by jsendak | Mar 11, 2024 | GR & QC Articles
arXiv:2403.04827v1 Announce Type: new
Abstract: We show via an explicit construction how an infinite tower of higher-curvature corrections generically leads to a resolution of the Schwarzschild singularity in any spacetime dimension $D ge 5$. The theories we consider have two key properties that ensure the results are general and robust: (1) they provide a basis for (vacuum) gravitational effective field theory in five and higher-dimensions, (2) for each value of the mass, they have a unique static spherically symmetric solution. We present several exact solutions of the theories that include the Hayward black hole and metrics similar to the Bardeen and Dymnikova ones. Unlike previous constructions, these regular black holes arise as vacuum solutions, as we include no matter fields whatsoever in our analysis. We show how the black hole thermodynamics can be studied in a completely universal and unambiguous way for all solutions.
In this article, the authors discuss their findings on how an infinite tower of higher-curvature corrections can resolve the Schwarzschild singularity in spacetime dimensions greater than or equal to five. They highlight two key properties of the theories they consider: (1) they provide a basis for gravitational effective field theory in higher dimensions and (2) they have unique static spherically symmetric solutions for each mass value. Several exact solutions, including the Hayward black hole and metrics similar to the Bardeen and Dymnikova ones, are presented. Notably, these regular black holes are vacuum solutions, meaning no matter fields are included in the analysis. Furthermore, the authors demonstrate that the black hole thermodynamics can be universally and unambiguously studied for all solutions.
Future Roadmap
Moving forward, this research opens up exciting possibilities and avenues for exploration. Here is a potential roadmap for readers interested in this topic:
1. Further Analysis of Higher-Curvature Corrections
To deepen our understanding of the resolution of the Schwarzschild singularity, future research should focus on a more detailed analysis of the infinite tower of higher-curvature corrections. By examining the effects of these corrections on the black hole solutions, researchers can gain insights into the underlying physics and test the robustness of the findings.
2. Exploration of Alternative Vacuum Solutions
While the article presents several exact solutions, such as the Hayward black hole and metrics similar to the Bardeen and Dymnikova ones, there may be additional vacuum solutions yet to be discovered. Researchers can investigate alternative mathematical formulations, explore different boundary conditions, or consider variations in the theories to uncover new regular black holes that arise without matter fields.
3. Thermodynamics of Regular Black Holes
The article briefly mentions the study of black hole thermodynamics in a universal and unambiguous way for all solutions. Future studies can delve deeper into this aspect, examining the thermodynamic properties, entropy, and behavior of regular black holes. Understanding the thermodynamics of these black holes can provide valuable insights into their stability, relation to information theory, and potential connections with other areas of physics.
4. Experimental and Observational Verifications
While the theoretical findings are intriguing, it is essential to test them against observational and experimental data. Researchers can explore the possibility of detecting regular black holes or their effects in astrophysical observations, gravitational wave detections, or particle accelerator experiments. Such verifications would provide strong evidence for the existence and significance of these regular black holes.
5. Application to Cosmological Models
Considering the implications of regular black holes for cosmology is another exciting avenue to explore. Researchers can investigate how these black holes might affect the evolution of the universe, the nature of the early universe, or the behavior of dark matter and dark energy. By incorporating the findings into cosmological models, we can gain a more comprehensive understanding of the universe’s dynamics and address open questions in cosmology.
Challenges and Opportunities
While the research presents exciting possibilities, it also comes with its set of challenges and opportunities:
- Theoretical Challenges: Exploring the infinite tower of higher-curvature corrections and their effects on gravitational theories is a complex task. Researchers will need to develop advanced mathematical techniques, computational tools, and frameworks to simplify and analyze these theories effectively.
- Experimental Limitations: Verifying the existence of regular black holes or their effects experimentally can be challenging. Researchers may face limitations in observational data, the sensitivity of detectors, or the feasibility of conducting certain experiments. Developing innovative detection methods or collaborations between theorists and experimentalists could help overcome these limitations.
- Interdisciplinary Collaboration: Given the wide-ranging implications of this research, interdisciplinary collaboration between theorists, astrophysicists, cosmologists, and experimentalists is essential. Leveraging expertise from different fields can help address challenges, provide diverse perspectives, and stimulate further breakthroughs.
- Public Engagement: Communicating the significance of regular black holes to the general public and garnering support for future research may require effective science communication strategies. Researchers can engage with the public through popular science articles, public talks, or interactive exhibitions to foster interest and increase awareness.
Overall, the resolution of the Schwarzschild singularity through an infinite tower of higher-curvature corrections holds great potential for advancing our understanding of gravity, black holes, and the universe. By following the outlined roadmap, overcoming challenges, and seizing opportunities, researchers can continue to explore and uncover the fascinating properties and implications of regular black holes.
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by jsendak | Mar 8, 2024 | GR & QC Articles
arXiv:2403.03965v1 Announce Type: new
Abstract: We show by direct calculation that the common Equivalence Principle explanation for why gravity must deflect light is quantitatively incorrect by a factor of three in Schwarzschild geometry. It is therefore possible, at least as a matter of principle, to tell the difference between local acceleration and a true gravitational field by measuring the local deflection of light. We calculate as well the deflection of test particles of arbitrary energy, and construct a leading-order coordinate transformation from Schwarzschild to local inertial coordinates, which shows explicitly how the effects of spatial curvature manifest locally for relativistic trajectories of both finite and vanishing rest mass particles.
Article Title: Challenges and Opportunities in Understanding the Deflection of Light in Schwarzschild Geometry
Introduction:
The following article presents groundbreaking research that challenges the common Equivalence Principle explanation for why gravity must deflect light. The research demonstrates that the commonly accepted explanation is quantitatively incorrect by a factor of three in Schwarzschild geometry. The implications of this finding suggest the possibility of distinguishing between local acceleration and a true gravitational field by measuring the local deflection of light. Additionally, the article examines the deflection of test particles with arbitrary energy and provides insights into the manifestation of spatial curvature effects for relativistic trajectories of both finite and vanishing rest mass particles.
Future Roadmap:
1. Validation and Replication of Findings
- Initially, scientists must aim to validate the results obtained in the research through replication experiments and calculations by independent researchers. This is crucial to ensure the accuracy and reliability of the findings.
- Scientific communities and research institutions should encourage further investigations to confirm the quantitative discrepancy and explore the implications for the Equivalence Principle.
2. Refining the Measurement Techniques
- The development of more precise and advanced instruments for measuring the deflection of light is paramount to detect the small differences between local acceleration and true gravitational fields.
- Innovations in technology, such as improved telescopes or advanced interferometric techniques, should be explored to enhance the accuracy and sensitivity of measurements.
3. Extending the Research to Other Geometries
- Researchers should investigate if the quantitative discrepancy found in Schwarzschild geometry also applies to other geometries, such as Kerr or Reissner-Nordström. This may provide a more comprehensive understanding of the deflection of light in various gravitational fields.
- Comparative studies between different geometries will help identify unique characteristics and potentially unveil new insights into the behavior of light in gravitationally curved spacetime.
4. Developing Comprehensive Models
- Efforts should be made to construct more detailed models that involve arbitrary energy test particles and accurately describe the deflection of light in different gravitational fields.
- Further investigation is necessary to explore the relationship between spatial curvature and relativistic trajectories of particles with both finite and vanishing rest mass. This will contribute to a more comprehensive understanding of how spatial curvature manifests locally.
5. Practical Applications and Implications
- Explore potential applications of the knowledge gained from this research, such as improving the accuracy of gravitational wave detectors or aiding in the development of more efficient space navigation systems.
- Investigate potential implications for our understanding of black holes, as well as the possibility of distinguishing between different types of astrophysical objects based on their gravitational effects on light.
6. Educational and Outreach Opportunities
- Develop educational resources, such as tutorials and lectures, to disseminate the findings of this research to a broader audience, including students, researchers, and science enthusiasts.
- Organize conferences, seminars, and workshops to foster collaboration and exchange of ideas among scientists working in the field of gravitational physics and general relativity.
Conclusion:
This research challenges the conventional understanding of the Equivalence Principle and presents an exciting avenue for further investigation. Validating the findings, refining measurement techniques, exploring other geometries, developing comprehensive models, and exploring practical applications will contribute to a deeper understanding of the deflection of light in gravitational fields. There is great potential in leveraging these new insights for technological advancements and expanding our understanding of the universe.
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by jsendak | Mar 7, 2024 | GR & QC Articles
arXiv:2403.03227v1 Announce Type: new
Abstract: In recent years, there has been an increase in the number of papers regarding general-relativistic explanations for the dark matter phenomena in disc galaxies. The main focus of this scientific discussion is whether a previously unexamined relativistic dragging vortex could support flat rotation curves, with various research groups taking different stances on its feasibility. In this paper, we discuss the different points of view by placing the various arguments within a general theoretical context. We explicitly state the conceptual assumptions, and indicate what we believe to be the correct interpretation for the physical quantities of interest. We show how the dragging conjecture fails under certain hypotheses, and discuss the flaws of the most common dragging models: the linearised gravitomagnetic description and the one of Balasin&Grumiller. On the other hand, we illustrate how to avoid failure scenarios for the conjecture, emphasizing the features for a physically reasonable disc galaxy dragging model. In particular, we stress that the non-linearities of the Einstein Equations must play an essential role in generating what we define as “pseudo-solitonic” solutions — the only non-trivial physically viable solutions for the class of models considered. Furthermore, the dragging vortex is proven to show important contributions to the gravitational lensing in these models, thus providing an ulterior measure of its relevance. Moreover, by qualitatively exploring these pseudo-solitonic solutions, we find that a dragging speed of just a few kilometers per second would be enough to explain a non-negligible fraction of the galactic dark matter. Finally, we propose and analyse the feasibility of three independent measurements which could be carried out to detect the presence of dragging vortices in disc galaxies.
Conclusion:
General-relativistic explanations for the dark matter phenomena in disc galaxies have been a topic of increasing interest in recent years. The feasibility of a dragging vortex as a support for flat rotation curves has been a subject of debate among research groups. This paper discusses the different points of view and places the arguments within a general theoretical context. It identifies the flaws in the most common dragging models and proposes a physically reasonable model that avoids failure scenarios. The dragging vortex is shown to have important contributions to gravitational lensing, further highlighting its relevance. The paper also suggests that a dragging speed of just a few kilometers per second could explain a non-negligible fraction of the galactic dark matter. Finally, it proposes three independent measurements to detect the presence of dragging vortices in disc galaxies.
Future Roadmap:
- Further Research: Given the ongoing debate and differing viewpoints, further research is needed to explore and refine the dragging vortex model. This includes investigating the non-linearities of the Einstein Equations and their role in generating physically viable solutions.
- Experimental Validation: The feasibility of the proposed dragging vortex model and its contribution to dark matter can be tested through three independent measurements. These measurements should be conducted to provide empirical evidence for the existence and properties of dragging vortices in disc galaxies.
- Challenges: One challenge that researchers may face is obtaining accurate and reliable measurements of dragging speeds and their effects on gravitational lensing. Additionally, the identification and quantification of the fraction of dark matter explained by the dragging vortex model may require advanced data analysis techniques.
- Opportunities: The successful validation of the dragging vortex model and its role in explaining dark matter could lead to a deeper understanding of the nature of dark matter and its implications for the laws of gravity. It may also open up new avenues for studying and manipulating gravitational fields.
Overall, the future roadmap for readers includes further research, experimental validation, overcoming challenges in measurement and analysis, and seizing potential opportunities for scientific advancements in the study of dark matter in disc galaxies.
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by jsendak | Mar 6, 2024 | GR & QC Articles
arXiv:2403.02351v1 Announce Type: new
Abstract: Using the Raychaudhuri equation, we associate quantum probability amplitudes (propagators) to equatorial principal ingoing and outgoing null geodesic congruences in the Kerr metric. The expansion scalars diverge at the ring singularity; however, the propagators remain finite, which is an indication that at the quantum level singularities might disappear or, at least, become softened.
Quantum Propagators and Singularity Softening in the Kerr Metric
Introduction
In this study, we utilize the Raychaudhuri equation to investigate the behavior of quantum probability amplitudes, known as propagators, associated with equatorial principal ingoing and outgoing null geodesic congruences in the Kerr metric. Our analysis reveals interesting findings regarding the potential disappearance or softening of singularities at the quantum level.
Background
The Kerr metric describes the spacetime geometry around a rotating black hole. Previous studies have shown that the expansion scalars, which measure the rate of change of the congruence flow, diverge at the ring singularity in the Kerr metric. This divergence suggests the presence of a classical singularity with extreme spacetime curvature.
Methodology
By applying the Raychaudhuri equation, we associate quantum propagators with the null geodesic congruences in the Kerr metric. The propagators represent the quantum probability amplitudes for the geodesic flow. We specifically focus on the equatorial principal ingoing and outgoing null geodesic congruences.
Results
Surprisingly, our analysis reveals that while the expansion scalars diverge at the ring singularity, the propagators remain finite. This observation suggests that at the quantum level, the presence of singularities might either disappear entirely or become significantly softened. This finding opens up new possibilities for understanding the nature of black hole singularities and their behavior under quantum effects.
Future Roadmap
Building upon this research, future investigations could explore the implications of the disappearance or softening of singularities at the quantum level within the context of black holes and general relativity. This roadmap outlines potential challenges and opportunities that lie ahead:
1. Quantum Gravity and Singularities
Further investigations are needed to deepen our understanding of how quantum gravity theory could explain the disappearance or softening of singularities. This would involve exploring the interplay between quantum effects and the extreme curvature of spacetime near black hole singularities.
2. Experimental Verification
Experimental validation of our theoretical findings is an essential step in determining the physical relevance of the observed effects. Designing and conducting experiments that can probe the behavior of singularities at the quantum level poses significant challenges but offers exciting opportunities for advancing our knowledge of fundamental physics.
3. Cosmological Implications
Investigating the cosmological implications of singularity softening or disappearance is another avenue of research. By studying the behavior of singularities in different astrophysical scenarios, we can gain insights into the evolution and nature of the universe on both small and large scales.
4. Technological Applications
The potential softening or disappearance of singularities at the quantum level may have practical applications in fields such as quantum computing and information theory. Exploring how these effects can be harnessed for technological advancements could lead to breakthroughs in quantum technologies.
5. Theoretical Frameworks
Developing new theoretical frameworks that can incorporate the disappearance or softening of singularities is a critical task. This would involve extending our current understanding of quantum gravity and its implications for the behavior of spacetime near extreme curvatures.
6. Interdisciplinary Collaboration
Addressing the challenges and opportunities presented by the potential disappearance or softening of singularities requires interdisciplinary collaboration. Bringing together experts from fields such as quantum physics, general relativity, astrophysics, and computer science can foster innovative approaches and accelerate progress.
Conclusion
The observation that quantum propagators remain finite while expansion scalars diverge at the ring singularity in the Kerr metric opens up exciting possibilities for understanding the behavior of singularities at the quantum level. By outlining a future roadmap, this study provides a foundation for further research, highlighting potential challenges and opportunities in exploring the implications of singularity disappearance or softening, with implications for fields ranging from fundamental physics to technological advancements.
DOI: https://doi.org/10.xxxx
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by jsendak | Mar 4, 2024 | GR & QC Articles
arXiv:2403.00021v1 Announce Type: new
Abstract: Here, we investigate the formation of primordial black holes (PBHs) in non-minimal coupling Gauss-Bonnet inflationary model in the presence of power-law potentials. We employ a two part coupling function to enhance primordial curvatures at small scales as well as satisfy Planck measurements at the CMB scale. Moreover, our model satisfies the swampland criteria. We find PBHs with different mass scales and demonstrate that PBHs with masses around $mathcal{O}(10^{-14})M_{odot}$ can account for almost all of the dark matter in the universe. In addition, we investigate the implications of the reheating stage and show that the PBHs in our model are generated during the radiation-dominated era. Furthermore, we investigate the production of scalar-induced gravitational waves (GWs). More interestingly enough, is that for the specific cases $D_{rm n}$ in our model, the GWs can be considered as a source of NANOGrav signal. %evaluate the idea that the induced GWs propagating concurrently with the PBH production are the source of NANOGrav signal. Also, we conclude that the GWs energy density parameter at the nano-Hz regime can be parameterized as $Omega_{rm GW_0} (f) sim f^{5-gamma}$, where the obtained $gamma$ is consistent with the NANOGrav 15 years data.
Formation of Primordial Black Holes in Non-Minimal Coupling Gauss-Bonnet Inflationary Model
In this study, we investigate the formation of primordial black holes (PBHs) in a non-minimal coupling Gauss-Bonnet inflationary model with power-law potentials. We propose a two-part coupling function that enhances primordial curvatures at small scales and is consistent with Planck measurements at the Cosmic Microwave Background (CMB) scale. Importantly, our model also satisfies the swampland criteria.
PBHs as Dark Matter Candidates
We find that PBHs with different mass scales can be formed in our model. Particularly, PBHs with masses around $mathcal{O}(10^{-14})M_{odot}$ are capable of explaining a significant portion of the dark matter in the universe. This discovery opens up new possibilities for understanding the nature of dark matter.
Implications of Reheating Stage
In addition to PBH formation, we also investigate the implications of the reheating stage in our model. Our findings suggest that the PBHs are generated during the radiation-dominated era. This insight provides valuable information about the early universe and the dynamics of inflation.
Scalar-Induced Gravitational Waves
We further delve into the production of scalar-induced gravitational waves (GWs). Interestingly, we identify special cases in our model where the GWs can be considered as a source of the NANOGrav signal. This connection between PBHs and GWs presents an exciting avenue for future research.
Note: NANOGrav refers to the North American Nanohertz Observatory for Gravitational Waves, which is a collaboration striving to detect low-frequency gravitational waves.
Predicting GWs Energy Density
Additionally, our study allows us to predict the energy density parameter of GWs in the nano-Hertz regime. We propose a parameterization of $Omega_{rm GW_0} (f) sim f^{5-gamma}$, where the value of $gamma$ obtained from our model is consistent with the NANOGrav 15 years data. This alignment with observational data strengthens the validity of our theoretical framework.
Future Roadmap
- Further investigate the non-minimal coupling Gauss-Bonnet inflationary model to analyze its implications on primordial black hole formation and other cosmological phenomena.
- Conduct observational studies to validate the presence and properties of primordial black holes with masses around $mathcal{O}(10^{-14})M_{odot}$, potentially shedding light on the nature of dark matter.
- Explore the connection between scalar-induced gravitational waves and the NANOGrav signal, considering different scenarios and refining the predictions for future experiments.
- Refine the parameterization of the energy density parameter for gravitational waves in the nano-Hertz regime, potentially contributing to a better understanding of the universe’s gravitational wave background.
- Continuously compare and validate theoretical predictions with new observational data, such as future NANOGrav measurements, to further validate and refine the proposed model.
Overall, the findings from this study open up exciting opportunities for research in the field of primordial black holes, dark matter, gravitational waves, and early universe cosmology. By addressing the challenges and building upon the conclusions of this work, future studies can provide a more comprehensive understanding of the universe’s fundamental properties.
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by jsendak | Mar 1, 2024 | GR & QC Articles
arXiv:2402.18604v1 Announce Type: new
Abstract: Background cosmological dynamics for a universe with matter, a scalar field non-minimally derivative coupling to Einstein tensor under power-law potential and holographic vacuum energy is considered here. The holographic IR cutoff scale is apparent horizon which, for accelerating universe, forms a trapped null surface in the same spirit as blackhole’s event horizon. For non-flat case, effective gravitational constant can not be expressed in the Friedmann equation. Therefore holographic vacuum density is defined with standard gravitational constant in stead of the effective one. Dynamical and stability analysis shows four independent fixed points. One fixed point is stable and it corresponds to $w_{text{eff}} = -1$. One branch of the stable fixed-point solutions corresponds to de-Sitter expansion. The others are either unstable or saddle nodes. Numerical integration of the dynamical system are performed and plotted confronting with $H(z)$ data. It is found that for flat universe, $H(z)$ observational data favors large negative value of $kappa$. Larger holographic contribution, $c$, and larger negative NMDC coupling increase slope and magnitude of the $w_{text{eff}}$ and $H(z)$. Negative NMDC coupling can contribute to phantom equation of state, $w_{text{eff}} < -1$. The NMDC-spatial curvature coupling could also have phantom energy contribution. Moreover, free negative spatial curvature term can also contribute to phantom equation of state, but only with significantly large negative value of the spatial curvature.
Background cosmological dynamics for a universe with matter, a scalar field non-minimally derivative coupling to Einstein tensor under power-law potential and holographic vacuum energy is considered in this study. The holographic IR cutoff scale is the apparent horizon, which forms a trapped null surface similar to a black hole’s event horizon.
In the case of a non-flat universe, the effective gravitational constant cannot be expressed in the Friedmann equation. Therefore, the holographic vacuum density is defined with the standard gravitational constant instead of the effective one. By performing dynamical and stability analysis, it is found that there are four independent fixed points. One of these fixed points is stable and corresponds to an effective equation of state, $w_{text{eff}}$, of -1.
One branch of the stable fixed-point solutions corresponds to de-Sitter expansion. The other fixed points are either unstable or saddle nodes. Numerical integration of the dynamical system is performed and plotted against $H(z)$ data. The analysis reveals that for a flat universe, the observed $H(z)$ data favors a large negative value of $kappa$.
A larger holographic contribution, $c$, and a larger negative NMDC (non-minimally derivative coupling) increase the slope and magnitude of the effective equation of state, $w_{text{eff}}$, and the Hubble parameter, $H(z)$. The negative NMDC coupling can contribute to a phantom equation of state, $w_{text{eff}} < -1$. Additionally, the NMDC-spatial curvature coupling may also result in a phantom energy contribution. The inclusion of a negative spatial curvature term can also contribute to a phantom equation of state, but only if it has a significantly large negative value.
Future Roadmap
- Further exploration of the effects of holographic vacuum energy and the non-minimal derivative coupling on cosmological dynamics is warranted.
- Investigate the stability and behavior of the other fixed points identified in the analysis.
- Perform more extensive numerical integrations and comparisons with observational data to validate the findings.
- Examine the impact of different values of the holographic contribution, $c$, and the negative NMDC coupling on the evolution of the universe.
- Investigate the potential consequences of including the NMDC-spatial curvature coupling and the negative spatial curvature term on cosmological dynamics.
Challenges
- Obtaining accurate observational data for $H(z)$ to compare with the numerical results.
- The complexity of the dynamical system may pose challenges in obtaining precise numerical solutions.
- Understanding the physical interpretation of the fixed points and their implications for the evolution of the universe.
Opportunities
- The study provides insights into the effects of holographic vacuum energy and non-minimal derivative couplings on cosmological dynamics.
- Understanding the behavior of the stable fixed point and its link to de-Sitter expansion can shed light on the nature of accelerated expansion in the universe.
- The exploration of phantom equation of state and the potential contributions from different couplings and spatial curvature provides opportunities for testing and refining cosmological models.
- Further investigations can contribute to a deeper understanding of the fundamental properties and evolution of the universe.
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