continued research can focus on exploring the properties and implications of the developed analytic model.
- Conduct numerical simulations to validate and refine the model’s predictions and understand its behavior under different conditions.
- Investigate the model’s applicability in various astrophysical scenarios, such as black hole evaporation and cosmological phenomena.
2. Experimental Verification
- Collaborate with observational astronomers and physicists to design experiments or observations that can provide empirical evidence supporting the predictions of the analytic model.
- Explore possibilities for detecting the effects of radiative dynamics and electric charge in white hole-like objects, if they exist in the universe.
3. Theoretical Extensions
- Extend the model to incorporate other factors that play a role in gravitational phenomena, such as angular momentum and quantum effects.
- Explore possible connections between the developed model and other theories, such as quantum gravity or string theory.
Potential Challenges
- One potential challenge is the complexity of the mathematical framework used in the model. Further research might be required to fully understand and utilize it effectively.
- Experimental verification could be challenging due to the rarity or nonexistence of white holes, making direct observations or experiments difficult.
- Addressing the limitations and assumptions of the model, and potentially refining or expanding it to account for more realistic scenarios, may pose theoretical challenges.
Potential Opportunities
- The developed model opens up possibilities for better understanding the behavior and properties of white holes, which are still largely unexplored.
- Exploring the interplay of radiation and electromagnetic effects in the context of white holes may lead to new insights into the relationship between gravity and quantum mechanics.
- The model provides a solid foundation for further research and theoretical advancements in the field of gravitational physics.
- If empirical evidence supports the model’s predictions, it could revolutionize our understanding of the universe and the nature of spacetime.
Overall, the presented analytic model provides a valuable framework for studying white hole geometries with radiative dynamics and electric charge. The roadmap for future research involves further exploration, experimental verification, and theoretical extensions. While challenges exist in terms of complexity, the rarity of white holes, and theoretical limitations, the opportunities for advancing our understanding of the universe and gravity are immense.
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