by jsendak | Jan 21, 2024 | GR & QC Articles
We investigate the data-driven holographic transport models without
translation symmetry. Our data are chosen as the real part of the
frequency-dependent shear viscosity. We develop a radial flow equation for a
large class of holographic models, which determine the shear viscosity by the
black hole metric and the graviton mass. The latter serves as the bulk dual of
the translation symmetry breaking on the boundary. We convert the flow equation
to a Neural Ordinary Differential Equation (Neural ODE), which is a neural
network with continuous depth and produces output through a black-box ODE
solver. Given either the metric or the mass, we illustrate that the Neural ODE
can learn the other with high accuracy. Our work demonstrates the capabilities
of Neural ODEs in bulk reconstruction and applied holography.
The conclusions of the article are as follows:
- Holographic transport models without translation symmetry can be investigated using data-driven approaches.
- The real part of the frequency-dependent shear viscosity is chosen as the data for analysis.
- A radial flow equation is developed for a large class of holographic models, which determines the shear viscosity based on the black hole metric and the graviton mass.
- The flow equation is converted to a Neural Ordinary Differential Equation (Neural ODE), which is a neural network with continuous depth and solves the equation as a black-box ODE solver.
- The Neural ODE can accurately learn either the black hole metric or the graviton mass when given the other as input.
- This work demonstrates the potential of Neural ODEs in bulk reconstruction and applied holography.
Future Roadmap:
Looking ahead, there are several challenges and opportunities on the horizon:
1. Refining and expanding the dataset:
To further improve the accuracy of the Neural ODE’s learning capabilities, a more comprehensive dataset can be assembled. This could involve collecting additional data on shear viscosity under different conditions or incorporating other relevant variables.
2. Exploring more complex holographic models:
The current study focused on a large class of holographic models with translation symmetry breaking. Future research could investigate more complex models that involve additional factors or variables, potentially uncovering new insights into the behavior of holographic transport systems.
3. Fine-tuning the Neural ODE architecture:
The Neural ODE used in this study has shown promise in accurately learning the black hole metric and graviton mass. However, further optimization and fine-tuning of the neural network architecture could enhance its performance and efficiency even more.
4. Applying Neural ODEs to other areas of physics:
The success of Neural ODEs in bulk reconstruction and applied holography suggests that this approach could be applied to other areas of physics as well. Researchers could explore the potential of Neural ODEs in different scientific contexts, expanding their utility beyond holography.
5. Collaborative research and cross-disciplinary studies:
To fully leverage the capabilities of Neural ODEs and address the challenges posed by more complex holographic models, collaboration between experts in different fields, such as physics, mathematics, and computer science, would be beneficial. Cross-disciplinary studies could lead to innovative solutions and novel applications of Neural ODEs.
Conclusion:
The application of Neural ODEs to study holographic transport models without translation symmetry shows promising results. As researchers refine the methodology, explore more complex models, and apply Neural ODEs to other areas of physics, the field of applied holography is likely to advance. Collaboration and cross-disciplinary approaches can further enhance the potential of Neural ODEs in solving complex problems and uncovering new insights.
Read the original article
by jsendak | Jan 21, 2024 | GR & QC Articles
In this study, we investigate the pseudospectrum and spectrum (in)stability
of a quantum corrected black hole. Methodologically, we use the hyperboloidal
framework to cast the QNM problem into an eigenvalue problem associated with a
non-selfadjoint operator, and exploit the invariant subspace method to improve
the computational efficiency for pseudospectrum. The investigation of the
spectrum (in)stability have two aspects. On the one hand, we calculate the
spectra of the quantum corrected black hole, then the impact of the quantum
correction effect on the Schwarzschild black hole has been studied through
migration ratios. The results indicate that the so-called “migration ratio
instability” will occur for small black holes with small angular momentum
number l. In the eikonal limit, the migration ratios remain the same for each
overtone. On the other hand, we study the spectrum (in)stability of the quantum
corrected black hole by directly adding some particular perturbations into the
effective potential, where perturbations are located at the event horizon and
null infinity, respectively. There are two interesting observations under the
same perturbation energy norm. First, perturbations at infinity are more
capable of generating spectrum instability than those at the event horizon.
Second, we find that the peak distribution can lead to the instability of QNM
spectrum more efficiently than the average distribution.
In this study, the authors investigate the pseudospectrum and spectrum instability of a quantum corrected black hole. They use the hyperboloidal framework and the invariant subspace method to analyze the problem. The investigation of the spectrum instability has two aspects.
First Aspect: Quantum Correction Effect
The authors calculate the spectra of the quantum corrected black hole and study the impact of the quantum correction effect on the Schwarzschild black hole through migration ratios. The results show that “migration ratio instability” occurs for small black holes with small angular momentum. In the eikonal limit, the migration ratios remain the same for each overtone.
Second Aspect: Perturbations
The authors study the spectrum instability of the quantum corrected black hole by adding particular perturbations into the effective potential. These perturbations are located at the event horizon and null infinity. Two interesting observations are made:
- Perturbations at infinity are more capable of generating spectrum instability compared to those at the event horizon.
- The peak distribution of perturbations can lead to the instability of QNM spectrum more efficiently than the average distribution.
Roadmap for Readers
Based on the conclusions of the study, readers interested in this topic can explore several potential directions:
- Further investigation into the migration ratio instability in small black holes with small angular momentum numbers.
- Exploration of the eikonal limit and its implications for migration ratios in black hole spectra.
- Further research on the effects of perturbations located at the event horizon and null infinity, and their role in spectrum instability.
- Investigation into why perturbations at infinity are more effective in generating spectrum instability compared to those at the event horizon.
- Study of the impact of different distribution patterns of perturbations on QNM spectrum instability.
Challenges and Opportunities
Researchers delving into this field will encounter several challenges and opportunities:
- Complex Mathematics: The study involves the use of the hyperboloidal framework, non-selfadjoint operators, and eigenvalue problems, which require a solid understanding of advanced mathematical concepts.
- Data Efficiency: The investigation of pseudospectrum and spectrum instability requires computationally efficient methods to handle large datasets and calculate migration ratios.
- Experimental Validation: Theoretical findings should be tested through experiments or numerical simulations to validate their accuracy and practical applications.
- Potential Applications: Understanding spectrum instability in quantum corrected black holes can have implications for various fields, such as astrophysics, cosmology, and quantum gravity research.
Disclaimer: The information presented in this study is based on theoretical analysis. Further research and empirical evidence are needed to fully understand the implications and applications of the findings.
Read the original article
by jsendak | Jan 20, 2024 | GR & QC Articles
We study the geometry of $Tbar{T}$-deformed BTZ black hole and find it can
be regarded as a quotient of hyperbolic space. We then consider the massive
scalar field propagating in the $Tbar{T}$-deformed BTZ black hole background.
The one-loop partition function of scalar field is calculated using the heat
kernel method and the Wilson spool proposal. These two methods give consistent
result which implies the Wilson spool proposal still holds under $Tbar{T}$
deformation. Moreover, we also calculate the one-loop partition function of
graviton in $Tbar{T}$-deformed BTZ black hole. We find the deformed one-loop
partition functions are modified in a simple way, which corresponds to a
replacement of the modular parameter. The result precisely matches the large
$c$ expansion of $Tbar{T}$-deformed CFT partition function. These results
provide a further check about the correspondence between $Tbar{T}$-deformed
CFT$_2$ and AdS$_3$ with mixed boundary condition.
Examining the Conclusions and Outlining a Future Roadmap
The study of the geometry of the $Tbar{T}$-deformed BTZ black hole has yielded interesting results that provide insight into the connection between $Tbar{T}$-deformed CFT (Conformal Field Theory) and AdS (Anti-de Sitter) spacetime with mixed boundary condition. In addition, the calculations of the one-loop partition functions for the massive scalar field and graviton in the deformed black hole background have shown consistent results and modifications that align with the $Tbar{T}$ deformation.
Potential Challenges
- Further investigation is required to understand the precise implications and consequences of the replacement of the modular parameter and its impact on the deformed one-loop partition functions.
- Exploring the physical interpretation of the modified partition functions and their connection to other aspects of quantum gravity and quantum field theory.
- Understanding the broader implications of the consistent results obtained from both the heat kernel method and the Wilson spool proposal.
Potential Opportunities
- Utilizing the insights gained from this study to further explore the correspondence between $Tbar{T}$-deformed CFT$_2$ and AdS$_3$ with mixed boundary condition.
- Investigating the potential applications of these findings in other areas of theoretical physics, such as holography and black hole physics.
- Considering the implications for quantum information theory and quantum gravity, particularly in relation to entanglement entropy and the holographic principle.
In summary, the examination of the $Tbar{T}$-deformed BTZ black hole geometry and the calculation of the one-loop partition functions for scalar fields and gravitons have provided valuable insights into the correspondences between $Tbar{T}$-deformed CFT and AdS spacetime with mixed boundary condition. However, further exploration and investigation are needed to fully understand the implications of these results and to explore their broader applications in theoretical physics.
Read the original article
by jsendak | Jan 20, 2024 | GR & QC Articles
Among the compact objects observed in gravitational wave merger events a few
have masses in the gap between the most massive neutron stars (NSs) and least
massive black holes (BHs) known. Their nature and the formation of their
merging binaries are not well understood. We report on pulsar timing
observations using the Karoo Array Telescope (MeerKAT) of PSR J0514-4002E, an
eccentric binary millisecond pulsar in the globular cluster NGC 1851 with a
total binary mass of $3.887 pm 0.004$ solar masses. The companion to the
pulsar is a compact object and its mass (between $2.09$ and $2.71$ solar
masses, 95% confidence interval) is in the mass gap, so it either is a very
massive NS or a low-mass BH. We propose the companion was formed by a merger
between two earlier NSs.
Conclusion:
Based on pulsar timing observations using the Karoo Array Telescope (MeerKAT), PSR J0514-4002E, an eccentric binary millisecond pulsar in the globular cluster NGC 1851, has a companion with a mass in the gap between neutron stars and black holes. The mass of the companion is estimated to be between 2.09 and 2.71 solar masses, suggesting it could be either a very massive neutron star or a low-mass black hole. The formation of this merging binary and the nature of the companion are not well understood.
Roadmap:
Challenges:
- Understanding the nature of the companion: The mass of the companion falls within the mass gap, which poses challenges in determining whether it is a neutron star or a black hole. Further research and theoretical modeling are required to better understand its properties and characteristics.
- Formation of merging binaries: The formation of merging binaries, especially those with objects in the mass gap, is not well understood. Exploring the mechanisms and processes involved in the formation of these binaries will be crucial in unraveling the mysteries surrounding compact objects.
Opportunities:
- Advancement in pulsar timing observations: Continued advancements in telescopes and observational techniques, such as MeerKAT, provide opportunities to study and analyze more binary millisecond pulsars. By observing similar systems, researchers can gather more data to refine their understanding of compact objects and their formation.
- Theoretical modeling and simulations: The discovery of PSR J0514-4002E and its companion opens up opportunities for theoretical physicists and astrophysicists to develop models and simulations that can explain the formation and evolution of compact objects in the universe. These models can help test various hypotheses and provide insights into the nature of these enigmatic objects.
Overall, the discovery of PSR J0514-4002E and its companion presents an exciting avenue for further exploration and investigation. By addressing the challenges and leveraging the opportunities, scientists can deepen our understanding of compact objects and their origins.
Read the original article
by jsendak | Jan 20, 2024 | GR & QC Articles
Holographic superconductor phase transition and spontaneous scalarization are
triggered by the instability of the underlying vacuum black hole spacetime.
Although both hairy black hole solutions are closely associated with the
tachyonic instability of the scalar degree of freedom, they are understood to
be driven by distinct causes. It is, therefore, interesting to explore the
interplay between the two phenomena in the context of a scenario where both
mechanisms are present. To this end, we investigate the
Einstein-scalar-Gauss-Bonnet theory in asymptotically anti-de Sitter spacetime
with a Maxwell field. On the one hand, the presence of the charged scalar and
Maxwell fields in anti-de Sitter spacetime furnishes the celebrated framework
for a holographic superconductor. On the other hand, the non-minimal
Gauss-Bonnet coupling between the scalar field and the gravitational sector
triggers spontaneous scalarization. However, near the transition curve, the two
phases are found to be largely indistinguishable regarding both the radial
profile and effective potential. This raises the question of whether the hairy
black holes triggered by different mechanisms are smoothly joined by a phase
transition or whether these are actually identical solutions. To assess the
transition more closely, we evaluate the phase diagram in terms of temperature
and chemical potential and discover a smooth but first-order transition between
the two hairy solutions by explicitly evaluating Gibbs free energy and its
derivatives. In particular, one can elaborate a thermodynamic process through
which a superconducting black hole transits into a scalarized one by raising or
decreasing the temperature. Exhausting the underlying phase space, we analyze
the properties and the interplay between the two hairy solutions.
Introduction
In this article, we examine the conclusions of a recent study on the interplay between holographic superconductors and spontaneous scalarization in black holes. The study investigates the Einstein-scalar-Gauss-Bonnet theory in anti-de Sitter spacetime with a Maxwell field, which provides a framework for both holographic superconductors and spontaneous scalarization. We explore the possibility of a phase transition between these two hairy black hole solutions and analyze the properties and interplay between them.
Holographic Superconductors and Scalarization
Holographic superconductors are systems that exhibit properties similar to superconductors in condensed matter physics, but are described by gravity theories in higher dimensions. The presence of charged scalar and Maxwell fields in anti-de Sitter spacetime allows for the formation of these superconducting black holes.
Spontaneous scalarization, on the other hand, is triggered by the non-minimal Gauss-Bonnet coupling between the scalar field and the gravitational sector. This coupling leads to the emergence of scalar hairs on black holes, which was previously thought to be impossible in Einstein’s theory of gravity.
Exploring the Interplay
The main focus of this study is to investigate the interaction between holographic superconductors and spontaneous scalarization. By considering the Einstein-scalar-Gauss-Bonnet theory with a Maxwell field, the researchers aim to understand whether these two phenomena can coexist and if there is a phase transition between them.
The study finds that near the transition curve, the two phases of hairy black holes are indistinguishable regarding their radial profile and effective potential. This raises questions about their true nature and whether they are actually identical solutions.
Evaluating the Phase Diagram
To assess the phase transition between holographic superconductors and scalarized black holes, the researchers evaluate the phase diagram in terms of temperature and chemical potential. They discover a smooth but first-order transition between the two solutions by analyzing the Gibbs free energy and its derivatives.
This implies that it is possible to transit a superconducting black hole into a scalarized one by raising or decreasing the temperature in a well-defined thermodynamic process.
Challenges and Opportunities
Understanding the interplay between holographic superconductors and spontaneous scalarization opens up new possibilities for exploring exotic phenomena in black hole physics. It provides insights into the nature of these hairy black hole solutions and how they can transition between different phases.
However, there are also challenges in further investigating this interplay. The underlying phase space needs to be thoroughly exhausted to analyze the properties and behavior of both solutions. Additionally, more research is needed to fully understand the significance of the phase transition and its implications for the broader field of gravity theories.
Conclusion
Overall, this study highlights the intriguing connection between holographic superconductors and spontaneous scalarization in black holes. It demonstrates that there is a smooth but first-order phase transition between these two hairy solutions. By evaluating the phase diagram and analyzing thermodynamic processes, we gain a deeper understanding of the interplay between these phenomena. Further exploration of this field holds promise for uncovering new insights into the nature of black holes and gravity theories.
Sources:
- Research paper: [INSERT LINK]
Read the original article
by jsendak | Jan 20, 2024 | GR & QC Articles
Recently, several regional pulsar timing array collaborations, including
CPTA, EPTA, PPTA, and NANOGrav, have individually reported compelling evidence
for a stochastic signal at nanohertz frequencies. This signal originates
potentially from scalar-induced gravitational waves associated with significant
primordial curvature perturbations on small scales. In this letter, we employ
data from the EPTA DR2, PPTA DR3, and NANOGrav 15-year data set, to explore the
speed of scalar-induced gravitational waves using a comprehensive Bayesian
analysis. Our results suggest that, to be consistent with pulsar timing array
observations, the speed of scalar-induced gravitational waves should be $c_g
gtrsim 0.61$ at a $95%$ credible interval for a lognormal power spectrum of
curvature perturbations. Additionally, this constraint aligns with the
prediction of general relativity that $c_g=1$ within a $90%$ credible
interval. Our findings underscore the capacity of pulsar timing arrays as a
powerful tool for probing the speed of scalar-induced gravitational waves.
Recently, several regional pulsar timing array collaborations have reported evidence for a stochastic signal at nanohertz frequencies, potentially originating from scalar-induced gravitational waves associated with primordial curvature perturbations. In this letter, we used data from the EPTA DR2, PPTA DR3, and NANOGrav 15-year data set to analyze the speed of scalar-induced gravitational waves using Bayesian analysis.
Our results suggest that, to be consistent with pulsar timing array observations, the speed of scalar-induced gravitational waves should be $c_g gtrsim 0.61$ at a 95% credible interval for a lognormal power spectrum of curvature perturbations. This finding is in alignment with the prediction of general relativity that the speed of gravitational waves is equal to the speed of light, $c_g=1$, within a 90% credible interval.
This research highlights the potential of pulsar timing arrays as a powerful tool for studying the speed of scalar-induced gravitational waves. The following roadmap outlines potential challenges and opportunities for future research in this field:
Future Roadmap: Challenges and Opportunities
1. Improve Data Collection and Analysis
- Continue collecting and analyzing data from regional pulsar timing array collaborations such as CPTA, EPTA, PPTA, and NANOGrav.
- Develop more advanced statistical techniques for analyzing the data to further improve the precision and accuracy of measurements.
2. Increase Sensitivity of Pulsar Timing Arrays
- Invest in technological advancements to enhance the sensitivity of pulsar timing arrays, allowing detection of weaker signals and more precise measurements.
- Expand the number of observed pulsars and increase the baseline of observations to improve the overall sensitivity of the arrays.
3. Explore Alternative Models and Sources
- Investigate alternative models for scalar-induced gravitational waves and curvature perturbations to further validate the current findings.
- Study other potential sources of nanohertz gravitational waves, such as cosmic strings or mergers of supermassive black holes, to expand our understanding of the Universe.
4. Collaboration and Data Sharing
- Foster collaboration and data sharing between different regional pulsar timing array collaborations to combine their efforts and maximize the reach and impact of their research.
- Establish international collaborations and partnerships to facilitate the exchange of knowledge and resources in the field.
By addressing these challenges and pursuing the opportunities outlined above, future research in the field of scalar-induced gravitational waves using pulsar timing arrays has the potential to make significant progress in our understanding of the nature of gravity and the early Universe.
Read the original article
