by jsendak | Jan 1, 2024 | GR & QC Articles
We apply the inverse Gertsenshtein effect, i.e., the graviton-photon
conversion in the presence of a magnetic field, to constrain high-frequency
gravitational waves (HFGWs). Using existing astrophysical measurements, we
compute upper limits on the GW energy densities $Omega_{rm GW}$ at 16
different frequency bands. Given the observed magnetisation of galaxy clusters
with field strength $Bsimmu{rm G}$ correlated on $mathcal{O}(10),{rm
kpc}$ scales, we estimate HFGW constraints in the $mathcal{O}(10^2),{rm
GHz}$ regime to be $Omega_{rm GW}lesssim10^{16}$ with the temperature
measurements of the Atacama Cosmology Telescope (ACT). Similarly, we
conservatively obtain $Omega_{rm GW}lesssim10^{13} (10^{11})$ in the
$mathcal{O}(10^2),{rm MHz}$ ($mathcal{O}(10),{rm GHz}$) regime by
assuming uniform magnetic field with strength $Bsim0.1,{rm nG}$ and
saturating the excess signal over the Cosmic Microwave Background (CMB)
reported by radio telescopes such as the Experiment to Detect the Global EoR
Signature (EDGES), LOw Frequency ARray (LOFAR), and Murchison Widefield Array
(MWA), and the balloon-borne second generation Absolute Radiometer for
Cosmology, Astrophysics, and Diffuse Emission (ARCADE2) with graviton-induced
photons. Although none of these existing constraints fall below the critical
value of $Omega_{rm GW} = 1$ or reaches the Big Bang Nucleosynthesis (BBN)
bound of $Omega_{rm GW}simeq1.2times10^{-6}$, the upcoming Square Kilometer
Array (SKA) can improve the sensitivities by roughly 10 orders of magnitude and
potentially become realistic probes of HFGWs. We also explore several
next-generation CMB surveys, including Primordial Inflation Explorer (PIXIE),
Polarized Radiation Interferometer for Spectral disTortions and INflation
Exploration (PRISTINE) and Voyage 2050, that could potentially provide
constraints competitive to the current BBN bound.
The Roadmap for High-Frequency Gravitational Wave Research
In this article, we have examined the constraints on high-frequency gravitational waves (HFGWs) and outlined a roadmap for future research in this field. Here, we summarize the key conclusions and highlight potential challenges and opportunities on the horizon.
Conclusions
- We applied the inverse Gertsenshtein effect, which involves graviton-photon conversion in the presence of a magnetic field, to constrain HFGWs.
- Using existing astrophysical measurements, we computed upper limits on the GW energy densities at 16 different frequency bands.
- Our analysis revealed that HFGW constraints in the range of $mathcal{O}(10^2),{rm GHz}$ regime are estimated to be $Omega_{rm GW}lesssim10^{16}$, based on magnetization of galaxy clusters.
- Similarly, assuming a uniform magnetic field with strength $Bsim0.1,{rm nG}$, we obtain $Omega_{rm GW}lesssim10^{13} (10^{11})$ in the $mathcal{O}(10^2),{rm MHz}$ ($mathcal{O}(10),{rm GHz}$) regime by saturating the excess signal reported by various radio telescopes.
- Although none of the existing constraints reach the critical value of $Omega_{rm GW} = 1$ or the Big Bang Nucleosynthesis (BBN) bound of $Omega_{rm GW}simeq1.2times10^{-6}$, future observations hold promise for more significant discoveries.
Future Roadmap
- Square Kilometer Array (SKA): The upcoming SKA has the potential to improve sensitivities by approximately 10 orders of magnitude. This significant boost in capabilities could make it a realistic probe for HFGWs.
- Next-generation CMB Surveys: Several next-generation surveys, including Primordial Inflation Explorer (PIXIE), Polarized Radiation Interferometer for Spectral disTortions and INflation Exploration (PRISTINE), and Voyage 2050, are being considered. These surveys have the potential to provide constraints that are competitive with the current BBN bound.
Challenges and Opportunities
- Challenges:
- The development and implementation of cutting-edge technologies and instruments capable of detecting and analyzing HFGWs with high precision.
- The need for more accurate measurements of magnetization in galaxy clusters to improve constraints on HFGWs.
- Addressing potential sources of noise and interference in radio telescope observations to enhance sensitivity to HFGWs.
- Opportunities:
- Advancements in technology, such as the development of more sensitive detectors and improved data analysis techniques, can greatly enhance our ability to study HFGWs.
- The collaborative efforts between different research teams, observatories, and space agencies can lead to innovative solutions and new discoveries in the field.
Overall, the future of HFGW research looks promising. With the upcoming SKA and next-generation CMB surveys, we have the potential to make breakthroughs in our understanding of these elusive phenomena. Overcoming technical challenges and leveraging new opportunities will be key to unlocking the mysteries of high-frequency gravitational waves.
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by jsendak | Jan 1, 2024 | GR & QC Articles
We study transformations of the dynamical fields – a metric, a flat affine
connection and a scalar field – in scalar-teleparallel gravity theories. The
theories we study belong either to the general teleparallel setting, where no
further condition besides vanishing curvature is imposed on the affine
connection, or the symmetric or metric teleparallel gravity, where one also
imposes vanishing torsion or nonmetricity, respectively. For each of these
three settings, we find a general class of scalar-teleparallel action
functionals which retain their form under the aforementioned field
transformations. This is achieved by generalizing the constraint of vanishing
torsion or nonmetricity to non-vanishing, but algebraically constrained torsion
or nonmetricity. We find a number of invariant quantities which characterize
these theories independently of the choice of field variables, and relate these
invariants to analogues of the conformal frames known from scalar-curvature
gravity. Using these invariants, we are able to identify a number of physically
relevant subclasses of scalar-teleparallel theories. We also generalize our
results to multiple scalar fields, and speculate on further extended theories
with non-vanishing, but algebraically constrained curvature.
Conclusions:
The study examines transformations of the dynamical fields in scalar-teleparallel gravity theories. It analyzes theories under different settings, including general teleparallel, symmetric teleparallel, and metric teleparallel gravity. The study finds a general class of scalar-teleparallel action functionals that remain unchanged under the field transformations by imposing algebraically constrained torsion or nonmetricity. Several invariant quantities are identified that characterize these theories independently of the choice of field variables, and are related to conformal frames in scalar-curvature gravity. The study also extends the results to multiple scalar fields and speculates on further extended theories with algebraically constrained curvature.
Future Roadmap:
The findings of this study open up several potential opportunities and challenges for further exploration in the field of scalar-teleparallel gravity theories.
Potential Challenges:
- Validation: One of the challenges is the validation of these theories through experiments or observations. Further research is needed to test the predictions made by these scalar-teleparallel theories and compare them with existing gravitational theories.
- Mathematical Complexity: The introduction of algebraically constrained torsion or nonmetricity adds complexity to the mathematical formulations. Finding exact solutions and performing calculations in these extended theories may pose challenges.
- Consistency with Other Theories: It is important to investigate the consistency of these scalar-teleparallel theories with other established theories, such as general relativity. The compatibility and agreement between different theoretical frameworks should be explored.
Potential Opportunities:
- Extension to Multiple Scalar Fields: The study suggests that the results can be generalized to include multiple scalar fields. This opens up possibilities for studying interactions and dynamics between multiple scalar fields in the context of scalar-teleparallel gravity.
- Identification of Physically Relevant Subclasses: The identification of physically relevant subclasses of scalar-teleparallel theories provides a foundation for further investigations. These subclasses can be studied in greater detail to explore their implications for various physical phenomena.
- Exploration of Extended Theories: The speculation about extended theories with algebraically constrained curvature presents an opportunity for future research. Investigating the consequences and implications of such extended theories can provide new insights into the nature of gravity.
Conclusion:
The findings of this study lay the groundwork for further exploration in the field of scalar-teleparallel gravity theories. While challenges such as validation and mathematical complexity exist, there are also opportunities to extend the theories to multiple scalar fields, identify physically relevant subclasses, and explore extended theories with constrained curvature. Future research in these directions can significantly contribute to our understanding of gravity and its fundamental properties.
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by jsendak | Jan 1, 2024 | GR & QC Articles
We study the collisions of two scalar wave packets in the asymptotically flat
spacetime and asymptotically anti-de Sitter spacetime in spherical symmetry. An
energy transfer formula is obtained, $y=Cm_{i}m_{o}/r$, where $y$ is the
transferred energy in the collisions of the two wave packets, $m_i$ and $m_o$
are the Misner-Sharp energies for the ingoing and outgoing wave packets,
respectively, $r$ is the areal radius and collision place, and $C=1.873$ and
$C=1.875$ for the asymptotically flat spacetime and asymptotically anti-de
Sitter spacetime circumstances, respectively. The formula is universal,
independent of the initial profiles of the scalar fields.
The study examines the collisions of two scalar wave packets in both asymptotically flat spacetime and asymptotically anti-de Sitter spacetime in spherical symmetry. The researchers derived an energy transfer formula, which states that the transferred energy, y, in the collisions of the two wave packets is given by y = Cmimo/r, where mi and mo are the Misner-Sharp energies for the ingoing and outgoing wave packets, r is the areal radius and collision place, and C has different values based on the spacetime circumstances – C=1.873 for asymptotically flat spacetime and C=1.875 for asymptotically anti-de Sitter spacetime. Notably, the formula is universal and independent of the initial profiles of the scalar fields.
Future Roadmap
Potential Challenges
- Further Verification: The derived energy transfer formula needs to be further verified through experiments or simulations to validate its accuracy and applicability in real-world scenarios.
- Limitations of Spherical Symmetry: The study focuses on collisions in spherical symmetry, which may limit its applicability to more complex scenarios.
- Generalization: While the formula is stated as universal, its generalizability to scenarios beyond scalar wave packets may pose challenges and require additional research.
Potential Opportunities
- Energy Transfer Studies: The derived formula opens up opportunities for further studies on energy transfer in various spacetime configurations, providing insights into the dynamics of wave collisions.
- Application in Different Fields: The universal nature of the energy transfer formula makes it potentially useful in diverse fields such as astrophysics, quantum physics, and cosmology.
- Exploration of Non-Spherical Collisions: Building upon the findings of this study, future research can explore collisions that deviate from spherical symmetry, expanding our understanding of wave interactions in different geometries.
In conclusion, the study presents a derived energy transfer formula for the collisions of scalar wave packets in asymptotically flat and asymptotically anti-de Sitter spacetime. While the formula’s application may face challenges such as verification and limitations of spherical symmetry, it also opens up opportunities for further energy transfer studies and potential applications in different fields. Additionally, future research can explore non-spherical collisions to broaden our understanding of wave interactions.
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by jsendak | Jan 1, 2024 | GR & QC Articles
We describe the dynamical formation of the shadow of a collapsing star in a
Hayward spacetime in terms of an observer far away from the center and a free
falling observer. By solving the time-like and light-like radial geodesics we
determine the angular size of the shadow as a function of time. We found that
the formation of the shadow is a finite process for both observers and its size
is affected by the Hayward spacetime parameters. We consider several scenarios,
from the Schwarzschild limit to an extreme Hayward black hole.
Examining the Conclusions of the Text:
In the given text, the authors describe the dynamical formation of the shadow of a collapsing star in a Hayward spacetime. By studying the behaviors of an observer far away from the center and a free-falling observer, the authors determine the angular size of the shadow as a function of time. They find that the formation of the shadow is a finite process for both observers and that its size is influenced by the parameters of the Hayward spacetime.
Future Roadmap and Potential Challenges:
- Further Investigation of the Shadow Formation: Building on the findings of this study, future research could focus on understanding the intricacies of the shadow formation process in a Hayward spacetime. This could involve studying different collapsing star scenarios and varying the parameters of the spacetime to explore their impact on the size and dynamics of the shadow.
- Comparative Analysis with Other Spacetimes: To gain a comprehensive understanding of shadow formation, comparative analysis with other types of spacetimes, such as Schwarzschild or Kerr, may be necessary. This would help establish similarities and differences in the behavior of shadows under various gravitational influences.
- Experimental Validation: The theoretical predictions derived from this study could be tested through observational data, such as astrophysical observations or simulations. Experimental validation would provide concrete evidence for the formation process and allow for further refinement of theoretical models.
- Gravitational Wave Effects: Investigating the influence of gravitational waves on shadow formation in a Hayward spacetime could be an interesting area for future research. Understanding how these waves interact with collapsing stars and affect the size and dynamics of the resulting shadows could deepen our knowledge of both gravitational wave physics and black hole astrophysics.
Opportunities on the Horizon:
The findings presented in this study open up several opportunities for future research and exploration in the field of black hole astrophysics. The following opportunities could be pursued:
- Advancing our Understanding of Black Hole Dynamics: By further investigating the formation and evolution of black hole shadows in different spacetimes, we can enhance our understanding of the complex dynamics involved in these extreme gravitational systems. This knowledge could contribute to our overall comprehension of black hole astrophysics.
- Contributions to Fundamental Physics Theories: The study of shadow formation in different spacetimes, including the Hayward spacetime considered here, may have implications for fundamental physics theories such as general relativity, quantum gravity, and black hole thermodynamics. Insights gained from these studies may offer invaluable contributions to these fields.
- Potential Applications in Astrophysical Observations: Understanding the behavior of shadows in collapsing star scenarios and under different spacetime parameters can have practical applications in astrophysical observations. By analyzing the observed shadows, scientists could gain insights into the properties of the central collapsed objects, providing valuable information about their mass, spin, and other characteristics.
In conclusion, the study of shadow formation in a Hayward spacetime has revealed important insights into the dynamics of collapsing stars and their resulting shadows. Building on these findings, future research directions include further investigating the shadow formation process, comparative analysis with other spacetimes, experimental validation, and studying the influence of gravitational waves. These opportunities hold the potential to significantly advance our understanding of black hole astrophysics, contribute to fundamental physics theories, and find applications in astrophysical observations.
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by jsendak | Jan 1, 2024 | GR & QC Articles
In higher-dimensional theories, a graviton propagating in the bulk can follow
a shorter path, known as a shortcut, compared to a photon propagating in a
$4$-dimensional spacetime. Thus by combining the observations of gravitational
waves and their electromagnetic counterparts, one can gain insights into the
structure and number of extra dimensions. In this paper, we construct a
braneworld model that allows the existence of shortcuts in a
$D(=4+d)$-dimensional spacetime. It has been proven that the equations for
modelling brane cosmology recover the standard Friedmann equations for the late
universe. We derive analytically the graviton and photon horizon radii on the
brane under the low-energy limit. With the event GW170817/GRB 170817A, we find
that the number of extra dimensions has an upper limit of $dleq9$. Because of
the errors in the source redshift and time delay, this upper limit can be
shifted to $dleq4$ and $dleq12$. Considering various astrophysical processes,
the upper limit of $dleq4$ is the most robust.
Conclusions:
- In higher-dimensional theories, a graviton can follow a shorter path compared to a photon in a 4-dimensional spacetime.
- Combining observations of gravitational waves and their electromagnetic counterparts can provide insights into the structure and number of extra dimensions.
- A braneworld model that allows the existence of shortcuts in a D-dimensional spacetime is constructed.
- The equations for modeling brane cosmology recover the standard Friedmann equations for the late universe.
- Under the low-energy limit, the graviton and photon horizon radii on the brane are derived analytically.
- The event GW170817/GRB 170817A suggests an upper limit of d≤9 for the number of extra dimensions.
- Errors in source redshift and time delay can shift the upper limit to d≤4 and d≤12.
- The most robust upper limit based on various astrophysical processes is d≤4.
Future Roadmap:
Based on the conclusions of the study, there are several potential opportunities and challenges that lie ahead in the field of higher-dimensional theories and braneworld models:
Potential Opportunities:
- Further exploration of gravitational waves and their electromagnetic counterparts to gain deeper insights into the structure and number of extra dimensions. This can lead to a better understanding of the fundamental nature of spacetime.
- The development of more sophisticated models for braneworld cosmology, taking into account the shortcuts in higher-dimensional spacetime. This can provide a new framework for explaining the behavior of the universe.
- The utilization of analytical techniques to derive the graviton and photon horizon radii on the brane. This can aid in the development of experimental tests and predictions for future observations.
Potential Challenges:
- Addressing the uncertainties and errors in source redshift and time delay measurements, which can impact the determination of the upper limit for the number of extra dimensions.
- Overcoming technical and computational challenges in constructing and studying braneworld models, as they involve higher-dimensional spacetime and complex gravitational interactions.
- Exploring and understanding the physical implications and consequences of the upper limit of d≤4 for the number of extra dimensions, and how it aligns with other theories and observations.
Overall, the findings of this study open up new avenues for research and exploration in higher-dimensional theories, gravitational waves, and cosmology. The roadmap for the future involves further investigations into extra dimensions, refinement of braneworld models, and experimental tests to confirm or refine the upper limit for the number of extra dimensions.
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by jsendak | Jan 1, 2024 | GR & QC Articles
We suggest commutation relations for a quantum measure. In one version of
these relations, the right-hand side takes account of the presence of curvature
of space; in the simplest case, this yields the action of general relativity.
We consider the cases of the quantization of the measure on spaces of constant
curvature and show that in this case the commutation relations for the quantum
measure are analogues of commutation relations in loop quantum gravity. It is
assumed that, in contrast to loop quantum gravity, a triangulation of space is
a necessary trick for quantizing such a nonlocal quantity like a measure; in
doing so, the space remains a smooth manifold. We consider the self-consistent
problem of the interaction of the quantum measure and classical gravitation. It
is shown that this inevitably leads to the appearance of modified gravities.
Also, we consider the problem of defining the Euler-Lagrange equations for a
matter field in the background of a space endowed with quantum measure.
Quantum Measure and General Relativity
In this article, we have explored the commutation relations for a quantum measure and its relationship to general relativity. By considering the quantization of the measure on spaces of constant curvature, we have shown that the commutation relations for the quantum measure resemble those found in loop quantum gravity.
Unlike loop quantum gravity, however, we argue that a triangulation of space is necessary for quantizing such a nonlocal quantity as a measure while still preserving the smoothness of the manifold. This allows us to address the self-consistent problem of the interaction between the quantum measure and classical gravitation.
Modified Gravities and the Quantum Measure
One of the key conclusions of our study is that the interaction between the quantum measure and classical gravitation inevitably leads to the emergence of modified gravities. This suggests that the presence of a quantum measure has profound implications for our understanding of the fundamental laws of gravity.
To fully comprehend these modified gravities, further research is required to define the Euler-Lagrange equations for a matter field in the background of a space endowed with a quantum measure. This entails exploring how the presence of the quantum measure affects the dynamics of matter fields and refining our mathematical framework for describing these interactions.
Future Roadmap: Challenges and Opportunities
- Investigating Quantum Measure in Curved Spaces: A crucial avenue for future research is to explore quantization techniques for measures in curved spaces beyond constant curvature cases. Understanding how curvature affects the commutation relations and the resulting modified gravities will deepen our knowledge about the interplay between quantum measures and geometry.
- Refining Quantization Methods: The use of triangulation to quantize nonlocal quantities like a measure is an innovative approach. However, challenges remain in developing more precise and efficient quantization methods that can handle complex geometries. Overcoming these challenges will enhance our ability to study quantum measures in a wider range of spacetime configurations.
- Investigating Matter-Quantum Measure Interactions: Greater attention should be given to studying the interaction between matter fields and the quantum measure. Defining the Euler-Lagrange equations in the presence of a quantum measure will be instrumental in understanding the dynamics of matter in this modified gravitational framework. This research will likely uncover new phenomena and potentially open avenues for experimental validation.
In conclusion, the exploration of quantum measures and their relationship to general relativity provides exciting opportunities for advancing our understanding of fundamental laws and the nature of spacetime. While challenges lie ahead, overcoming these obstacles will lead to new insights and possibilities for theoretical and experimental investigations.
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