by jsendak | Jan 22, 2024 | GR & QC Articles
We delve into the first-order thermodynamics of Horndeski gravity, focusing
on spatially flat, homogeneous, and isotropic cosmologies. Our exploration
begins with a comprehensive review of the effective fluid representation within
viable Horndeski gravity. Notably, we uncover a surprising alignment between
the constitutive relations governing the “Horndeski fluid” and those of
Eckart’s thermodynamics. Narrowing our focus, we specialize our discussion to
spatially flat Friedmann-Lema{^i}tre-Robertson-Walker spacetimes. Within this
specific cosmological framework, we systematically analyze two classes of
theories: shift-symmetric and asymptotically shift-symmetric. These theories
are characterized by a non-vanishing braiding parameter, adding a nuanced
dimension to our investigation. On the one hand, unlike the case of the
“traditional” scalar-tensor gravity, these peculiar subclasses of viable
Horndeski gravity never relax to General Relativity (seen within this formalism
as an equilibrium state at zero temperature), but give rise to additional
equilibrium states with non-vanishing viscosity. On the other hand, this
analysis further confirms previous findings according to which curvature
singularities are “hot” and exhibit a diverging temperature, which suggests
that deviations of scalar-tensor theories from General Relativity become
extreme at spacetime singularities. Furthermore, we provide a novel exact
cosmological solution for an asymptotically shift-symmetric theory as a toy
model for our thermodynamic analysis.
Horndeski gravity is a topic of interest in the study of cosmology. In this article, we delve into the first-order thermodynamics of Horndeski gravity, specifically focusing on spatially flat, homogeneous, and isotropic cosmologies.
Before diving into the specifics, we provide a comprehensive review of the effective fluid representation within viable Horndeski gravity. Surprisingly, we uncover an alignment between the constitutive relations governing the “Horndeski fluid” and those of Eckart’s thermodynamics.
Next, we narrow our focus to spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes. Within this specific cosmological framework, we systematically analyze two classes of theories: shift-symmetric and asymptotically shift-symmetric. These theories are characterized by a non-vanishing braiding parameter, which adds depth to our investigation.
Our analysis reveals that unlike traditional scalar-tensor gravity, the peculiar subclasses of viable Horndeski gravity never relax to General Relativity as an equilibrium state at zero temperature. Instead, they give rise to additional equilibrium states with non-vanishing viscosity. This highlights the unique properties of Horndeski gravity.
Additionally, our findings confirm previous research showing that curvature singularities are “hot” and exhibit a diverging temperature. This implies that deviations of scalar-tensor theories from General Relativity become extreme at spacetime singularities.
To further support our analysis, we present a novel exact cosmological solution for an asymptotically shift-symmetric theory. This solution serves as a toy model for our thermodynamic analysis and adds another layer to our understanding.
Future Roadmap
The exploration of Horndeski gravity in the context of first-order thermodynamics opens up several potential avenues for future research. Here is a roadmap outlining potential challenges and opportunities on the horizon:
1. Investigating Other Cosmological Frameworks
While our analysis focuses on spatially flat FLRW spacetimes, it would be valuable to extend the study to other cosmological frameworks, such as non-flat or anisotropic spacetimes. Exploring the thermodynamics of Horndeski gravity in these contexts may reveal new insights and properties.
2. Experimental and Observational Confirmation
Validating the predictions and findings of our thermodynamic analysis through experiments or observations would further solidify the understanding of Horndeski gravity. This could involve testing the existence of additional equilibrium states with non-vanishing viscosity or investigating the temperature behavior near curvature singularities.
3. Quantum Effects and Thermodynamics
Examining the interplay between quantum effects and thermodynamics within the context of Horndeski gravity could lead to exciting discoveries. Investigating the behavior of Horndeski gravity at extreme energies or exploring the connection between thermodynamics and quantum field theory may unlock new perspectives.
4. Generalizing the Analysis
Expanding the analysis beyond the specific subclasses of shift-symmetric and asymptotically shift-symmetric theories could reveal a broader picture of Horndeski gravity. Generalizing the thermodynamic analysis to include a wider range of theories and scenarios would provide a more comprehensive understanding of the subject.
5. Applications in Cosmological Evolution
Exploring how the thermodynamics of Horndeski gravity affect cosmological evolution could have practical applications. This could involve studying the influence of additional equilibrium states with non-vanishing viscosity on the dynamics of the universe or investigating how the temperature behavior near curvature singularities impacts the evolution of cosmic structures.
Overall, the study of first-order thermodynamics in Horndeski gravity offers a rich field for future exploration. By addressing the outlined challenges and opportunities, researchers can gain a deeper understanding of the subject and potentially uncover new phenomena and insights.
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by jsendak | Jan 20, 2024 | GR & QC Articles
We study the geometry of $Tbar{T}$-deformed BTZ black hole and find it can
be regarded as a quotient of hyperbolic space. We then consider the massive
scalar field propagating in the $Tbar{T}$-deformed BTZ black hole background.
The one-loop partition function of scalar field is calculated using the heat
kernel method and the Wilson spool proposal. These two methods give consistent
result which implies the Wilson spool proposal still holds under $Tbar{T}$
deformation. Moreover, we also calculate the one-loop partition function of
graviton in $Tbar{T}$-deformed BTZ black hole. We find the deformed one-loop
partition functions are modified in a simple way, which corresponds to a
replacement of the modular parameter. The result precisely matches the large
$c$ expansion of $Tbar{T}$-deformed CFT partition function. These results
provide a further check about the correspondence between $Tbar{T}$-deformed
CFT$_2$ and AdS$_3$ with mixed boundary condition.
Examining the Conclusions and Outlining a Future Roadmap
The study of the geometry of the $Tbar{T}$-deformed BTZ black hole has yielded interesting results that provide insight into the connection between $Tbar{T}$-deformed CFT (Conformal Field Theory) and AdS (Anti-de Sitter) spacetime with mixed boundary condition. In addition, the calculations of the one-loop partition functions for the massive scalar field and graviton in the deformed black hole background have shown consistent results and modifications that align with the $Tbar{T}$ deformation.
Potential Challenges
- Further investigation is required to understand the precise implications and consequences of the replacement of the modular parameter and its impact on the deformed one-loop partition functions.
- Exploring the physical interpretation of the modified partition functions and their connection to other aspects of quantum gravity and quantum field theory.
- Understanding the broader implications of the consistent results obtained from both the heat kernel method and the Wilson spool proposal.
Potential Opportunities
- Utilizing the insights gained from this study to further explore the correspondence between $Tbar{T}$-deformed CFT$_2$ and AdS$_3$ with mixed boundary condition.
- Investigating the potential applications of these findings in other areas of theoretical physics, such as holography and black hole physics.
- Considering the implications for quantum information theory and quantum gravity, particularly in relation to entanglement entropy and the holographic principle.
In summary, the examination of the $Tbar{T}$-deformed BTZ black hole geometry and the calculation of the one-loop partition functions for scalar fields and gravitons have provided valuable insights into the correspondences between $Tbar{T}$-deformed CFT and AdS spacetime with mixed boundary condition. However, further exploration and investigation are needed to fully understand the implications of these results and to explore their broader applications in theoretical physics.
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by jsendak | Jan 18, 2024 | GR & QC Articles
We develop a purely quantum theory based on the novel principle of
relativity, termed the quantum principle of relativity, without introducing
general relativity. We demonstrate that the essence of the principle of
relativity can be naturally extended into the quantum realm, maintaining the
identical structures of active and passive transformations. By employing this
principle, we show that gravitational effects are naturally incorporated into
the renormalizable theory, with general relativity emerging in the classical
regime. We derive graviton propagators and provide several examples grounded in
this novel theory.
The Quantum Principle of Relativity
In this article, we introduce a purely quantum theory called the quantum principle of relativity. Unlike general relativity, which deals with the classical regime, our theory extends the principle of relativity into the quantum realm. By doing so, we maintain the identical structures of active and passive transformations.
Natural Incorporation of Gravitational Effects
One of the key findings of our theory is that gravitational effects can be naturally incorporated into a renormalizable theory. This means that we do not have to introduce general relativity to account for gravity in a quantum framework. By employing the quantum principle of relativity, we show how gravitational effects emerge within this new theory.
Graviton Propagators and Examples
We have derived graviton propagators based on the quantum principle of relativity. These propagators allow us to understand the behavior of gravitons in our theory. Moreover, we provide several examples grounded in this novel theory, demonstrating its applicability in different scenarios.
Future Roadmap
As we look ahead, there are both challenges and opportunities on the horizon for our quantum principle of relativity.
Challenges
- Further theoretical development: While we have laid the foundation for the quantum principle of relativity, there is still much work to be done in terms of theoretical development. Our theory should be further refined and tested against existing experimental data.
- Experimental validation: It is crucial to design and conduct experiments that can validate the predictions of our theory. This will require advanced experimental techniques and collaborations with experimental physicists.
- Integration with other theories: The quantum principle of relativity should eventually be integrated with other fundamental theories, such as quantum mechanics and quantum field theory. Achieving this integration will be a complex task that requires interdisciplinary collaboration.
Opportunities
- New insights into gravity: The quantum principle of relativity opens up new avenues for understanding the nature of gravity. It provides a fresh perspective on how gravitational effects emerge in a quantum framework, offering potential breakthroughs in our understanding of the fundamental forces of nature.
- Advancements in quantum technology: The development of a purely quantum theory like the quantum principle of relativity may lead to advancements in quantum technology. Understanding graviton behavior and gravitational interactions at a quantum level could have practical applications in fields such as quantum computing and quantum communication.
- Unifying theories: The integration of the quantum principle of relativity with other fundamental theories has the potential to lead to a unified theory of physics. This would provide a comprehensive framework for understanding the behavior of particles and forces in the universe.
In conclusion, the quantum principle of relativity offers a new perspective on the relationship between quantum theory and gravity. While there are challenges ahead in terms of theoretical development and experimental validation, there are also exciting opportunities for deepening our understanding of gravity and advancing quantum technology.
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by jsendak | Jan 18, 2024 | GR & QC Articles
We study the non-unitary relation between quantum gravitational models
defined using different internal times. We show that despite the non-unitarity,
it is possible to provide a prescription for making unambiguous, though
restricted, physical predictions independent of specific clocks. To illustrate
this result, we employ a model of quantum gravitational waves in a quantum
Friedmann universe.
Examining the Conclusions of the Study
The study investigates the non-unitary relation between quantum gravitational models that are defined using different internal times. Despite the non-unitarity, the researchers find that it is possible to formulate a prescription for making unambiguous physical predictions. These predictions are independent of specific clocks, suggesting a way to overcome the challenges posed by non-unitarity.
Roadmap for Readers
- Introduction: Provide an overview of the study’s purpose and objectives. Explain the significance of understanding the non-unitary relation between quantum gravitational models.
- Background: Explain the concept of quantum gravitational models and their dependence on internal times. Discuss the challenges posed by non-unitarity in these models.
- Methodology: Describe the approach taken by the researchers to investigate the non-unitary relation. Include details about the model of quantum gravitational waves in a quantum Friedmann universe used as an illustration.
- Results: Highlight the key findings of the study, emphasizing the possibility of providing unambiguous physical predictions independent of specific clocks.
- Discussion: Analyze the implications and significance of the results. Discuss how the prescription for making predictions can help overcome the limitations imposed by non-unitarity and enhance our understanding of quantum gravitational models.
- Conclusion: Summarize the main conclusions and contributions of the study. Highlight potential future directions for research in this field.
Potential Challenges and Opportunities on the Horizon
While the study presents a promising approach to addressing non-unitarity challenges in quantum gravitational models, several potential challenges and opportunities lie ahead:
Challenges:
- Validating the results: Further research and experimentation are necessary to validate the findings and ensure their applicability to a broader range of quantum gravitational models.
- Extending to other contexts: Exploring the non-unitary relation in different quantum gravitational contexts could introduce additional complexities and challenges.
- Practical implementation: Translating the prescription for making predictions into practical applications may present technical and theoretical challenges.
Opportunities:
- Advancing theoretical frameworks: The study opens avenues for refining existing theoretical frameworks of quantum gravity and furthering our understanding of the underlying principles.
- Potential breakthroughs: Overcoming non-unitarity challenges could lead to significant breakthroughs in our ability to accurately describe and predict quantum gravitational phenomena.
- Integration with other fields: Bridging the gap between quantum gravitational models and other areas, such as cosmology or quantum field theory, could lead to novel insights and interdisciplinary collaborations.
In Conclusion
This study offers a prescription for making unambiguous physical predictions independent of specific clocks in quantum gravitational models despite their non-unitary nature. By understanding and overcoming the challenges posed by non-unitarity, we can enhance our knowledge of quantum gravity and potentially uncover new frontiers in fundamental physics. However, continued research, validation, and practical implementation are necessary to fully realize the opportunities presented by these findings.
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by jsendak | Jan 14, 2024 | GR & QC Articles
Here, we present an algebraic and kinematical analysis of non-commutative
$kappa$-Minkowski spaces within Galilean (non-relativistic) and Carrollian
(ultra-relativistic) regimes. Utilizing the theory of Wigner-In”{o}nu
contractions, we begin with a brief review of how one can apply these
contractions to the well-known Poincar'{e} algebra, yielding the corresponding
Galilean (both massive and mass-less) and Carrollian algebras as $c to infty$
and $cto 0$, respectively. Subsequently, we methodically apply these
contractions to non-commutative $kappa$-deformed spaces, revealing compelling
insights into the interplay among the non-commutative parameters $a^mu$ (with
$|a^nu|$ being of the order of Planck length scale) and the speed of light $c$
as it approaches both infinity and zero. Our exploration predicts a sort of
“branching” of the non-commutative parameters $a^mu$, leading to the emergence
of a novel length scale and time scale in either limit. Furthermore, our
investigation extends to the examination of curved momentum spaces and their
geodesic distances in appropriate subspaces of the $kappa$-deformed Newtonian
and Carrollian space-times. We finally delve into the study of their deformed
dispersion relations, arising from these deformed geodesic distances, providing
a comprehensive understanding of the nature of these space-times.
Here, we present an analysis of non-commutative $kappa$-Minkowski spaces within Galilean and Carrollian regimes. We use the theory of Wigner-In”{o}nu contractions to apply these contractions to the well-known Poincar'{e} algebra, obtaining the corresponding Galilean and Carrollian algebras as $c$ approaches infinity and zero, respectively.
Next, we apply these contractions to non-commutative $kappa$-deformed spaces, exploring the interplay between the non-commutative parameters $a^mu$ (of the order of Planck length scale) and the speed of light $c$ as it approaches both infinity and zero. Interestingly, our analysis predicts a “branching” of the non-commutative parameters $a^mu$, leading to the emergence of a novel length scale and time scale in each limit.
We also investigate curved momentum spaces and their geodesic distances in appropriate subspaces of the $kappa$-deformed Newtonian and Carrollian space-times. This exploration allows us to study deformed dispersion relations arising from these deformed geodesic distances, providing a comprehensive understanding of the nature of these space-times.
Future Roadmap
Our analysis opens up several avenues for future research in the field of non-commutative $kappa$-Minkiwoski spaces and their applications. Here is a suggested roadmap for readers interested in further exploration:
1. Experimental Tests
One potential challenge is to design and perform experimental tests to validate the predictions made by our analysis. Investigating the effects of non-commutativity at high-energy regimes or in extreme gravitational fields could provide valuable insights into the validity of these theoretical concepts.
2. Mathematical Refinements
There is still room for further mathematical refinements in the study of non-commutative $kappa$-Minkowski spaces. Analyzing the algebraic properties and symmetry transformations of these spaces in more detail could lead to a deeper understanding of their structures.
3. Cosmological Implications
It would be interesting to explore the cosmological implications of non-commutative $kappa$-Minkowski spaces. Investigating their effects on inflationary models or the early universe could provide valuable insights into the fundamental nature of space and time.
4. Quantum Field Theory on Non-Commutative $kappa$-Minkowski Spaces
Extending the study to quantum field theory on non-commutative $kappa$-Minkowski spaces could shed light on the behavior of fundamental particles in these exotic space-time backgrounds. Understanding their effects on particle interactions and scattering processes could have significant implications for particle physics.
5. Generalizations to Other Non-Relativistic and Ultra-Relativistic Regimes
Exploring the applicability of our analysis to other non-relativistic and ultra-relativistic regimes beyond Galilean and Carrollian algebras could unveil new insights and possibilities. Investigating the behavior of non-commutative $kappa$-Minkowski spaces in different physical contexts could lead to unexpected phenomena.
6. Gravitational Aspects
An intriguing avenue for future research is to incorporate gravitational aspects into the study of non-commutative $kappa$-Minkowski spaces. Analyzing the interplay between gravity and non-commutativity could uncover novel gravitational effects and potentially reconcile quantum mechanics with general relativity.
In summary, our analysis of non-commutative $kappa$-Minkowski spaces opens up a wide range of future research directions. While there are challenges in experimental validation and mathematical refinement, the opportunities for exploring cosmological implications, quantum field theory, generalizations to other regimes, and gravitational aspects are promising.
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