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.
Read the original article
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.
Read the original article
by jsendak | Mar 20, 2024 | GR & QC Articles
arXiv:2403.12136v1 Announce Type: new
Abstract: One of the foremost concern in the analysis of quantum gravity is whether the locations of classical horizons are stable under a full quantum analysis. In principle, any classical description, when interpolated to the microscopic level, can become prone to fluctuations. The curious question in that case is if there indeed are such fluctuations at the Planck scale, do they have any significance for physics taking place at scales much away from the Planck scale? In this work, we try to attempt the question of small scales and address whether there are definitive signatures of Planck scale shifts in the horizon structure. In a recent work (arXiv:2107.03406), it was suggested that in a nested sequence of Rindler causal wedges, the vacua of preceding Rindler frames appear thermally populated to a shifted Rindler frame. The Bogoliubov analysis used relies on the global notion of the quantum field theory and might be unable to see the local character of such horizon shifts. We investigate this system by means of the Unruh-DeWitt detector and see if this local probe of the quantum field theory is sensitive enough to the shift parameters to reveal any microscopic effects. For the case of infinite-time response, we recover the thermal spectrum, thus reaffirming that the infinite-time response probes the global properties of the field. On the other hand, the finite-time response turns out to be sensitive to the shift parameter in a peculiar way that any detector with energy gap $Omega c/a sim 1$ and is operational for time scale $T a/c sim 1$ has a measurably different response for a macroscopic and microscopic shift of the horizon, giving us direct probe to the tiniest separation between the causal domains of such Rindler wedges. Thus, this study provides an operational method to identify Planck scale effects which can be generalized to various other interesting gravitational settings.
Quantum Gravity and the Stability of Classical Horizons
In the analysis of quantum gravity, one of the key concerns is whether the locations of classical horizons remain stable under a full quantum analysis. When a classical description is extrapolated to the microscopic level, it becomes susceptible to fluctuations. Therefore, it is important to investigate whether these fluctuations at the Planck scale have any significant impact on physics at scales far removed from the Planck scale.
Searching for Signatures of Planck Scale Shifts in Horizon Structure
In a recent work (arXiv:2107.03406), it was proposed that in a nested sequence of Rindler causal wedges, the vacua of preceding Rindler frames appear thermally populated to a shifted Rindler frame. However, the analysis used in this work relies on the global notion of quantum field theory and may overlook the local character of such horizon shifts. Therefore, it is necessary to investigate this system using a local probe, such as the Unruh-DeWitt detector, to determine if it is sensitive enough to the shift parameters to reveal any microscopic effects.
Investigating the Sensitivity of the Unruh-DeWitt Detector
We conducted a study using the Unruh-DeWitt detector to examine the sensitivity of this local probe to the shift parameters of the horizon structure. The results showed that for the case of infinite-time response, the detector recovered the thermal spectrum, confirming that it probes the global properties of the field. However, the finite-time response exhibited a peculiar sensitivity to the shift parameter. We observed that any detector with an energy gap of $Omega c/a sim 1$ and operational for a time scale of $T a/c sim 1$ had a measurably different response for both macroscopic and microscopic shifts of the horizon.
Identifying Planck Scale Effects and Generalization
Our study provides a practical method to identify Planck scale effects using the Unruh-DeWitt detector. This method can be extended to various other interesting gravitational settings and allows for the detection of the tiniest separation between the causal domains of Rindler wedges. By investigating these microscopic effects, we can gain a deeper understanding of the stability and behavior of classical horizons under quantum analysis.
Future Roadmap
- Further refine the Unruh-DeWitt detector methodology for enhanced sensitivity and accuracy.
- Explore other gravitational settings and test the applicability of the method in different scenarios.
- Investigate the implications of Planck scale shifts in horizon structure for various physical phenomena.
- Collaborate with experimentalists to design and conduct experiments to validate the findings.
- Integrate the findings into the broader framework of quantum gravity and continue the quest to understand the fundamental nature of the universe.
Challenges and Opportunities
Challenges:
- Developing experimental setups that can measure the tiniest separation between causal domains.
- Overcoming technical limitations and noise in detector measurements.
- Understanding the implications of Planck scale shifts for different gravitational settings and phenomena.
Opportunities:
- Understanding the stability and behavior of classical horizons under quantum analysis.
- Gaining insights into the fundamental nature of the universe through the exploration of quantum gravity.
- Opening up new avenues for experimental verification and validation of theoretical predictions.
- Potential applications in other areas of physics beyond quantum gravity.
Overall, the study of Planck scale shifts in horizon structure and the detection of associated microscopic effects offer exciting prospects for advancing our understanding of quantum gravity and its implications for the broader framework of physics.
Read the original article
by jsendak | Mar 19, 2024 | GR & QC Articles
arXiv:2403.10605v1 Announce Type: new
Abstract: We study the physics of photon rings in a wide range of axisymmetric black holes admitting a separable Hamilton-Jacobi equation for the geodesics. Utilizing the Killing-Yano tensor, we derive the Penrose limit of the black holes, which describes the physics near the photon ring. The obtained plane wave geometry is directly linked to the frequency matrix of the massless wave equation, as well as the instabilities and Lyapunov exponents of the null geodesics. Consequently, the Lyapunov exponents and frequencies of the photon geodesics, along with the quasinormal modes, can be all extracted from a Hamiltonian in the Penrose limit plane wave metric. Additionally, we explore potential bounds on the Lyapunov exponent, the orbital and precession frequencies, in connection with the corresponding inverted harmonic oscillators and we discuss the possibility of photon rings serving as holographic horizons in a holographic duality framework for astrophysical black holes. Our formalism is applicable to spacetimes encompassing various types of black holes, including stationary ones like Kerr, Kerr-Newman, as well as static black holes such as Schwarzschild, Reissner-Nordstr”om, among others.
Future Roadmap: Challenges and Opportunities on the Horizon
Introduction
In this study, we delve into the fascinating realm of photon rings in a diverse range of axisymmetric black holes. Our primary objective is to examine the physics of these photon rings and explore the potential applications and possibilities they offer. We also discuss the relevance of our findings to various black hole types and their implications in astrophysical scenarios. Below, we outline a future roadmap for readers, highlighting the challenges and opportunities on the horizon.
Understanding the Physics of Photon Rings
To comprehend the physics behind photon rings, we start by investigating black holes that allow for a separable Hamilton-Jacobi equation for the geodesics. Through careful analysis and utilization of the Killing-Yano tensor, we obtain the Penrose limit of these black holes. This important result describes the physics occurring near the photon ring, a crucial region of interest.
Linking the Plane Wave Geometry and Wave Equation
The obtained plane wave geometry is directly linked to the frequency matrix of the massless wave equation. By studying these connections, we gain insights into the instabilities and Lyapunov exponents of the null geodesics. These Lyapunov exponents and frequencies of photon geodesics, along with the quasinormal modes, can be extracted from the Hamiltonian in the Penrose limit plane wave metric.
Potential Bounds and Inverted Harmonic Oscillators
We further explore the potential bounds on the Lyapunov exponent, the orbital and precession frequencies. We establish connections between these quantities and corresponding inverted harmonic oscillators. This analysis offers intriguing possibilities for understanding the behavior and limitations of photon rings in different black hole spacetimes.
Holographic Duality Framework for Astrophysical Black Holes
Our investigation also delves into the concept of holographic horizons and their applicability to astrophysical black holes. We examine the potential of photon rings serving as holographic horizons within a holographic duality framework. This framework opens up new avenues for understanding the nature of black holes and their connection to holography.
Applicability to Various Black Hole Types
Our formalism is applicable to a wide range of black hole types. We consider stationary black holes like Kerr and Kerr-Newman, as well as static black holes such as Schwarzschild and Reissner-Nordström, among others. This broad applicability enhances the relevance and potential impact of our findings in diverse astrophysical scenarios.
Conclusion
By delving into the physics of photon rings in a range of axisymmetric black holes, we have uncovered valuable insights and potential applications. Our investigation into the Penrose limit, the relationship to frequency matrices and Lyapunov exponents, as well as the exploration of holographic horizons, sets the stage for exciting future research. Despite potential challenges in terms of computational complexity and theoretical formulation, the opportunities for advancing our understanding of black holes and their dynamics are vast.
Read the original article
by jsendak | Mar 18, 2024 | GR & QC Articles
arXiv:2403.09748v1 Announce Type: new
Abstract: Physics-informed neural network (PINN) analysis of the dynamics of S-stars in the vicinity of the supermassive black hole in the Galactic center is performed within General Relativity treatment. The aim is to reveal the role of possible extended mass (dark matter) configuration in the dynamics of the S-stars, in addition to the dominating central black hole’s mass. The PINN training fails to detect the extended mass perturbation in the observational data for S2 star within the existing data accuracy, and the precession constraint indicates no signature of extended mass up to 0.01% of the central mass inside the apocenter of S2. Neural networks analysis thus confirm its efficiency in the analysis of the S-star dynamics.
Analysis of S-Star Dynamics in the Galactic Center
In this study, a Physics-informed neural network (PINN) analysis is conducted to examine the dynamics of S-stars in the vicinity of the supermassive black hole in the Galactic center. The goal is to investigate the potential influence of an extended mass configuration, possibly dark matter, on the S-star dynamics alongside the dominant central black hole’s mass.
The PINN training process, however, fails to detect any evidence of the extended mass perturbation in the observational data for the S2 star, considering the existing level of data accuracy. Moreover, the precession constraint analysis does not reveal any discernible signature of extended mass up to 0.01% of the central mass inside the apocenter of S2. These findings indicate that the neural network analysis confirms its efficiency in studying the dynamics of S-stars.
Roadmap for Future Studies
Despite the current limitations in detecting the extended mass configuration in the S-star dynamics, further research in this field holds promise for potential advancements. The following steps can be taken to enhance our understanding:
- Improved Data Accuracy: One of the foremost challenges is improving the accuracy of the observational data for S2 and other S-stars. Until higher precision data is available, the examination of the extended mass perturbation will remain inconclusive.
- Refinement of PINN Methodology: Continual refinement of the PINN methodology can optimize its effectiveness in analyzing the dynamics of S-stars. Exploring different network architectures and incorporating additional physical constraints may produce more accurate results.
- Expansion of Sample Size: Expanding the sample size beyond the S2 star to include more S-stars can provide a broader dataset for analysis. This will enable the detection of smaller extended mass perturbations and enhance our understanding of their influence on the dynamics.
- Investigation of Dark Matter: To gain insights into the role of dark matter in the dynamics of S-stars, specific studies dedicated to understanding the properties and distribution of dark matter around the central black hole can be conducted in parallel.
By addressing these challenges and exploring the suggested opportunities, future research can advance our knowledge of the S-star dynamics in the Galactic center, shedding light on the significance of extended mass configurations and the role of dark matter.
Reference: [arXiv:2403.09748v1]
Read the original article
by jsendak | Mar 15, 2024 | GR & QC Articles
arXiv:2403.08864v1 Announce Type: new
Abstract: This is a third installment in a program to develop a method for alleviating the scale disparity in binary black hole simulations with mass ratios in the intermediate astrophysical range, where simulation cost is prohibitive while purely perturbative methods may not be adequate. The method is based on excising a “worldtube” around the smaller object, much larger than the object itself, replacing it with an analytical model that approximates a tidally deformed black hole. Previously (arXiv:2304.05329) we have tested the idea in a toy model of a scalar charge in a fixed circular geodesic orbit around a Schwarzschild black hole, solving for the massless Klein-Gordon field in 3+1 dimensions on the SpECTRE platform. Here we take the significant further step of allowing the orbit to evolve radiatively, in a self-consistent manner, under the effect of back-reaction from the scalar field. We compute the inspiral orbit and the emitted scalar-field waveform, showing a good agreement with perturbative calculations in the adiabatic approximation. We also demonstrate how our simulations accurately resolve post-adiabatic effects (for which we do not have perturbative results). In this work we focus on quasi-circular inspirals. Our implementation will shortly be publicly accessible in the SpECTRE numerical relativity code.
Future Roadmap: Challenges and Opportunities
Challenges:
- Scale Disparity: One of the main challenges is the scale disparity in binary black hole simulations with mass ratios in the intermediate astrophysical range. The simulation cost is currently prohibitive, and purely perturbative methods may not be adequate. Overcoming this challenge will require developing a new method to alleviate the scale disparity.
- Computational Cost: The current method of excising a “worldtube” around the smaller object and replacing it with an analytical model still has limitations. The computational cost of this method needs to be optimized to make it more efficient and practical for larger-scale simulations.
- Accuracy: While the method shows good agreement with perturbative calculations in the adiabatic approximation, it is important to further improve accuracy by resolving post-adiabatic effects. This requires developing new techniques and algorithms to accurately capture the dynamics of the system.
Opportunities:
- Public Accessibility: The implementation of the method used in this study will be made publicly accessible in the SpECTRE numerical relativity code. This opens up opportunities for other researchers and scientists to use and build upon this work, potentially leading to further advancements in black hole simulations.
- Realistic Orbit Evolution: The significant further step of allowing the orbit to evolve radiatively under the effect of back-reaction from the scalar field introduces a more realistic aspect to the simulations. This opens up opportunities to study more complex scenarios and investigate the impact of dynamic interactions on black hole simulations.
In conclusion, the development of a method to alleviate the scale disparity in binary black hole simulations is an ongoing challenge. However, the current study has made significant progress by allowing the orbit to evolve radiatively and showing good agreement with perturbative calculations. The future roadmap involves addressing challenges related to scale disparity, computational cost, and accuracy, while also exploring opportunities for public accessibility and studying more realistic orbit evolution. The implementation of the method in the SpECTRE numerical relativity code is a positive step towards enabling further research and advancements in this field.
Read the original article
