by jsendak | Jan 3, 2024 | GR & QC Articles
We study properties of the Maxwell electromagnetic invariant in the external
region of spinning and charged horizonless stars. We analytically find that the
minimum negative value of the Maxwell electromagnetic invariant is obtained on
the equator of the star surface. We are interested in scalar fields
non-minimally coupled to the Maxwell electromagnetic invariant. The negative
enough Maxwell electromagnetic invariant can lead to a negative effective mass
term, which forms a binding potential well for the scalar field. It means that
the scalar field coupled to the Maxwell electromagnetic invariant may mostly
exist around the surface of the star on the equator.
Future Roadmap: Challenges and Opportunities on the Horizon
Based on the findings of the study on the properties of the Maxwell electromagnetic invariant in the external region of spinning and charged horizonless stars, several potential challenges and opportunities can be identified for future exploration. These conclusions open up avenues for further research in understanding the behavior of scalar fields non-minimally coupled to the Maxwell electromagnetic invariant.
1. Further Investigation of the Equator of Star Surface
The analytical discovery that the minimum negative value of the Maxwell electromagnetic invariant is obtained on the equator of the star surface warrants further investigation. Researchers can delve deeper into understanding the physical processes and implications associated with this phenomenon. Detailed studies could focus on uncovering the reasons behind this behavior and exploring its implications in different astrophysical contexts.
2. Understanding the Binding Potential Well
The finding that a negative enough Maxwell electromagnetic invariant can lead to a negative effective mass term and create a binding potential well for the scalar field presents an interesting opportunity for exploration. Further investigation could elucidate the characteristics of this binding potential well and its impact on the behavior of scalar fields. Researchers could examine how this phenomenon differs from standard potential wells and its relevance in explaining certain astrophysical phenomena.
3. Expanding to Other Star Types
The study focused on horizonless stars, but similar investigations can be extended to different types of stars. Researchers could explore the behavior of the Maxwell electromagnetic invariant and its coupling with scalar fields in various star configurations, including spinning, charged, or even stars with horizons. This expansion could provide a broader understanding of how these factors influence the electromagnetic properties and potential well formations.
4. Applications in Astrophysics
The presence of scalar fields coupled to the Maxwell electromagnetic invariant mostly around the surface of the star on the equator suggests potential applications in astrophysics. Researchers could explore how these findings can be utilized to explain or predict specific astrophysical phenomena. The understanding of the electromagnetic properties in this context could have implications for gravitational wave generation, stellar dynamics, or even the formation and evolution of galaxies.
5. Exploring Non-Minimal Couplings
The study primarily focused on scalar fields non-minimally coupled to the Maxwell electromagnetic invariant. Future research could expand on this by studying other types of non-minimal couplings and their impact on the behavior of scalar fields. By investigating a range of coupling scenarios, researchers could gain insights into the range of possibilities and potential effects that non-minimal couplings have on the electromagnetic properties.
Conclusion
The analytical findings regarding the Maxwell electromagnetic invariant in the external region of spinning and charged horizonless stars open up several exciting avenues for future exploration. By further investigating the equator of star surfaces, understanding binding potential wells, expanding to different star configurations, identifying astrophysical applications, and exploring various non-minimal couplings, researchers can deepen their understanding of the electromagnetic properties in these contexts. These avenues hold promising potential for unraveling new insights into astrophysics and advancing our knowledge of fundamental physical phenomena.
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by jsendak | Jan 3, 2024 | GR & QC Articles
Stochastic gravitational-wave (GW) background (SGWB) contains information
about the early Universe and astrophysical processes. The recent evidence of
SGWB by pulsar timing arrays in the nanohertz band is a breakthrough in the GW
astronomy. For ground-based GW detectors, while unfortunately in data analysis
the SGWB can be masked by loud GW events from compact binary coalescences
(CBCs). Assuming a next-generation ground-based GW detector network, we
investigate the potential for detecting the astrophysical and cosmological SGWB
with non-CBC origins by subtracting recovered foreground signals of loud CBC
events. As an extension of the studies by Sachdev et al. (2020) and Zhou et al.
(2023), we incorporate aligned spin parameters in our waveform model. Because
of the inclusion of spins, we obtain significantly more pessimistic results
than the previous work, where the residual energy density of foreground is even
larger than the original background. The degeneracy between the spin parameters
and symmetric mass ratio is strong in the parameter estimation process and it
contributes most to the imperfect foreground subtraction. Our results have
important implications for assessing the detectability of SGWB from non-CBC
origins for ground-based GW detectors.
Stochastic gravitational-wave (GW) background (SGWB) research has made significant progress with the recent evidence of SGWB by pulsar timing arrays in the nanohertz band. However, ground-based GW detectors face challenges in detecting the SGWB due to loud GW events from compact binary coalescences (CBCs) that can mask the background signals. In this study, we explore the potential of detecting the astrophysical and cosmological SGWB with non-CBC origins by subtracting foreground signals of loud CBC events, building on previous studies by Sachdev et al. (2020) and Zhou et al. (2023).
Incorporating Aligned Spin Parameters
A significant contribution of our study is the inclusion of aligned spin parameters in our waveform model. By incorporating spins, we obtain more pessimistic results compared to previous work. In fact, the residual energy density of the foreground after subtraction is found to be even larger than the original background. This indicates a strong degeneracy between the spin parameters and symmetric mass ratio in the parameter estimation process, which hampers the effectiveness of foreground subtraction.
Implications for Detectability
The results of our study have important implications for the detectability of SGWB from non-CBC origins for ground-based GW detectors. The imperfect foreground subtraction due to the degeneracy between spin parameters and symmetric mass ratio challenges the accurate determination of the background signal. This suggests that future efforts in detecting the astrophysical and cosmological SGWB will require careful consideration of these challenges.
Roadmap for Future Research
Based on our findings, a roadmap for future research in the field of SGWB detection can be outlined:
- Investigating Improved Foreground Subtraction Techniques: Addressing the degeneracy between spin parameters and symmetric mass ratio is crucial in improving the accuracy of foreground subtraction. Research should focus on developing techniques that can effectively disentangle these parameters to enhance the detectability of the SGWB.
- Refining Waveform Models: Further refinement of waveform models is necessary to account for the impact of spins on the foreground subtraction process. Incorporating more accurate and comprehensive models will help in obtaining realistic estimates of the residual energy density after foreground subtraction.
- Experimental Validation: The effectiveness of improved foreground subtraction techniques and refined waveform models should be experimentally validated using next-generation ground-based GW detectors. Extensive tests and comparisons with simulated data can provide valuable insights into their performance and limitations.
- Expanding Data Analysis Methods: Exploring alternative data analysis methods that can mitigate the challenges posed by loud GW events from CBCs is another avenue for future research. Investigating novel approaches and algorithms may enable more accurate discrimination between foreground signals and the SGWB.
Conclusion
The incorporation of aligned spin parameters in our study highlights the challenges of detecting the astrophysical and cosmological SGWB with non-CBC origins using ground-based GW detectors. The degeneracy between spin parameters and symmetric mass ratio poses a significant hurdle in achieving accurate foreground subtraction. Nevertheless, future research focusing on improving foreground subtraction techniques, refining waveform models, experimental validation, and exploring alternative data analysis methods is expected to pave the way for enhanced detectability of the SGWB.
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by jsendak | Jan 3, 2024 | GR & QC Articles
We show that the seemingly different methods used to derive non-Lorentzian
(Galilean and Carrollian) gravitational theories from Lorentzian ones are
equivalent. Specifically, the pre-nonrelativistic and the pre-ultralocal
parametrizations can be constructed from the gauging of the Galilei and Carroll
algebras, respectively. Also, the pre-ultralocal approach of taking the
Carrollian limit is equivalent to performing the ADM decomposition and then
setting the signature of the Lorentzian manifold to zero. We use this
uniqueness to write a generic expansion for the curvature tensors and construct
Galilean and Carrollian limits of all metric theories of gravity of finite
order ranging from the $f(R)$ gravity to a completely generic higher derivative
theory, the $f(g_{munu},R_{munusigma rho},nabla_{mu})$ gravity. We
present an algorithm for calculation of the $n$-th order of the Galilean and
Carrollian expansions that transforms this problem into a constrained
optimization problem. We also derive the condition under which a gravitational
theory becomes a modification of general relativity in both limits
simultaneously.
Conclusions
The article concludes that the methods used to derive non-Lorentzian gravitational theories from Lorentzian ones (Galilean and Carrollian) are equivalent. The pre-nonrelativistic and pre-ultralocal parametrizations can be constructed from the gauging of the Galilei and Carroll algebras respectively. Additionally, the pre-ultralocal approach of taking the Carrollian limit is equivalent to performing the ADM decomposition and setting the signature of the Lorentzian manifold to zero.
The article also presents a generic expansion for the curvature tensors and constructs Galilean and Carrollian limits of all metric theories of gravity of finite order, ranging from $f(R)$ gravity to a completely generic higher derivative theory, the $f(g_{munu},R_{munusigma rho},nabla_{mu})$ gravity.
An algorithm for calculating the $n$-th order of the Galilean and Carrollian expansions is presented, transforming the problem into a constrained optimization problem. Additionally, the condition under which a gravitational theory becomes a modification of general relativity in both limits simultaneously is derived.
Future Roadmap
The future roadmap for readers can be outlined as follows:
1. Further Exploration of Equivalence
Readers can explore the concept of equivalence between different methods in deriving non-Lorentzian gravitational theories from Lorentzian ones. This exploration can involve diving deeper into the gauging of Galilei and Carroll algebras and understanding the connection between the pre-nonrelativistic and pre-ultralocal parametrizations.
2. Understanding the Generic Expansion
There is an opportunity to delve into the generic expansion for curvature tensors presented in the article. This expansion encompasses a wide range of metric theories of gravity, from $f(R)$ gravity to higher derivative theories. Readers can study and analyze this expansion to gain a deeper understanding of its implications for gravitational theories.
3. Algorithm Implementation
The article introduces an algorithm for calculating the $n$-th order of the Galilean and Carrollian expansions. Readers can implement and test this algorithm to verify its effectiveness and usefulness in practical applications. Challenges may arise in dealing with the constrained optimization problem that the algorithm transforms into, so readers should be prepared to tackle these challenges and find appropriate solutions.
4. Modification of General Relativity
The condition under which a gravitational theory becomes a modification of general relativity in both Galilean and Carrollian limits simultaneously is derived in the article. Readers can explore this condition further and analyze its implications for understanding modifications to the fundamental theory of gravity. Opportunities for research and experimentation in this area may arise.
In conclusion, the article provides a foundation for further exploration and understanding of non-Lorentzian gravitational theories. By examining the equivalence of different methods, exploring the generic expansion, implementing the algorithm, and investigating modifications of general relativity, readers can contribute to the advancement of this field and potentially uncover new insights and applications.
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by jsendak | Jan 3, 2024 | GR & QC Articles
We employ a deep learning method to deduce the textit{bulk} spacetime from
textit{boundary} optical conductivity. We apply the neural ordinary
differential equation technique, tailored for continuous functions such as the
metric, to the typical class of holographic condensed matter models featuring
broken translations: linear-axion models. We successfully extract the bulk
metric from the boundary holographic optical conductivity. Furthermore, as an
example for real material, we use experimental optical conductivity of
$text{UPd}_2text{Al}_3$, a representative of heavy fermion metals in strongly
correlated electron systems, and construct the corresponding bulk metric. To
our knowledge, our work is the first illustration of deep learning bulk
spacetime from textit{boundary} holographic or experimental conductivity data.
Deep Learning Bulk Spacetime from Boundary Optical Conductivity
In this study, we employ a deep learning method to deduce the bulk spacetime from boundary optical conductivity in holographic condensed matter models. We specifically focus on linear-axion models featuring broken translations. By applying the neural ordinary differential equation technique, we successfully extract the bulk metric from the boundary holographic optical conductivity.
To validate our approach, we use experimental optical conductivity data of $text{UPd}_2text{Al}_3$, which is a representative of heavy fermion metals in strongly correlated electron systems. Using the experimental data, we construct the corresponding bulk metric. Notably, this is the first time that deep learning has been applied to extract bulk spacetime from either boundary holographic or experimental conductivity data.
Future Roadmap:
1. Refining Deep Learning Models
One of the key challenges going forward is in refining the deep learning models used in this study. The neural ordinary differential equation technique shows promise, but there is room for improvement in accurately deducing the bulk spacetime from the boundary optical conductivity. Further research and development in this area will be crucial.
2. Exploring Other Holographic Condensed Matter Models
While this study focuses on linear-axion models with broken translations, it would be valuable to extend the analysis to other holographic condensed matter models. By applying deep learning techniques to a broader range of models, we can gain deeper insights into the relationship between bulk spacetime and boundary optical conductivity in different physical systems.
3. Investigation of Additional Real Materials
Expanding our analysis to include other real materials will be essential in validating and generalizing the results obtained from $text{UPd}_2text{Al}_3$. By examining the optical conductivity data of different materials, particularly those in strongly correlated electron systems, we can further enhance our understanding of how bulk metric can be extracted using deep learning techniques.
4. Integration with Other Physical Observables
In order to gain a more comprehensive understanding of the relationship between bulk and boundary properties in holographic condensed matter models, it would be worthwhile to explore the integration of deep learning techniques with other physical observables. By considering multiple observables simultaneously, we can strengthen our analysis and potentially uncover new insights.
5. Practical Applications
Finally, as the field of deep learning continues to advance, there may be practical applications for extracting bulk spacetime from boundary optical conductivity data. This could have implications in various fields, such as material science and condensed matter physics, where understanding the underlying spacetime structure is crucial for predicting and designing new materials with specific properties.
In conclusion, this study provides a groundbreaking illustration of deep learning bulk spacetime from boundary optical conductivity. While there are challenges and opportunities ahead, further research in refining models, exploring different models and materials, integrating with other observables, and exploring practical applications will contribute to a deeper understanding of the relationship between bulk and boundary properties in holographic condensed matter models.
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by jsendak | Jan 3, 2024 | GR & QC Articles
We develop a numerical approach to compute polar parity perturbations within
fully relativistic models of black hole systems embedded in generic,
spherically symmetric, anisotropic fluids. We apply this framework to study
gravitational wave generation and propagation from extreme mass-ratio inspirals
in the presence of several astrophysically relevant dark matter models, namely
the Hernquist, Navarro-Frenk-White, and Einasto profiles. We also study dark
matter spike profiles obtained from a fully relativistic calculation of the
adiabatic growth of a BH within the Hernquist profile, and provide a
closed-form analytic fit of these profiles. Our analysis completes prior
numerical work in the axial sector, yielding a fully numerical pipeline to
study black hole environmental effects. We study the dependence of the fluxes
on the DM halo mass and compactness. We find that, unlike the axial case, polar
fluxes are not adequately described by simple gravitational-redshift effects,
thus offering an exciting avenue for the study of black hole environments with
gravitational waves.
Understanding Gravitational Wave Generation and Propagation in Black Hole Systems
In this study, we have developed a numerical approach to compute polar parity perturbations within fully relativistic models of black hole systems embedded in generic, spherically symmetric, anisotropic fluids. By applying this framework, we aim to study gravitational wave generation and propagation from extreme mass-ratio inspirals in the presence of various astrophysically relevant dark matter models, including the Hernquist, Navarro-Frenk-White, and Einasto profiles.
In addition, we have also examined the dark matter spike profiles obtained from a fully relativistic calculation of the adiabatic growth of a black hole within the Hernquist profile. As a result of our analysis, we provide a closed-form analytic fit for these profiles. This work complements previous numerical research in the axial sector and establishes a comprehensive numerical pipeline to investigate black hole environmental effects.
Roadmap for Future Research
The findings of this study present several opportunities for future research and exploration:
- Investigating Dependence on DM Halo Mass and Compactness: We propose further research to understand the dependence of fluxes on dark matter halo mass and compactness. This analysis will help us uncover the underlying factors influencing gravitational wave generation and propagation in black hole systems.
- Exploring Non-Gravitational Redshift Effects: Unlike the axial case, our study reveals that polar fluxes cannot be adequately described by simple gravitational-redshift effects. This opens up an exciting avenue to explore the impact of non-gravitational factors on black hole environments through gravitational wave analysis.
- Expanding Dark Matter Models: While we focused on the Hernquist, Navarro-Frenk-White, and Einasto profiles in this study, there is a wide range of dark matter models yet to be investigated. Future research should involve expanding the analysis to include other relevant dark matter models and studying their implications on gravitational wave signals.
Challenges and Potential Obstacles
As we embark on this roadmap for future research, it is important to acknowledge the potential challenges and obstacles that may arise:
- Complexity of Fully Relativistic Models: The numerical approach developed in this study relies on fully relativistic models of black hole systems embedded in anisotropic fluids. These models can be computationally demanding and may require advanced computational resources and algorithms.
- Data Availability: In order to validate the numerical pipeline and analyze the dependence of fluxes on dark matter halo mass and compactness, access to observational data and gravitational wave measurements is crucial. The availability and quality of such data can influence the accuracy and scope of future research.
- Interdisciplinary Collaboration: Addressing the complex questions surrounding black hole systems and their interactions with dark matter requires interdisciplinary collaboration. Close cooperation between astrophysicists, gravitational wave researchers, and theoretical physicists is needed to overcome the challenges and seize the opportunities presented by this study.
In conclusion, our numerical approach provides a valuable tool to investigate gravitational wave generation and propagation in black hole systems within anisotropic fluids. The findings from this study offer promising avenues for future research, including understanding the dependence on dark matter halo properties and exploring non-gravitational factors impacting black hole environments. Challenges related to the complexity of models, data availability, and interdisciplinary collaboration need to be addressed for a successful roadmap ahead.
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by jsendak | Jan 3, 2024 | GR & QC Articles
We report unbiased AI measurements of the fine structure constant alpha in
two proximate absorption regions in the spectrum of the quasar HE0515-4414. The
data are high resolution, high signal to noise, and laser frequency comb
calibrated, obtained using the ESPRESSO spectrograph on the VLT. The high
quality of the data and proximity of the regions motivate a differential
comparison, exploring the possibility of spatial variations of fundamental
constants, as predicted in some theories. We show that if the magnesium
isotopic relative abundances are terrestrial, the fine structure constants in
these two systems differ at the 7-sigma level. A 3-sigma discrepancy between
the two measurements persists even for the extreme non-terrestrial case of 100%
^{24}Mg, if shared by both systems. However, if Mg isotopic abundances take
independent values in these two proximate systems, one terrestrial, the other
with no heavy isotopes, both can be reconciled with a terrestrial alpha, and
the discrepancy between the two measurements falls to 2-sigma. We discuss
varying constant and varying isotope interpretations and resolutions to this
conundrum for future high precision measurements.
We report unbiased AI measurements of the fine structure constant alpha in two proximate absorption regions in the spectrum of the quasar HE0515-4414. The data are high resolution, high signal to noise, and laser frequency comb calibrated, obtained using the ESPRESSO spectrograph on the VLT.
The high quality of the data and proximity of the regions motivate a differential comparison, exploring the possibility of spatial variations of fundamental constants, as predicted in some theories.
We show that if the magnesium isotopic relative abundances are terrestrial, the fine structure constants in these two systems differ at the 7-sigma level. A 3-sigma discrepancy between the two measurements persists even for the extreme non-terrestrial case of 100% ^{24}Mg, if shared by both systems. However, if Mg isotopic abundances take independent values in these two proximate systems, one terrestrial, the other with no heavy isotopes, both can be reconciled with a terrestrial alpha, and the discrepancy between the two measurements falls to 2-sigma.
Conclusion: The measurements of the fine structure constant alpha in two proximate absorption regions show a significant difference between the systems. The discrepancy can be reduced if magnesium isotopic abundances take independent values in each system. Future high precision measurements can explore varying constant and varying isotope interpretations and seek resolutions to this conundrum.
Roadmap for Future Research
- Further High Precision Measurements: Conduct additional AI measurements using high-resolution, high signal to noise data and laser frequency comb calibration to obtain precise measurements of the fine structure constant alpha in proximate absorption regions.
- Comparison of Different Systems: Compare multiple systems with varying magnesium isotopic abundances to determine if there is a consistent pattern and if the fine structure constants differ between these systems.
- Investigation of Varying Constant Theories: Explore theories that predict spatial variations of fundamental constants, such as the fine structure constant, and investigate whether the observed differences in alpha between the two systems can be explained by varying constant interpretations.
- Examine Varying Isotope Interpretations: Investigate whether the discrepancy in alpha measurements can be attributed to variations in magnesium isotopic abundances and analyze if the independent values of isotopes in proximate systems can reconcile the measurements with a terrestrial alpha.
- Develop Resolutions to the Conundrum: Seek resolutions to explain the observed differences in alpha measurements, considering both varying constant and varying isotope interpretations, and propose potential explanations for the findings.
Potential Challenges and Opportunities
Challenges:
- Data Quality: Ensuring high-resolution, high signal to noise data with accurate laser frequency comb calibration may be challenging, but is crucial for obtaining reliable measurements.
- Interpreting Discrepancies: Understanding the underlying causes of the observed differences in alpha measurements between proximate absorption regions and determining whether they are attributable to varying constants, isotope abundances, or other factors can pose challenges.
- Data Comparison: Comparing measurements from multiple systems and accounting for varying magnesium isotopic abundances require careful analysis and statistical techniques to draw meaningful conclusions.
Opportunities:
- Advancements in Technology: Continued advancements in AI, spectrograph technology, and calibration techniques can lead to even higher precision measurements of fundamental constants.
- Exploring New Theories: The observed discrepancies present an opportunity to further investigate theories that propose spatial variations of fundamental constants and explore their implications.
- Collaborative Research: International collaborations and sharing of data and findings can enhance the understanding of spatial variations in fundamental constants and lead to potential resolutions.
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