by jsendak | Dec 31, 2023 | GR & QC Articles
In this work, we delve into the model of the shift symmetric and
parity-preserving Beyond Horndeski theory in all its generality. We present an
explicit algorithm to extract static and spherically symmetric black holes with
primary scalar charge adhering to the conservation of the Noether current
emanating from the shift symmetry. We show that when the functionals $G_2$ and
$G_4$ of the theory are linearly dependent, analytic homogeneous black-hole
solutions exist, which can become regular by virtue of the primary charge
contribution. Such geometries can easily enjoy the preservation of the Weak
Energy Conditions, elevating them into healthier compact objects than most
hairy black holes in modified theories of gravity. Finally, we revisit the
concept of disformal transformations as a solution-generating mechanism and
discuss the case of generic $G_2$ and $G_4$ functionals.
Future Roadmap:
1. Introduction
Begin the article by introducing the topic of the shift symmetric and parity-preserving Beyond Horndeski theory. Explain why this theory is important and relevant in the study of black holes and modified theories of gravity.
2. Model Description
Provide a detailed description of the model, including its mathematical formulation and the role of the Noether current in conserving the primary scalar charge. Explain the significance of the linear dependence between the functionals G_2 and G_4.
3. Extraction of Static and Spherically Symmetric Black Holes
Present the explicit algorithm developed in this work to extract static and spherically symmetric black hole solutions in the model. Discuss the conditions under which these solutions exist and demonstrate how they adhere to the conservation of the Noether current.
4. Regularization of Black Hole Solutions
Highlight the regularity of the black hole solutions obtained through the primary charge contribution. Discuss how these solutions can preserve the Weak Energy Conditions, making them healthier compact objects compared to other hairy black holes in modified theories of gravity. Present evidence or examples supporting this conclusion.
5. Revisiting Disformal Transformations
Revisit and explore the concept of disformal transformations as a solution-generating mechanism in the model. Discuss how generic G_2 and G_4 functionals influence or contribute to this mechanism. Provide insights or examples to illustrate this concept.
6. Conclusion
Summarize the key findings and conclusions of the study, emphasizing the potential of the shift symmetric and parity-preserving Beyond Horndeski theory in understanding and studying black holes in modified theories of gravity. Highlight any implications or future directions for research based on the results obtained.
Challenges and Opportunities:
- One potential challenge in further exploring this model is the complexity of the mathematical formulation. Research and development of more efficient algorithms or computational methods may be necessary to extract and analyze a larger variety of black hole solutions.
- Another challenge is the validation and verification of the regularity and preservation of Weak Energy Conditions in the obtained black hole solutions. Further theoretical analysis and numerical simulations could help address these challenges.
- An opportunity lies in investigating the physical properties and astrophysical implications of the regularized black hole solutions in the model. Understanding how these solutions behave under various conditions or in the presence of other objects or forces could lead to valuable insights and potential applications in astrophysics and cosmology.
- The concept of disformal transformations presents an interesting avenue for future research. Exploring different types of functionals, their effects on solution generation, and their physical interpretations could uncover new possibilities and deepen our understanding of black hole physics.
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by jsendak | Dec 31, 2023 | GR & QC Articles
The topological aspects of Einstein gravity suggest that topological
invariance could be a more profound principle in understanding quantum gravity.
In this work, we explore a topological supergravity action that initially
describes a universe without Riemann curvature, which seems trivial. However,
we made a surprising discovery by introducing a small deformation parameter
$lambda$, which can be regarded as an AdS generalization of supersymmetry
(SUSY). We find that the deformed topological quantum field theory (TQFT)
becomes unstable at low energy, resulting in the emergence of a classical
metric, whose dynamics are controlled by the Einstein equation. Our findings
suggest that a quantum theory of gravity could be governed by a UV fixed point
of a SUSY TQFT, and classical spacetime ceases to exist beyond the Planck
scale.
Exploring the Potential of Topological Invariance in Understanding Quantum Gravity
Topological invariance has the potential to be a profound principle in understanding quantum gravity. In this work, we delve into a topological supergravity action that may initially seem trivial due to the absence of Riemann curvature. However, we make a surprising discovery by introducing a small deformation parameter, $lambda$, which can be considered as an AdS generalization of supersymmetry (SUSY).
Our research reveals that the deformed topological quantum field theory (TQFT) becomes unstable at low energy. This instability leads to the emergence of a classical metric, where the dynamics are governed by the famous Einstein equation. These findings suggest that a quantum theory of gravity could be regulated by a UV fixed point of a SUSY TQFT. Moreover, it indicates that classical spacetime might cease to exist beyond the Planck scale.
Roadmap for the Future
The potential offered by topological invariance in understanding quantum gravity opens up exciting avenues for future research. Here is a roadmap outlining potential challenges and opportunities on the horizon:
- Further Exploration of Deformed TQFT: Investigate the behavior and properties of the deformed TQFT at different energy scales. Understand the interplay between topological invariance, deformation parameter $lambda$, and emergence of classical metrics.
- Experimental Verification: Develop experimental frameworks to test the predictions and implications of the deformed TQFT theory. Explore ways to measure and observe the stability and emergence of classical metrics in different energy regimes.
- UV Fixed Point Analysis: Study the nature and characteristics of the UV fixed point of SUSY TQFT. Investigate its implications for a quantized theory of gravity and explore potential methods to mathematically describe and manipulate this fixed point.
- Interdisciplinary Collaborations: Foster collaborations between theoretical physicists, mathematicians, and quantum gravity researchers to gain diverse perspectives on the potential of topological invariance. Explore new mathematical tools and frameworks that can aid in unveiling the underlying principles of quantum gravity.
- Planck Scale Investigations: Conduct experiments and calculations to probe the behavior of spacetime beyond the Planck scale. Examine the limitations and challenges encountered, as well as potential phenomena and theories that may arise in this extreme regime.
Conclusion
The study of topological invariance in the context of quantum gravity offers a promising direction for future research. By exploring the behavior of deformed TQFT and its connection to classical metrics, we may unlock new insights into the nature of gravity and spacetime beyond the Planck scale. This roadmap outlines potential challenges and opportunities that lie ahead, providing a foundation for further investigations in this exciting field.
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by jsendak | Dec 31, 2023 | GR & QC Articles
We study finite-coupling effects of QFT on a rigid de Sitter (dS) background
taking the $O(N)$ vector model at large $N$ as a solvable example. Extending
standard large $N$ techniques to the dS background, we analyze the phase
structure and late-time four-point functions. Explicit computations reveal that
the spontaneous breaking of continuous symmetries is prohibited due to strong
IR effects, akin to flat two-dimensional space. Resumming loop diagrams, we
compute the late-time four-point functions of vector fields at large $N$,
demonstrating that their spectral density is meromorphic in the spectral plane
and positive along the principal series. These results offer highly nontrivial
checks of unitarity and analyticity for cosmological correlators.
Based on our study of finite-coupling effects of quantum field theory (QFT) on a rigid de Sitter (dS) background, specifically using the $O(N)$ vector model at large $N$ as an example, we have made several conclusions and identified potential opportunities and challenges for future research.
Conclusions
- The analysis of phase structure on the dS background has revealed that the spontaneous breaking of continuous symmetries is prohibited due to strong IR effects, similar to flat two-dimensional space.
- By resumming loop diagrams, we have computed the late-time four-point functions of vector fields at large $N$, leading to several noteworthy findings:
- The spectral density of the four-point functions is meromorphic in the spectral plane.
- The spectral density is positive along the principal series.
- These results provide highly nontrivial checks of unitarity and analyticity for cosmological correlators.
Future Roadmap
In light of our conclusions, there are several avenues for future research in the field of QFT on a dS background. These include:
1. Further Investigation of Strong IR Effects
While our study has revealed that strong IR effects prohibit the spontaneous breaking of continuous symmetries in the $O(N)$ vector model, it would be valuable to explore this phenomenon in other models and better understand its underlying mechanisms.
2. Generalization to Other QFT Models
Expanding our analysis to other QFT models on a dS background would provide a broader understanding of the effects of finite coupling and could potentially uncover new insights into the phase structure and late-time behavior of these models.
3. Verification of Results in Different Backgrounds
It would be beneficial to verify our results by studying QFT on different backgrounds, such as anti-de Sitter (AdS) spacetime. By comparing the outcomes in various backgrounds, we can further validate the significance and applicability of our findings.
4. Extending the Study to Quantum Gravity
Considering the profound implications of our results for unitarity and analyticity in cosmological correlators, it would be worthwhile to explore the extension of our study to incorporate the effects of quantum gravity. Investigating the interplay between QFT and gravity on a dS background could shed light on fundamental aspects of the universe.
Challenges and Opportunities
While this field of research presents exciting prospects, there are challenges that need to be addressed:
1. Computational Complexity
Explicit computations in QFT on a dS background can be computationally intensive and complex. Developing efficient computational techniques and algorithms will be crucial to making progress in this area.
2. Limitations of Large N Techniques
While the $O(N)$ vector model at large $N$ provides solvable examples, it is important to recognize the limitations of these techniques. Extending our understanding beyond large $N$ and exploring finite $N$ effects will be essential for a comprehensive understanding of dS background QFT.
3. Experimental Verification
Experimental verification of our theoretical findings poses a significant challenge. As cosmological correlators are difficult to measure directly, innovative indirect methods or simulations may be necessary to test the predictions arising from our analysis.
In summary, our study of finite-coupling effects of QFT on a dS background using the $O(N)$ vector model at large $N$ has provided insights into the phase structure and late-time four-point functions. While there are opportunities for further investigation and generalization, challenges such as computational complexity and experimental verification need to be addressed. Nonetheless, these findings pave the way for future research in understanding the interplay between QFT and cosmological dynamics.
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by jsendak | Dec 31, 2023 | GR & QC Articles
In this paper, we provide a self-contained investigation of the Weyl double
copy in the Newman-Penrose formalism. We examine the Weyl double copy
constraints for the general asymptotically flat solution in the Newman-Unit
gauge. We find that two transparent solutions of the asymptotic Weyl double
copy constraints lead to truncated solutions for both linearized and Einstein
gravity theory where the solutions are in the manifest form of Petrov type N or
type D in the Newman-Unit gauge.
Introduction
In this paper, we explore the concept of the Weyl double copy in the Newman-Penrose formalism. We specifically investigate the Weyl double copy constraints for the general asymptotically flat solution in the Newman-Unit gauge. By examining these constraints, we are able to derive truncated solutions for both linearized and Einstein gravity theory.
Background
The Weyl double copy is a mathematical technique that allows for the construction of new solutions in gravitational theories by relating them to corresponding solutions in gauge theories. This concept has been of great interest in recent theoretical physics research as it offers new insights and connections between different areas of study.
The Newman-Penrose formalism, on the other hand, provides a powerful framework for understanding gravitational fields through a set of complex null tetrad variables. By applying this formalism, we can analyze and express gravitational solutions in a more comprehensible manner.
Research Methodology
We begin our investigation by considering the general asymptotically flat solution within the Newman-Unit gauge. By imposing the Weyl double copy constraints, we explore various possibilities for constructing solutions that satisfy these constraints.
We utilize mathematical techniques and equations within the Newman-Penrose framework to derive solutions that correspond to truncated forms of both linearized and Einstein gravity theories. Our focus is on solutions that manifest in the form of Petrov type N or type D within the Newman-Unit gauge.
Findings
Our analysis reveals two distinct transparent solutions that satisfy the asymptotic Weyl double copy constraints. These solutions correspond to truncated forms of both linearized and Einstein gravity theories. Importantly, these solutions exhibit a manifest form of Petrov type N or type D when expressed within the Newman-Unit gauge.
Roadmap for Future Research
While this study provides valuable insights into the Weyl double copy in the Newman-Penrose formalism, there are several avenues for further investigation:
- Exploration of additional gauge choices: The investigation could be extended to explore the Weyl double copy constraints within alternative gauge choices, potentially revealing new solutions and connections.
- Generalization to other gravitational theories: It would be interesting to apply the Weyl double copy technique to other gravitational theories beyond linearized and Einstein gravity, such as modified gravity theories.
- Quantum gravity implications: Investigating the implications of the Weyl double copy in the context of quantum gravity theories may provide novel insights into the relation between gravity and other fundamental forces.
Conclusion
This study has demonstrated the power of the Weyl double copy in the Newman-Penrose formalism for deriving truncated solutions in both linearized and Einstein gravity theories. The manifest Petrov types N and D within the Newman-Unit gauge offer a tangible connection between gravitational and gauge theories. Further research opportunities exist in exploring different gauge choices, generalizing to other gravitational theories, and investigating quantum gravity implications.
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by jsendak | Dec 31, 2023 | GR & QC Articles
The quantum fluctuations of fields can exhibit subtle correlations in space
and time. As the interval between a pair of measurements varies, the
correlation function can change sign, signaling a shift between correlation and
anti-correlation. A numerical simulation of the fluctuations requires a
knowledge of both the probability distribution and the correlation function.
Although there are widely used methods to generate a sequence of random numbers
which obey a given probability distribution, the imposition of a given
correlation function can be more difficult. Here we propose a simple method in
which the outcome of a given measurement determines a shift in the peak of the
probability distribution, to be used for the next measurement. We illustrate
this method for three examples of quantum field correlation functions, and show
that the resulting simulated function agree well with the original,
analytically derived function. We then discuss the application of this method
to numerical studies of the effects of correlations on the random walks of test
particles coupled to the fluctuating field.
Examining Quantum Field Correlations and Their Potential Application
The quantum fluctuations of fields can exhibit subtle correlations in space and time. These correlations can change sign as the interval between measurements varies, indicating a shift between correlation and anti-correlation. To numerically simulate these fluctuations, both the probability distribution and the correlation function need to be known. While there are established methods to generate random numbers obeying a given probability distribution, imposing a specific correlation function is more challenging.
A Proposed Solution: Shifting Probability Distributions
We propose a simple method to address the challenge of incorporating a desired correlation function into numerical simulations. In this method, the outcome of a measurement determines a shift in the peak of the probability distribution used for the next measurement.
Illustrating the Method
We demonstrate the effectiveness of our proposed method by applying it to three examples of quantum field correlation functions. Through these examples, we show that the resulting simulated functions closely match the original analytically derived functions.
Potential Applications
Having established the feasibility of our method for generating correlated quantum field simulations, we discuss its potential applications in numerical studies. One such application is exploring the effects of correlations on random walks of test particles that are coupled to the fluctuating field.
Roadmap for Readers
- Introduction: Explain the concept of quantum field correlations and their significance.
- Challenges in Numerical Simulations: Discuss the difficulty in incorporating correlation functions into simulations.
- Proposed Method: Present our simple method, where measurement outcomes determine shifts in probability distributions for subsequent measurements.
- Illustration: Provide three examples demonstrating the effectiveness of our method in generating simulated functions that match analytically derived ones.
- Potential Applications: Explore the application of our method in studying the influence of correlations on random walks of test particles coupled to the fluctuating field.
- Conclusion: Summarize the advantages of our proposed method and its potential impact in advancing numerical studies of quantum field correlations.
Challenges and Opportunities
While our proposed method offers a promising approach to generating correlated quantum field simulations, there are several challenges and opportunities to consider:
- Complexity of Correlation Functions: The method may become more challenging when attempting to incorporate highly complex correlation functions into simulations.
- Development of Advanced Techniques: Continuous research can lead to the development of more sophisticated techniques that improve the accuracy and efficiency of incorporating correlation functions.
- Expanded Applications: Further exploration of the effects of correlations on various phenomena can open doors to new applications in fields such as materials science, quantum computing, and quantum information theory.
“By developing innovative methods for incorporating correlation functions into numerical simulations of quantum field fluctuations, we pave the way for deeper insights into complex quantum phenomena and their practical applications.”
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by jsendak | Dec 31, 2023 | GR & QC Articles
We study numerically the existence in a false vacuum, of magnetic monopoles
which are “thin-walled”, ie, which correspond to a spherical region of
radius $R$ that is essentially trivial surrounded by a wall of thickness
$Deltall R$, hence the name thin wall, and finally an exterior region that
essentially corresponds to a pure Abelian magnetic monopole. Such monopoles
were dubbed false monopoles and can occur in non-abelian gauge theories where
the symmetry-broken vacuum is actually the false vacuum. This idea was first
proposed in cite{Kumar:2010mv}, however, their proof of the existence of false
monopoles was incorrect. Here we fill this lacuna and demonstrate numerically
the existence of thin-wall false monopoles. The decay via quantum tunnelling of
the false monopoles could be of importance to cosmological scenarios which
entertain epochs in which the universe is trapped in a symmetry-breaking false
vacuum.
The Existence of Thin-Walled False Monopoles
We have conducted numerical studies to investigate the existence of magnetic monopoles in a false vacuum that have a “thin-walled” structure. These monopoles are characterized by a central region with a radius of R, which is essentially trivial, surrounded by a thin wall with a thickness of Δ that is much smaller than R. The exterior region corresponds to a pure Abelian magnetic monopole.
Initially proposed in a paper by Kumar et al. (2010), the concept of false monopoles in non-Abelian gauge theories suggests that the symmetry-broken vacuum is actually a false vacuum. However, the original proof of the existence of false monopoles was found to be incorrect.
Numerical Evidence of Thin-Wall False Monopoles
In this study, we address the previous gap in research and provide numerical evidence for the existence of thin-wall false monopoles. Our investigations support the idea that these monopoles can indeed occur in certain non-Abelian gauge theories with a false vacuum.
Potential Significance in Cosmological Scenarios
The decay of false monopoles through quantum tunneling may have important implications for cosmological scenarios. In particular, this phenomenon could be relevant during epochs where the universe is trapped in a symmetry-breaking false vacuum. Understanding the behavior of thin-wall false monopoles can contribute to our knowledge of such cosmological events.
Roadmap for Future Research
- Further Validation: Additional numerical simulations and mathematical analyses are needed to validate our findings and confirm the existence of thin-wall false monopoles in various non-Abelian gauge theories.
- Quantum Tunneling Studies: Investigating the decay process of false monopoles through quantum tunneling is crucial for comprehending their behavior and potential cosmological consequences.
- Cosmological Applications: Explore the impact of thin-wall false monopoles on cosmological scenarios, such as inflationary models or early universe dynamics, to assess their significance in shaping the evolution of the universe.
- Extended Gauge Theories: Extend our investigations to more complex gauge theories beyond non-Abelian theories, considering the potential existence of thin-wall false monopoles in these extended frameworks.
Challenges:
- Complex Numerical Simulations: Numerically studying the properties and dynamics of thin-wall false monopoles requires computationally intensive simulations.
- Verification of Results: Ensuring the accuracy and reliability of numerical results through techniques like convergence tests and comparisons with other analytical or numerical approaches can be time-consuming.
Opportunities:
- Improved Cosmological Understanding: Gaining insights into the decay mechanisms and behavior of false monopoles can enhance our understanding of cosmological phenomena and potentially bridge gaps in current theories.
- Technological Advancements: Development of more efficient computational methods and high-performance computing infrastructure can expedite numerical investigations and facilitate larger-scale simulations.
Overall, the study of thin-wall false monopoles offers promising avenues for advancing our knowledge of non-Abelian gauge theories, the behavior of monopoles in false vacua, and their implications in cosmology. Further research and rigorous validation are essential for establishing the significance of these phenomena in broader theoretical frameworks and practical cosmological scenarios.
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