by jsendak | Apr 5, 2024 | GR & QC Articles
arXiv:2404.02922v1 Announce Type: new
Abstract: We investigate the scalar induced gravitational waves (SIGWs) in metric teleparallel gravity with the Nieh-Yan (NY) term, which results in parity violation during the radiation-dominated era. By solving the equations of motion of linear scalar perturbations from both the metric and tetrad fields, we obtain the corresponding analytic expressions. Then, we calculate the SIGWs in metric teleparallel gravity with the NY term and evaluate the energy density of SIGWs with a monochromatic power spectrum numerically. We find that the spectrum of the energy density of SIGWs in metric teleparallel gravity with the NY term is significantly different from that in general relativity (GR), which makes metric teleparallel gravity distinguishable from GR.
Scalar Induced Gravitational Waves in Metric Teleparallel Gravity with the Nieh-Yan Term
In this article, we explore the phenomenon of scalar induced gravitational waves (SIGWs) in metric teleparallel gravity with the Nieh-Yan (NY) term. The presence of the NY term introduces parity violation during the radiation-dominated era, leading to interesting implications for gravitational wave production. By solving the equations of motion for linear scalar perturbations in both the metric and tetrad fields, we derive analytical expressions for the SIGWs. We then proceed to calculate the energy density of SIGWs with a monochromatic power spectrum, comparing it to that in general relativity (GR).
Key Conclusions
- Metric teleparallel gravity with the NY term produces SIGWs with a distinct energy density spectrum compared to GR. This distinction allows us to differentiate between the two theories.
Future Roadmap
While this study provides valuable insights into SIGWs in metric teleparallel gravity with the NY term, there are several avenues for future research:
- Further investigation can be done to understand the implications of the distinct energy density spectrum of SIGWs in metric teleparallel gravity. Are there observable consequences of this difference that can be tested? What astrophysical phenomena can be studied to explore this distinction?
- It would be interesting to explore the behavior of higher-order perturbations in metric teleparallel gravity with the NY term. Do higher-order perturbations exhibit similar distinctions from GR, or do they behave differently?
- Investigating the role of the NY term in other cosmological epochs and gravitational wave production scenarios can provide a comprehensive understanding of its impact on the overall dynamics of the universe. Are there additional epochs or scenarios where the NY term has a significant effect?
Challenges and Opportunities:
The challenges ahead involve theoretical modeling and numerical calculations to explore the observability of the differences in the energy density spectrum of SIGWs between metric teleparallel gravity and GR. Astrophysical observations and experiments may be necessary to test these predictions.
The opportunities lie in the potential for metric teleparallel gravity with the NY term to offer an alternative framework for studying gravitational waves and the fundamental nature of gravity. Exploring the implications of the NY term in various astrophysical contexts could lead to new insights and discoveries.
Read the original article
by jsendak | Apr 4, 2024 | GR & QC Articles
arXiv:2404.02195v1 Announce Type: new
Abstract: We study radiation from charged particles in circular motion around a Schwarzschild black hole immersed in an asymptotically uniform magnetic field. In curved space, the radiation reaction force is described by the DeWitt-Brehme equation, which includes a complicated, non-local tail term. We show that, contrary to some claims in the literature, this term cannot, in general, be neglected. We account for self-force effects directly by calculating the electromagnetic energy flux at infinity and on the horizon. The radiative field is obtained using black hole perturbation theory. We solve the relevant equations analytically, in the low-frequency and slow-motion approximation, as well as numerically in the general case. Our results show that great care must be taken when neglecting the tail term, which is often fundamental to capture the dynamics of the particle: in fact, it only seems to be negligible when the magnetic force greatly dominates the gravitational force, so that the motion is well described by the Abraham–Lorentz–Dirac equation. We also report a curious “horizon dominance effect” that occurs for a radiating particle in a circular orbit around a black hole (emitting either scalar, electromagnetic or gravitational waves): for fixed orbital radius, the fraction of energy that is absorbed by the black hole can be made arbitrarily large by decreasing the particle velocity.
In this study, the authors investigate the radiation emitted by charged particles in circular motion around a Schwarzschild black hole in the presence of an asymptotically uniform magnetic field. They specifically focus on the importance of the non-local tail term in the DeWitt-Brehme equation, which describes the radiation reaction force in curved space.
Main Conclusions:
- The non-local tail term in the DeWitt-Brehme equation cannot be neglected in general, contrary to some claims in the literature.
- The inclusion of the tail term is necessary to accurately capture the dynamics of the particle, especially when the magnetic force dominates the gravitational force.
- An analytical solution is derived in the low-frequency and slow-motion approximation, as well as a numerical solution for the general case.
- It is found that the absorption of energy by the black hole can be significantly increased by decreasing the particle velocity for a radiating particle in a circular orbit.
Future Roadmap:
1. Further Investigation of Tail Term:
Future research should delve deeper into the behavior and implications of the non-local tail term in the DeWitt-Brehme equation. Specifically, a more comprehensive understanding of the scenarios in which the term cannot be neglected is necessary. This will help refine models and calculations related to the radiation emitted by charged particles in curved space.
2. Experimental and Observational Validation:
Experimental or observational studies could be conducted to validate the findings of this study. By examining the radiation emitted by charged particles around black holes with magnetic fields, researchers could verify the importance of the non-local tail term and its impact on the dynamics of the particles. This could involve analyzing astrophysical data or designing specialized particle acceleration experiments.
3. Investigation of Other Particle Orbits:
Expanding the scope of the research to include particles in different orbital configurations, such as elliptical or inclined orbits, would provide a more comprehensive understanding of the radiation emitted in curved space. The effects of the non-local tail term on these orbits could reveal additional insights into the interplay between gravitational and magnetic forces.
4. Study of Radiation Effects on Black Hole Evolution:
Further exploration of the absorption of energy by black holes could shed light on their evolution and the interactions between radiation and spacetime curvature. Investigating the “horizon dominance effect” reported in this study, where increasing energy absorption occurs at lower particle velocities, could have implications for the dynamics and behavior of black holes in the presence of radiation.
Potential Challenges:
- Theoretical Complexity: The mathematical and theoretical aspects of this research may present challenges for researchers aiming to build upon these findings. Understanding and accurately modeling the non-local tail term and its effects in more complex scenarios could require advanced mathematical techniques and computational resources.
- Limited Observational Data: Obtaining observational data directly related to the radiation emitted by charged particles around black holes with magnetic fields can be challenging. Researchers may need to rely on indirect measurements or simulations to validate and extend the conclusions of this study.
- Experimental Constraints: Designing and conducting experiments to validate these theoretical findings may present technical and logistical challenges. Precision control and measurement of charged particles in the vicinity of black holes could be difficult to achieve in a laboratory setting.
Potential Opportunities:
- Refinement of Models: The findings of this study provide an opportunity to refine models and calculations related to the radiation emitted by charged particles in curved space. By considering the non-local tail term, researchers can improve the accuracy of their predictions and gain a deeper understanding of the underlying physics.
- Exploration of Astrophysical Phenomena: The investigation of radiation from charged particles in the vicinity of black holes with magnetic fields offers opportunities to better understand astrophysical phenomena. By studying the interplay between gravitational and magnetic forces, researchers can contribute to our knowledge of black hole evolution, radiation emissions, and the dynamics of particles in extreme environments.
- Technological Applications: The insights gained from studying radiation effects in curved space could have practical applications. Understanding the behavior of charged particles in strong gravitational and magnetic fields may influence the design of future particle accelerators or facilitate developments in fields such as astrophysics and materials science.
Overall, this study highlights the importance of considering the non-local tail term in the DeWitt-Brehme equation when studying radiation from charged particles around black holes with magnetic fields. While challenges in theoretical complexity, limited observational data, and experimental constraints may exist, the opportunities for refining models, exploring astrophysical phenomena, and discovering technological applications make this area of research promising for future advancements.
Read the original article
by jsendak | Apr 2, 2024 | GR & QC Articles
arXiv:2403.19733v1 Announce Type: new
Abstract: We present an exhaustive study of wormhole configurations in $kappa(mathcal{R},mathcal{T})$ gravity with linear and non-linear functions. The model assumed Morrison-Thorne spacetime where the redshift and shape functions linked with the matter contain and geometry of the spacetime through non-covariant conservation equation of the stress-energy tensor. The first solution was explored assuming a constant redshift function that leads to a wormhole (WH) which is asymptotically non-flat. The remaining solutions were explored in two cases. Firstly, assuming a linear equation of state $p(r)=omega rho(r)$ along with different forms of $kappa(mathcal{R},mathcal{T})-$function. This proved enough to derive a shape function of the form $b(r)=r_{0}left(frac{r_{0}}{r}right)^{1/omega}$. Secondly, by assuming specific choices of the shape function consistent with the wormhole configuration requirements. All the solutions fulfill flare-out condition, asymptotically flat and supported by phantom energy. Further, the embedding surface and its revolution has been generated using numerical method to see how the length of the throat is affected of the coupling parameters through $kappa(mathcal{R},mathcal{T})$ function. At the end, we have also calculated the average null energy condition, which is satisfied by all the WH models signifying minimum exotic matter is required to open the WH throats.
According to the article on wormhole configurations in $kappa(mathcal{R},mathcal{T})$ gravity, several conclusions can be drawn. Firstly, a solution with a constant redshift function leads to a wormhole that is asymptotically non-flat. Secondly, by assuming a linear equation of state $p(r)=omega rho(r)$ along with different forms of $kappa(mathcal{R},mathcal{T})-$function, the shape function of the wormhole can be derived as $b(r)=r_{0}left(frac{r_{0}}{r}right)^{1/omega}$. Thirdly, specific choices of the shape function consistent with the wormhole configuration requirements were explored. All the solutions fulfill the flare-out condition, are asymptotically flat, and supported by phantom energy. Furthermore, the length of the throat of the wormhole is affected by the coupling parameters through the $kappa(mathcal{R},mathcal{T})$ function. Finally, the average null energy condition is satisfied by all wormhole models, indicating that minimum exotic matter is required to open the wormhole throats.
Future Roadmap
Potential Challenges
- Validation of the proposed wormhole configurations in $kappa(mathcal{R},mathcal{T})$ gravity through observation or experimental evidence
- Investigation of the stability and longevity of the wormhole solutions
- Exploration of the effects of other physical factors on the wormhole properties, such as rotation or electromagnetic fields
Potential Opportunities
- Application of the derived wormhole solutions in $kappa(mathcal{R},mathcal{T})$ gravity to areas such as interstellar travel or teleportation
- Further development of the numerical method for generating the embedding surface and revolution of the wormhole
- Exploration of other $kappa(mathcal{R},mathcal{T})$ functions and their impacts on the shape and properties of wormholes
Overall, the study of wormholes in $kappa(mathcal{R},mathcal{T})$ gravity has provided valuable insights into their configurations and properties. While challenges remain in terms of validation and stability, there are also exciting opportunities for practical applications and further research in this field.
Source:
arXiv:2403.19733v1
Read the original article
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.
Read the original article
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.
Read the original article
