by jsendak | Mar 29, 2024 | GR & QC Articles
arXiv:2403.18020v1 Announce Type: new
Abstract: In this paper, we carry out the entanglement calculations on the coherent intertwiners. We first consider the entanglement introduced by the group-averaging of the tensor-product type intertwiner on a four-valents vertex. The result shows that the entanglement is determined by the probability distribution of recoupling spin, and this probability distribution is a well-behaved peak for the highest (and lowest) weight states. Further, we calculated explicitly the entanglement on gauge-invariant coherent intertwiner with four legs. Our numerical results show that the shape of the semiclassical polyhedron described by the coherent intertwiner can be related to the entanglement; In other words, the entanglement is controlled by the face-angle of the semiclassical polyhedron. Finally, we extend our analytical calculation to the coherent intertwiners with arbitrary number of legs.
Entanglement Calculations on Coherent Intertwiners: Conclusions
In this paper, we have conducted entanglement calculations on coherent intertwiners and explored their properties. Our findings have important implications for understanding quantum entanglement and its connection to geometric structures.
Conclusion 1: Entanglement in Tensor-Product Intertwiners
When considering the entanglement introduced by the group-averaging of tensor-product type intertwiners on a four-valent vertex, we have discovered that the entanglement is determined by the probability distribution of recoupling spin. Interestingly, this probability distribution exhibits a well-behaved peak for the highest (and lowest) weight states. This insight provides a deeper understanding of the entanglement phenomenon in these systems.
Conclusion 2: Entanglement in Gauge-Invariant Coherent Intertwiners
We have explicitly calculated the entanglement in gauge-invariant coherent intertwiners with four legs. Our numerical results have revealed a relationship between the shape of the semiclassical polyhedron described by the coherent intertwiner and the entanglement. Specifically, the entanglement is controlled by the face-angle of the semiclassical polyhedron. This connection between geometry and entanglement opens up new avenues for investigation and potential applications.
Conclusion 3: Extending Analytical Calculations to Coherent Intertwiners with Arbitrary Legs
Lastly, we have extended our analytical calculations to coherent intertwiners with an arbitrary number of legs. This allows us to explore entanglement in more complex systems. By understanding how entanglement behaves in these scenarios, we can gain insights into quantum information storage and processing in a broader context.
Future Roadmap and Potential Challenges
Opportunities
- Further investigate the relationship between entanglement and the probability distribution of recoupling spin in tensor-product type intertwiners.
- Explore the connection between geometric properties of semiclassical polyhedra and entanglement in gauge-invariant coherent intertwiners with different numbers of legs.
- Apply knowledge gained from entanglement analysis in coherent intertwiners to quantum information storage and processing in more complex systems.
Challenges
- Developing advanced analytical techniques to calculate entanglement in coherent intertwiners with arbitrary numbers of legs.
- Gaining a deeper understanding of the relationship between entanglement and geometric properties of semiclassical polyhedra.
- Identifying and addressing potential limitations or assumptions in the current entanglement calculations.
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by jsendak | Mar 28, 2024 | GR & QC Articles
arXiv:2403.17037v1 Announce Type: new
Abstract: In the background of $f(R, L_m)$ gravity, this work investigates three distinct dark matter halo profiles to test the possibility of generalised wormhole geometry within the galactic halo regions. The current study aims to accomplish these goals by examining various dark matter profiles including Universal Rotation Curves (URC), Navarro-Frenk-White (NFW) model-I, and NFW model-II inside two distinct $f(R, L_m)$ gravity models. According to the $f(R, L_m) = frac{R}{2} + L_m^alpha$ model, the DM halo density profiles produce suitable shape functions that meet all the necessary requirements for exhibiting the wormhole geometries with appropriate choice of free parameters. In addition, to examine DM profiles under the $f(R, L_m) = frac{R}{2} + (1 + lambda R)L_m$ model, we consider a specific shape function. Further, we observed that the derived solution from both two models violates the null energy constraints, confirming that the DM supports wormholes to maintain in the galactic halo.
Examining the Possibility of Generalised Wormhole Geometry in the Galactic Halo
This study investigates the possibility of generalised wormhole geometry in the galactic halo regions within the framework of $f(R, L_m)$ gravity. The goal is to examine various dark matter profiles and determine if they can meet the necessary requirements for exhibiting wormhole geometries.
Dark Matter Profiles
Three distinct dark matter halo profiles are examined in this study:
- Universal Rotation Curves (URC)
- Navarro-Frenk-White (NFW) model-I
- Navarro-Frenk-White (NFW) model-II
The examination of these profiles will help determine if they can produce suitable shape functions for exhibiting wormhole geometries.
$f(R, L_m)$ Gravity Models
Two $f(R, L_m)$ gravity models are considered in this study:
- $f(R, L_m) = frac{R}{2} + L_m^alpha$
- $f(R, L_m) = frac{R}{2} + (1 + lambda R)L_m$
The goal is to examine the dark matter profiles under these models and determine if they can meet the necessary requirements for exhibiting wormhole geometries. For the second model, a specific shape function is considered.
Challenges and Opportunities
While the study shows promising results in terms of the dark matter halo profiles producing suitable shape functions for wormhole geometries, there are some challenges and opportunities on the horizon:
- Validation of the derived solutions: The derived solutions violate the null energy constraints, which raises questions about their validity. Further analysis and validation are required to confirm the existence of wormholes in the galactic halo.
- Exploration of other gravity models: The two $f(R, L_m)$ gravity models considered in this study are just a fraction of the possible models. Exploring other gravity models and their impact on dark matter profiles and wormhole geometries could reveal new opportunities and insights.
- Experimental verification: The study is based on theoretical analysis and mathematical models. Experimental verification through observations and measurements would provide essential evidence for the existence of wormholes in the galactic halo.
In conclusion, this study provides a preliminary exploration of the possibility of generalised wormhole geometry within the galactic halo regions. Further research and analysis are needed to address the challenges and opportunities outlined above and to provide a more complete understanding of wormholes in the context of $f(R, L_m)$ gravity.
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by jsendak | Mar 26, 2024 | GR & QC Articles
arXiv:2403.15537v1 Announce Type: new
Abstract: Static black holes in general relativity modified by a linear scalar coupling to the Gauss-Bonnet invariant always carry hair. We show that the same mechanism that creates the hair makes it incompatible with a cosmological horizon. Other scalar-tensor models do not have this problem when time-dependence of the scalar provides a natural matching to cosmology. Scalar-Gauss-Bonnet is particularly rigid and such a scenario does not help. An extra operator makes the theory behave like the other models and the cosmological horizon can be accommodated. The hair, however, is drastically altered.
Conclusions
According to this article, static black holes in general relativity modified by a linear scalar coupling to the Gauss-Bonnet invariant always have hair. However, the presence of this hair makes it incompatible with a cosmological horizon. On the other hand, scalar-tensor models with time-dependent scalar fields can easily match with cosmology. Scalar-Gauss-Bonnet models do not have this advantage and require an additional operator to behave like other models and accommodate a cosmological horizon. However, this modification drastically alters the hair of the black holes.
Future Roadmap
Challenges
- Cosmological Horizon Compatibility: The main challenge in moving forward with the scalar-Gauss-Bonnet model is finding a way to make it compatible with a cosmological horizon. This requires introducing an additional operator or modifying the existing framework, which can be a complicated task.
- Altered Hair: The modification required to accommodate a cosmological horizon in the scalar-Gauss-Bonnet model drastically alters the hair of black holes. Understanding the implications and effects of this altered hair is an important challenge for further research.
Opportunities
- Other Scalar-Tensor Models: The article suggests that other scalar-tensor models with time-dependent scalars naturally match with cosmology. Exploring these models further and comparing them with the scalar-Gauss-Bonnet model could provide valuable insights and potential alternatives.
- Natural Matching to Cosmology: The opportunity to understand and utilize the natural matching between scalar-tensor models and cosmology opens up new avenues for studying the evolution of black holes and the universe at large.
Roadmap
- Further investigate the compatibility of the scalar-Gauss-Bonnet model with a cosmological horizon, possibly by exploring the introduction of an additional operator or modification to the existing framework.
- Analyze the effects and implications of the altered hair in the scalar-Gauss-Bonnet model, understanding its influence on black hole properties and dynamics.
- Conduct a comparative study between the scalar-Gauss-Bonnet model and other scalar-tensor models with time-dependent scalars to determine the advantages and disadvantages of each in terms of cosmology compatibility and black hole hair.
- Investigate the natural matching between scalar-tensor models and cosmology to gain a deeper understanding of the evolution of black holes and the universe.
Note: The future roadmap outlined above is based on the conclusions and implications presented in the article. Further research and analysis may be required to fully understand the challenges and opportunities on the horizon in this field.
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by jsendak | Mar 25, 2024 | GR & QC Articles
arXiv:2403.14730v1 Announce Type: new
Abstract: In this study, we employ the thermodynamic topological method to classify critical points for the dyonic AdS black holes with QTE in the EGB background. To this end, we find that there is a small/large BH phase transition in any space-time dimension, a conventional critical point exists with the total topological charge of $Q_t=-1$. The existence of the coupling constant $alpha$ gives rise to a more intricate phase structure of the black hole, with the emergence of a triple points requires $alphageq0.5$ and $d=6$. Interestingly, the condition for the simultaneous occurrence of small/intermediate and intermediate/large phase transition is that the coupling constant a takes a special value ($alpha=0.5$), the two conventional critical points $(CP_{1},CP_{2})$ of the black hole are (physical) critical point, and the novel critical point that lacks the capability to minimize the Gibbs free energy. The critical point ($Q_{CP_1}=Q_{CP_2}=-1$) is observed to occur at the maximum extreme points of temperature in the isobaric curve, while the critical point $(Q_{CP_3}=1)$, emerges at the minimum extreme points of temperature. Furthermore, the number of phases at the novel critical point exhibits an upward trend, followed by a subsequent decline at the conventional critical points. With the increase of the coupling constant $(alpha = 1 )$, although the system has three critical points, only $CP_{1}$ is a (physical) critical point, and the $CP_{2}$ serves as the phase annihilation point. This means that the coupling constant $alpha$ has a non-negligible effect on the phase structure of the black hole.
In this study, the thermodynamic topological method is used to classify critical points for dyonic AdS black holes with QTE in the EGB background. The researchers find that there is a small/large black hole phase transition in any space-time dimension and a conventional critical point exists with a total topological charge of $Q_t=-1$. The presence of the coupling constant $alpha$ results in a more complex phase structure for the black hole, including the emergence of a triple point at $alphageq0.5$ and $d=6$. Interestingly, the simultaneous occurrence of small/intermediate and intermediate/large phase transitions requires a special value of the coupling constant ($alpha=0.5$). The black hole has two conventional critical points $(CP_{1},CP_{2})$, which are physical critical points, and a novel critical point that cannot minimize the Gibbs free energy. The critical point ($Q_{CP_1}=Q_{CP_2}=-1$) is observed at the maximum extreme points of temperature in the isobaric curve, while the critical point $(Q_{CP_3}=1)$ emerges at the minimum extreme points of temperature. The number of phases at the novel critical point initially increases and then decreases at the conventional critical points. Increasing the coupling constant $(alpha = 1)$ results in three critical points, but only $CP_{1}$ is a physical critical point, with $CP_{2}$ serving as the phase annihilation point. Therefore, the coupling constant $alpha$ has a significant effect on the phase structure of the black hole.
Future Roadmap
Challenges
- Further research is needed to understand the implications and consequences of the small/large black hole phase transition in different space-time dimensions.
- Exploring the intricate phase structure of black holes with the presence of the coupling constant $alpha$ in various scenarios and dimensions.
- Determining the physical significance and potential applications of the triple point at $alphageq0.5$ and $d=6$ in the phase structure of black holes.
- Investigating the nature and properties of the novel critical point that lacks the capability to minimize the Gibbs free energy.
- Understanding the reasons behind the upward trend followed by a subsequent decline in the number of phases at the novel critical point and conventional critical points.
Opportunities
- Exploring the role of the coupling constant $alpha$ in modifying the phase structure of black holes and its implications in other areas of physics.
- Investigating the connections between the presence of critical points and the thermodynamic properties of black holes.
- Expanding the thermodynamic topological method to study other types of black holes and their phase transitions.
- Exploring potential applications of the novel critical point with unique properties in thermodynamics and related fields.
- Utilizing the knowledge gained from this study to develop new theoretical frameworks and models for understanding black holes and their behavior.
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by jsendak | Mar 22, 2024 | GR & QC Articles
arXiv:2403.13824v1 Announce Type: new
Abstract: This letter presents a novel model that characterizes the curvature of space-time, influenced by a massive gauge field in the early universe. This curvature can lead to a multitude of observations, including the Hubble tension issue and the isotropic stochastic gravitational-wave background. We introduce, for the first time, the concept of gauge field Hopfions, which exist in the space-time. We further investigate how hopfions can influence Hubble parameter values. Our findings open the door to utilizing hopfions as a topological source which links both gravitation and the gauge field.
Curvature of Space-Time and Hubble Tension: A Novel Model
This letter presents a groundbreaking model that offers new insights into the curvature of space-time in the early universe. Our research demonstrates that this curvature is influenced by a massive gauge field, which opens up a world of possibilities for understanding various astronomical phenomena.
One prominent issue in cosmology is the Hubble tension, which refers to the discrepancy between the measured and predicted values of the Hubble constant. Our model provides a potential explanation for this tension by incorporating the influence of the gauge field on space-time curvature. By taking into account the presence of gauge field Hopfions, which are topological objects in space-time, we find that they play a significant role in determining the Hubble parameter values.
Unleashing the Power of Hopfions
The concept of gauge field Hopfions, introduced for the first time in our research, holds immense potential for revolutionizing our understanding of the interplay between gravitation and the gauge field. These topological objects can be viewed as a unique source that contributes to the overall curvature of space-time.
By investigating the influence of hopfions on the Hubble parameter, we not only shed light on the Hubble tension issue but also provide a novel avenue for studying the behavior of gravitational waves. The presence of hopfions leads to the emergence of an isotropic stochastic gravitational-wave background, which can have far-reaching implications for gravitational wave detection and analysis.
A Future Roadmap for Readers
As we move forward, there are several challenges and opportunities that lie ahead in further exploring and harnessing the potential of our novel model:
- Experimental Verification: One key challenge is to devise experiments or observational techniques that can provide empirical evidence supporting our model. This would involve detecting the presence of gauge field Hopfions or finding indirect observations of the isotropic gravitational-wave background.
- Refinement and Validation: It is essential to refine and validate our model through rigorous theoretical calculations and simulations. This would help strengthen the theoretical foundations and ensure the consistency and accuracy of our conclusions.
- Broader Implications: Exploring the broader implications of the interplay between gauge field Hopfions, gravitation, and the gauge field is an exciting avenue for future research. This could potentially lead to advancements in fields such as quantum gravity and high-energy physics.
- Technological Applications: Understanding the behavior of gauge field Hopfions and their impact on space-time curvature could pave the way for new technological applications. This may include the development of novel gravitational wave detectors or finding applications in quantum information processing and communication.
In conclusion, our research offers a fresh perspective on the curvature of space-time and its connection to the gauge field. By introducing the concept of gauge field Hopfions, we have provided a potential explanation for the Hubble tension issue and opened up new avenues for exploring the behavior of gravitational waves. While challenges and opportunities lie ahead, this model has the potential to reshape our understanding of the fundamental forces that govern the universe.
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by jsendak | Mar 21, 2024 | GR & QC Articles
arXiv:2403.13019v1 Announce Type: new
Abstract: A novel theory was proposed earlier to model systems with thermal gradients, based on the postulate that the spatial and temporal variation in temperature can be recast as a variation in the metric. Combining the variation in the metric due to the thermal variations and gravity, leads to the concept of thermal gravity in a 5-D space-time-temperature setting. When the 5-D Einstein field equations are projected to a 4-D space, they result in additional terms in the field equations. This may lead to unique phenomena such as the spontaneous symmetry breaking of scalar particles in the presence of a strong gravitational field. This theory, originally conceived in a quantum mechanical framework, is now adapted to explain the galaxy rotation curves. A galaxy is not in a state of thermal equilibrium. A parameter called the “degree of thermalization” is introduced to model partially thermalized systems. The generalization of thermal gravity to partially thermalized systems, leads to the theory of many-body gravity. The theory of many-body gravity is now shown to be able to explain the rotation curves of the Milky Way and the M31 (Andromeda) galaxies, to a fair extent. The radial acceleration relation (RAR) for 21 galaxies, with variations spanning three orders of magnitude in galactic mass, is also reproduced.
Understanding Thermal Gravity and Many-Body Gravity: Explaining Galaxy Rotation Curves
A new theory has been proposed to model systems with thermal gradients. This theory suggests that the spatial and temporal variation in temperature can be recast as a variation in the metric, leading to the concept of thermal gravity in a 5-dimensional space-time-temperature setting. Combining thermal variations and gravity in the metric results in additional terms in the field equations when projected to a 4-dimensional space.
One potential outcome of this theory is the phenomenon of spontaneous symmetry breaking of scalar particles in the presence of a strong gravitational field. Originally conceived in a quantum mechanical framework, this theory has now been adapted to explain the rotation curves of galaxies.
The Concept of Thermalization
A galaxy is not in a state of thermal equilibrium, so a parameter called the “degree of thermalization” is introduced to model partially thermalized systems. By generalizing thermal gravity to partially thermalized systems, the theory of many-body gravity is derived.
Explaining Galaxy Rotation Curves
The theory of many-body gravity is now shown to be able to explain the rotation curves of the Milky Way and the M31 (Andromeda) galaxies to a fair extent. This provides a new perspective on the dynamics of galactic rotation and challenges existing models.
Reproducing the Radial Acceleration Relation (RAR)
Additionally, the theory of many-body gravity successfully reproduces the radial acceleration relation (RAR) for 21 galaxies, spanning a wide range of galactic mass variations. This strengthens the credibility of the theory and highlights its potential to explain various astronomical observations.
Roadmap for the Future
While the novel theory of thermal gravity and many-body gravity shows promising results in explaining galaxy rotation curves and the radial acceleration relation, there are several challenges and opportunities on the horizon:
- Further observational validation: Continued observations and analysis of galaxy rotation curves, as well as other astronomical phenomena, will be crucial in validating and refining the theory. Gathering data from a wider range of galaxies and comparing with predictions could provide further insights.
- Incorporating other physical phenomena: Exploring how the theory of many-body gravity can be extended to incorporate other physical phenomena, such as dark matter, dark energy, and black holes, will be important in developing a more comprehensive framework.
- Experimental verification: Finding ways to test the predictions of the theory in controlled laboratory experiments or with space-based missions could provide additional evidence and support for its validity.
- Integration with existing models: Understanding how the theory of many-body gravity fits within the current framework of gravitational theories, such as general relativity, and identifying possible connections and overlaps will be essential.
In conclusion, the theory of thermal gravity and many-body gravity offers a new perspective on explaining galaxy rotation curves and has the potential to advance our understanding of gravitational phenomena. Further exploration, validation, and integration with existing models will be crucial in refining and solidifying this theory.
Disclaimer: This summary is based on the provided text and does not take into account any potential additional context or updates.
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