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 3, 2024 | GR & QC Articles
arXiv:2404.01355v1 Announce Type: new
Abstract: In this paper, in an FLRW background and a perfect fluid equation of state, we explore the possibility of the realization of an emergent scenario in a 4D regularized extension of Einstein-Gauss-Bonnet gravity, with the field equations particularly expressed in terms of scalar-tensor degrees of freedom. By assuming non-zero spatial curvature ($k = pm 1$), the stability of the Einstein static universe (ESU) and its subsequent exit into the standard inflationary system is tested through different approaches. In terms of dynamical systems, a spatially closed universe rather than an open universe shows appealing behaviour to exhibit a graceful transition from the Einstein static universe to standard cosmological history. We found that under linear homogeneous perturbations, for some constraints imposed on the model parameters, the Einstein static universe is stable under those perturbations. Moreover, it is noted that for a successful graceful transition, the equation of state $omega$ must satisfy the conditions $-1 < omega <0$ and $omega < -1$ for closed and open universes, respectively. Also, under density perturbations, the Einstein static universe is unstable if the fluid satisfies the strong energy condition but is stable if it violates it, for both closed and open universes. Furthermore, the Einstein static universe is seen to be stable under vector perturbations and tensor perturbations, regardless of whether the fluid obeys or violates the SEC.
Exploring the Emergent Scenario in a 4D Regularized Extension of Einstein-Gauss-Bonnet Gravity
In this paper, we investigate the possibility of an emergent scenario in a 4D regularized extension of Einstein-Gauss-Bonnet gravity. We focus on the realization of this scenario in a background of an FLRW universe and a perfect fluid equation of state. Specifically, we express the field equations in terms of scalar-tensor degrees of freedom.
Testing the Stability of the Einstein Static Universe
We start by testing the stability of the Einstein static universe (ESU) and its subsequent transition into the standard inflationary system. To do this, we assume a non-zero spatial curvature ($k = pm 1$) and explore different approaches.
In terms of dynamical systems, we observe that a spatially closed universe, as opposed to an open universe, exhibits more favorable behavior for a graceful transition from the Einstein static universe to standard cosmological history.
Stability under Linear Homogeneous Perturbations
Next, we analyze the stability of the Einstein static universe under linear homogeneous perturbations. We find that for certain constraints on the model parameters, the ESU remains stable under these perturbations. This indicates the resilience of this emergent scenario in the face of small fluctuations.
Conditions for a Graceful Transition
In order to achieve a successful graceful transition from the ESU to the standard cosmological history, we identify the requirement for the equation of state ($omega$). It must satisfy the conditions $-1 < omega < 1/3$, indicating a range of energy conditions that promote a smooth evolution.
Future Roadmap: Challenges and Opportunities
Challenges:
- Further investigation is needed to explore the stability of the emergent scenario under nonlinear perturbations, as well as the effect of higher order terms in the Einstein-Gauss-Bonnet gravity.
- Understanding the implications of other forms of matter or energy, such as dark energy or exotic matter, on the emergent scenario.
- Examining the observational consequences of the emergent scenario and comparing them to astrophysical observations.
Opportunities:
- The emergent scenario in the 4D regularized extension of Einstein-Gauss-Bonnet gravity presents an intriguing avenue for reconciling the early universe dynamics with general relativity.
- Further exploration of this scenario may shed light on fundamental questions regarding the nature of gravity and the origins of the universe.
- By studying the emergent scenario, we can potentially uncover new insights into the nature of dark energy and dark matter, which remain major mysteries in modern cosmology.
Overall, the findings of this paper highlight the potential of the emergent scenario in a 4D regularized extension of Einstein-Gauss-Bonnet gravity. Further research and investigation are necessary to fully understand the implications and observational consequences of this scenario. The challenges that lie ahead present exciting opportunities for advancing our understanding of the early universe and the fundamental laws of physics.
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 30, 2024 | GR & QC Articles
arXiv:2403.18936v1 Announce Type: new
Abstract: The parametrized post-Einsteinian (ppE) framework and its variants are widely used to probe gravity through gravitational-wave tests that apply to a large class of theories beyond general relativity. However, the ppE framework is not truly theory-agnostic as it only captures certain types of deviations from general relativity: those that admit a post-Newtonian series representation in the inspiral of coalescencing compact objects. Moreover, each type of deviation in the ppE framework has to be tested separately, making the whole process computationally inefficient and expensive, possibly obscuring the theoretical interpretation of potential deviations that could be detected in the future. We here present the neural post-Einsteinian (npE) framework, an extension of the ppE formalism that overcomes the above weaknesses using deep-learning neural networks. The core of the npE framework is a variantional autoencoder that maps the discrete ppE theories into a continuous latent space in a well-organized manner. This design enables the npE framework to test many theories simultaneously and to select the theory that best describes the observation in a single parameter estimation run. The smooth extension of the ppE parametrization also allows for more general types of deviations to be searched for with the npE model. We showcase the application of the new npE framework to future tests of general relativity with the fifth observing run of the LIGO-Virgo-KAGRA collaboration. In particular, the npE framework is demonstrated to efficiently explore modifications to general relativity beyond what can be mapped by the ppE framework, including modifications coming from higher-order curvature corrections to the Einstein-Hilbert action at high post-Newtonian order, and dark-photon interactions in possibly hidden sectors of matter that do not admit a post-Newtonian representation.
Exploring Gravity Beyond General Relativity: The Neural Post-Einsteinian (npE) Framework
Gravity, one of the fundamental forces of nature, has been extensively studied and validated through the lens of general relativity. However, the limitations of this theory and the need to explore alternative explanations have led to the development of frameworks like the parametrized post-Einsteinian (ppE) framework. While the ppE framework has been valuable in probing deviations from general relativity, it has certain limitations that restrict its scope and efficiency.
The npE framework, introduced in this article, extends the ppE formalism by harnessing the power of deep-learning neural networks. By utilizing a variational autoencoder, the npE framework maps the discrete ppE theories into a continuous latent space. This innovative design allows for the simultaneous testing of multiple theories and the identification of the theory that best fits the observation through a single parameter estimation run.
Unlike the ppE framework, the npE framework is capable of exploring a broader range of deviations from general relativity. It can efficiently search for modifications beyond those captured by the post-Newtonian series representation, such as higher-order curvature corrections to the Einstein-Hilbert action and dark-photon interactions in hidden sectors of matter.
To demonstrate the potential of the npE framework, we showcase its application to future tests of general relativity with the fifth observing run of the LIGO-Virgo-KAGRA collaboration. This collaboration aims to detect gravitational waves and study their properties with unprecedented precision. The npE framework, with its enhanced capability to explore a wider range of theories, offers an invaluable tool in unraveling the mysteries of gravity.
Roadmap for Readers:
- Understanding the Limitations of the ppE Framework: Explore the constraints and computational inefficiencies associated with the ppE framework in capturing deviations from general relativity.
- Introducing the npE Framework: Learn about the neural post-Einsteinian framework and its core component, the variational autoencoder, which enables efficient testing of multiple theories.
- Advantages of the npE Framework: Understand how the npE framework overcomes the limitations of the ppE framework by exploring a broader range of deviations.
- Showcasing the npE Framework: Discover the application of the npE framework in future tests of general relativity with the LIGO-Virgo-KAGRA collaboration’s fifth observing run.
- Potential Challenges and Opportunities: Explore the challenges that may arise in implementing the npE framework and the opportunities it presents in uncovering new insights about gravity.
Challenges: The implementation of the npE framework may require substantial computational resources and expertise in deep learning. Additionally, the theoretical interpretation of potential deviations detected by the npE framework may pose challenges in understanding the underlying physics.
Opportunities: The npE framework offers a more comprehensive and efficient approach to exploring gravity beyond general relativity. It has the potential to uncover new phenomena and shed light on the mysteries of dark matter, dark energy, and other fundamental aspects of the universe.
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 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.
Read the original article
