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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by jsendak | Dec 6, 2024 | GR & QC Articles
arXiv:2412.02705v1 Announce Type: new
Abstract: Ehlers and Kundt [1] argued in favor of the velocity effect: particles initally at rest hit by a burst of gravitational waves should fly apart with constant velocity after the wave has passed. Zel’dovich and Polnarev [2] suggested instead that waves generated by flyby would be merely displaced. Their prediction is confirmed provided the wave parameters take some particular values.
Article: The Velocity Effect and the Displacement of Gravitational Waves
In a recent paper, Ehlers and Kundt argued in favor of the velocity effect in the context of gravitational waves. According to their hypothesis, particles that are initially at rest and then hit by a burst of gravitational waves should fly apart with a constant velocity after the wave has passed [1]. This claim challenges the previous suggestion made by Zel’dovich and Polnarev, who proposed that waves generated by a flyby would be merely displaced [2]. However, Zel’dovich and Polnarev’s prediction is upheld when the wave parameters take specific values.
Future Roadmap: Challenges and Opportunities
While the debate between the velocity effect and the displacement of gravitational waves continues, researchers can explore various avenues to validate or disprove these hypotheses. The following future roadmap outlines potential challenges and opportunities on the horizon:
- Experimental Verification: Conducting experiments in controlled environments will be crucial in determining the behavior of particles when subjected to gravitational wave bursts. Dedicated laboratories and advanced equipment would need to be developed for this purpose.
- Observational Studies: Observing natural phenomena such as distant cosmic events or close flybys of massive objects could provide valuable insights into the behavior of gravitational waves. Collaborating with astronomers and astrophysicists would be essential to leverage existing observational data.
- Computational Simulations: Utilizing sophisticated numerical simulations can help model the effects of gravitational waves on particles. High-performance computing resources and specialized software would be necessary to accurately simulate and analyze different scenarios.
- Theoretical Investigations: Deepening our theoretical understanding of gravity and its interactions with matter will contribute to resolving the debate. The development of new theoretical frameworks and mathematical models may be required to explain the observed phenomena.
- Advanced Technological Innovations: Advancements in technology, such as improved detectors and sensors, can enhance our ability to detect and measure gravitational waves accurately. Investing in research and development of innovative technologies will be pivotal in overcoming current limitations.
As the research progresses, challenges may arise:
- Limited Data Availability: The scarcity of data documenting the behavior of particles under the influence of gravitational waves can pose difficulties in validating or refuting the hypotheses. International collaborations and data-sharing initiatives will be crucial in addressing this challenge.
- Complexity of Analysis: Analyzing the intricate interactions between gravitational waves and particles requires advanced mathematical and statistical techniques. Collaborations between physicists and mathematicians will be vital to overcome the complexity of the analysis process.
- Resource Constraints: Developing sophisticated experimental setups, running large-scale simulations, and conducting extensive theoretical investigations will require substantial financial and technical resources. Securing funding and garnering institutional support will be essential for successful research outcomes.
In conclusion, the ongoing debate between the velocity effect and the displacement of gravitational waves presents exciting opportunities for researchers to deepen their understanding of gravity and particle interactions. By undertaking experimental, observational, computational, and theoretical approaches while embracing technological advancements, scientists can expect to address the challenges and make significant progress in this field.
References:
- Ehlers, J., & Kundt, W. (Year). Title of Ehlers and Kundt’s paper. Journal Name, Volume(Issue), Page-Page.
- Zel’dovich, Y. B., & Polnarev, A. G. (Year). Title of Zel’dovich and Polnarev’s paper. Journal Name, Volume(Issue), Page-Page.
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by jsendak | Nov 11, 2024 | GR & QC Articles
arXiv:2411.05124v1 Announce Type: new
Abstract: In this paper, we obtain pointwise decay estimates in time for massive Vlasov fields on the exterior of Schwarzschild spacetime. We consider massive Vlasov fields supported on the closure of the largest domain of the mass-shell where timelike geodesics either cross $mathcal{H}^+$, or escape to infinity. For this class of Vlasov fields, we prove that the components of the energy-momentum tensor decay like $v^{-frac{1}{3}}$ in the bounded region ${rleq R}$, and like $u^{-frac{1}{3}}r^{-2}$ in the far-away region ${rgeq R}$, where $R>2M$ is sufficiently large. Here, $(u,v)$ denotes the standard Eddington–Finkelstein double null coordinate pair.
In this paper, the authors examine the decay estimates in time for massive Vlasov fields on the exterior of Schwarzschild spacetime. Specifically, they consider Vlasov fields supported on the closure of the largest domain of the mass-shell where timelike geodesics either cross $mathcal{H}^+$, the future event horizon, or escape to infinity.
The authors prove that the components of the energy-momentum tensor for this class of Vlasov fields decay in two different regions. In the bounded region ${rleq R}$, where $R>2M$ is sufficiently large, the energy-momentum tensor components decay like $v^{-frac{1}{3}}$. In the far-away region ${rgeq R}$, the components decay like $u^{-frac{1}{3}}r^{-2}$, where $(u,v)$ represents the Eddington–Finkelstein double null coordinate pair.
Future Roadmap
- Further Analysis: Researchers can build upon this study by performing further analysis on the behavior of massive Vlasov fields on the exterior of Schwarzschild spacetime. This could involve exploring different boundary conditions or studying the decay estimates in other coordinate systems.
- Applications in Astrophysics: The findings of this research have potential applications in astrophysics, particularly in understanding the behavior of matter and energy in the vicinity of black holes. Scientists can utilize these decay estimates to make predictions about the dynamics of Vlasov fields and their effects on the spacetime geometry near black holes.
- Numerical Simulations: To verify the theoretical results obtained in this paper, numerical simulations can be conducted. By simulating massive Vlasov fields on the exterior of Schwarzschild spacetime, researchers can compare the decay estimates with the actual behavior of the fields, providing empirical validation for the theoretical findings.
- Generalization to Other Spacetimes: The methods and techniques used in this study can be applied to other spacetimes with different geometries. By generalizing the results to other spacetimes, researchers can gain a broader understanding of the behavior of Vlasov fields in various gravitational environments.
Challenges
- Complexity: The study of Vlasov fields on the exterior of Schwarzschild spacetime is a complex topic that requires advanced mathematical and physical knowledge. Researchers attempting to delve deeper into this field may face challenges in understanding and applying the existing theories and techniques.
- Computational Resources: Numerical simulations to validate the theoretical findings can require substantial computational resources. Researchers may face limitations in terms of access to high-performance computing clusters or the time required to run extensive simulations.
- Data Availability: Depending on the specific astrophysical scenarios, obtaining accurate data for comparison with the theoretical predictions may be challenging. Researchers may need to rely on observational or experimental data that is limited in its availability and accuracy.
Opportunities
- Advancing Astrophysical Understanding: The research on massive Vlasov fields on the exterior of Schwarzschild spacetime provides an opportunity to enhance our understanding of the dynamics of matter and energy in extreme gravitational environments. This knowledge can contribute to advancements in astrophysics and our comprehension of the behavior of black holes.
- Interdisciplinary Collaboration: The complex nature of this research topic provides an opportunity for interdisciplinary collaboration. Mathematicians, physicists, and astrophysicists can work together to deepen our understanding of Vlasov fields, spacetime dynamics, and black hole physics.
- New Scientific Discoveries: Exploring the decay estimates and behavior of massive Vlasov fields in the vicinity of black holes may lead to new scientific discoveries. By uncovering unique patterns or unexpected phenomena, researchers can expand our knowledge of the fundamental laws of physics and the nature of the universe.
Overall, the study of massive Vlasov fields on the exterior of Schwarzschild spacetime opens up a new avenue for research in astrophysics and theoretical physics. The decay estimates obtained in this paper provide a foundation for further analysis, numerical simulations, and interdisciplinary collaboration. By overcoming the challenges and capitalizing on the opportunities, researchers can pave the way for groundbreaking discoveries in black hole physics and the study of extreme gravitational environments.
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by jsendak | Oct 11, 2024 | GR & QC Articles
arXiv:2410.07231v1 Announce Type: new
Abstract: We point out that the geometry of connected totally geodesic compact null hypersurfaces in Lorentzian manifolds is only slightly more specialized than that of Riemannian flows over compact manifolds, the latter mathematical theory having been much studied in the context of foliation theory since the work by Reinhart (1959). We are then able to import results on Riemannian flows to the horizon case, so obtaining theorems on the dynamical structure of compact horizons that do not rely on (non-)degeneracy assumptions. Furthermore, we clarify the relation between isometric/geodesible Riemannian flows and non-degeneracy conditions. This work also contains some positive results on the possibility of finding, in the degenerate case, lightlike fields tangent to the horizon that have zero surface gravity.
Future Roadmap for Readers: Challenges and Opportunities on the Horizon
To better understand the conclusions of the mentioned text and to highlight potential challenges and opportunities in the future, we provide a roadmap for readers:
1. Background: Riemannian Flows over Compact Manifolds
Start by revisiting the mathematical theory of Riemannian flows over compact manifolds. Understand the key concepts and results, with a focus on the work by Reinhart in 1959. Explore the relationship between Riemannian flows and foliation theory.
2. Connected Totally Geodesic Compact Null Hypersurfaces in Lorentzian Manifolds
Examine the geometry of connected totally geodesic compact null hypersurfaces in Lorentzian manifolds. Compare this specialization to that of Riemannian flows over compact manifolds. Understand how this connection opens up new possibilities and applications.
3. Importing Results on Riemannian Flows to the Horizon Case
Investigate how the results on Riemannian flows can be imported and applied to the horizon case. Explore the theorems on the dynamical structure of compact horizons that do not rely on (non-)degeneracy assumptions. Recognize the significance of this importation for understanding compact horizons.
4. Relationship between Isometric/Geodesible Riemannian Flows and Non-Degeneracy Conditions
Gain insights into the relation between isometric/geodesible Riemannian flows and non-degeneracy conditions. Explore the implications of this relationship for understanding the behavior of flows and the possibility of finding lightlike fields tangent to the horizon with zero surface gravity.
5. Positive Results on the Degenerate Case
Analyze the positive results presented in the work regarding the possibility of finding lightlike fields tangent to the horizon in the degenerate case with zero surface gravity. Understand the implications and potential applications of these findings.
Overall, this roadmap provides an overview of the important concepts and conclusions discussed in the mentioned text. It offers readers the opportunity to delve into the specialized field of connected totally geodesic compact null hypersurfaces in Lorentzian manifolds and the application of Riemannian flow theory. While the importation of results and the exploration of the relationship between different mathematical concepts present exciting opportunities, challenges may arise in understanding the complex geometry and applying the theorems in practical scenarios. The future endeavors in this field hold the potential for further advancements in the dynamical structure of compact horizons and finding zero surface gravity lightlike fields.
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