by jsendak | Jan 13, 2024 | GR & QC Articles
When classical degrees of freedom and quantum degrees of freedom are
consistently coupled, the former diffuse, while the latter undergo decoherence.
Here, we construct a theory of quantum matter fields and Nordstrom gravity in
which the space-time metric is treated classically. The dynamics is constructed
via the classical-quantum path integral and is completely positive, trace
preserving (CPTP), and respects the classical-quantum split. The weak field
limit of the model matches the Newtonian limit of the full covariant path
integral but it is easier to show that the theory is both diffeomorphism
invariant, CPTP, and has the appropriate classical limit.
The conclusions of the text are as follows:
- When classical degrees of freedom and quantum degrees of freedom are consistently coupled, the classical degrees of freedom diffuse, while the quantum degrees of freedom undergo decoherence.
- A theory of quantum matter fields and Nordstrom gravity is constructed in which the space-time metric is treated classically.
- The dynamics of the theory is constructed via the classical-quantum path integral and is completely positive, trace preserving (CPTP), and respects the classical-quantum split.
- The weak field limit of the model matches the Newtonian limit of the full covariant path integral.
- The theory is both diffeomorphism invariant, CPTP, and has the appropriate classical limit.
Future Roadmap
Based on the conclusions of the text, there are potential challenges and opportunities on the horizon for further research and development in the field. A future roadmap can be outlined as follows:
1. Studying Diffusion of Classical Degrees of Freedom
Further investigation is needed to understand and explore the diffusion of classical degrees of freedom when consistently coupled with quantum degrees of freedom. This can help in determining the extent to which classical information spreads and diffuses in such systems.
2. Investigating Quantum Decoherence
The phenomenon of quantum decoherence observed in the text requires deeper exploration to understand its implications and consequences. Research can focus on identifying methods to mitigate or control decoherence, allowing for the preservation of quantum coherence in interacting systems.
3. Refining the Theory of Quantum Matter Fields and Nordstrom Gravity
The theory proposed in the text, which treats the space-time metric classically, needs further refinement and development. Researchers can focus on enhancing the accuracy and applicability of the theory by incorporating additional factors and variables that affect the interaction between quantum matter fields and Nordstrom gravity.
4. Exploring Alternative Dynamics Construction Methods
The classical-quantum path integral used for constructing the dynamics in the proposed theory may not be the only approach available. Exploring alternative methods for constructing the dynamics can provide insights into different aspects of the system and potentially uncover new phenomena or behaviors.
5. Extending the Model to Non-Weak Field Limits
The current model’s weak field limit matches the Newtonian limit, which opens possibilities for investigating other limits of the model. Extending the analysis to non-weak field limits can lead to a deeper understanding of the behavior of the theory in different regimes and scenarios.
6. Validating Diffeomorphism Invariance and Classical Limits
Validating that the theory is both diffeomorphism invariant and has the appropriate classical limit is crucial to ensure its consistency and accuracy. Further studies can focus on rigorous mathematical proofs and experimental validations to confirm these properties of the proposed theory.
7. Practical Applications and Technological Impact
Exploring potential practical applications and technological implications of the developed theory is an essential aspect of future research. Investigating how the theory can be utilized in various fields, such as quantum computing, cosmology, or particle physics, can lead to innovative technologies and advancements.
Overall, the conclusions drawn from the text present exciting prospects for further research in understanding the coupling of classical and quantum degrees of freedom. The outlined future roadmap highlights potential challenges to address and opportunities for groundbreaking discoveries in the field.
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by jsendak | Jan 12, 2024 | GR & QC Articles
It has been established that Black Hole (BH) spacetimes obeying some general
set of assumptions always possess, at least, one light ring (per rotation
sense) [arXiv:2003.06445]. This theorem was originally established for
asymptotically flat, stationary, axial symmetric, 1+3 dimensional circular
spacetimes harbouring a non-extremal and topologically spherical Killing
horizon. Following the mantra that a theorem is only as strong as its
assumptions in this work we extend this theorem to non topologically spherical
(toroidal) BHs and to spacetimes harbouring more than one BH. As in
[arXiv:2003.06445], we show that each BH still contributes with, at least, one
LR (per rotation sense).
It has been established that Black Hole (BH) spacetimes always possess at least one light ring per rotation sense, given a set of general assumptions. Originally, this theorem applied to asymptotically flat, stationary, axial symmetric, 1+3 dimensional circular spacetimes with a non-extremal and topologically spherical Killing horizon.
In this work, we aim to extend this theorem to include non topologically spherical (toroidal) BHs and spacetimes with more than one BH. We adhere to the principle that a theorem is only as strong as its assumptions, and demonstrate that each BH still contributes with at least one light ring per rotation sense, just as in previous research.
Roadmap for the Future
Challenges:
- Generalizing the theorem to include non topologically spherical BHs may require a deeper understanding of the underlying physics and mathematical frameworks.
- Extending the theorem to spacetimes with multiple BHs introduces additional complexities, such as interactions between the BHs and potential interference with light rings.
Opportunities:
- By including non topologically spherical BHs, we can expand our understanding of the properties and behavior of these types of black holes.
- Studying spacetimes with multiple BHs can provide insights into the dynamics and structure of these systems, potentially leading to new discoveries about the nature of gravity and the formation of BHs.
In conclusion, the theorem that Black Hole spacetimes possess at least one light ring per rotation sense has been extended to accommodate non topologically spherical BHs and spacetimes with multiple BHs. While there may be challenges in terms of understanding the underlying physics and dealing with increased complexities, this extension opens up new opportunities for further exploration and gaining deeper insights into the properties and dynamics of black holes.
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by jsendak | Jan 12, 2024 | GR & QC Articles
In this article, we compute the two observables, impulse and waveform, in a
black hole scattering event for the Scalar-Tensor theory of gravity with a
generic scalar potential using the techniques of Worldline Quantum Field
Theory. We mainly investigate the corrections to the above mentioned
observables due to the extra scalar degree of freedom. For the computation of
impulse, we consider the most general scenario by making the scalar field
massive and then show that each computed diagram has a smooth massless limit.
We compute the waveform for scalar and graviton up to 2PM, taking the scalar as
massless. Furthermore, we discuss if the scalar has mass and how the radiation
integrals get more involved than the massless case. We also arrive at some
analytical results using stationary phase approximation. Interestingly, we also
show that the $lambda_4 varphi^4$ interaction vertex does not contribute to
the radiation by showing that the integral has no non-zero finite value.
Impulse and Waveform in Black Hole Scattering Event for Scalar-Tensor Theory of Gravity
In this article, we explore the computation of two observables, impulse and waveform, in a black hole scattering event within the context of the Scalar-Tensor theory of gravity with a generic scalar potential. We utilize the techniques of Worldline Quantum Field Theory to investigate the corrections to these observables due to the presence of an extra scalar degree of freedom.
Computing Impulse
To compute the impulse, we consider the most general scenario by introducing a mass for the scalar field. We then proceed to show that each computed diagram exhibits a smooth massless limit. This allows us to extract meaningful results in the massless case as well.
Computing Waveform
In addition to impulse, we also calculate the waveform for both the scalar and graviton. We focus on computing the waveform up to 2PM, assuming that the scalar field is massless. We take into account the effects of the scalar’s mass and explore how the radiation integrals become more involved compared to the massless case. To aid our analysis, we employ the stationary phase approximation method, leading to some insightful analytical results.
No Contribution from $lambda_4 varphi^4$ Interaction Vertex
An interesting finding in our investigation is that the $lambda_4 varphi^4$ interaction vertex does not contribute to the radiation. We demonstrate that the corresponding integral yields no non-zero finite value. This result provides valuable information about the nature of the radiation and the role of different interaction vertices in the Scalar-Tensor theory of gravity.
Future Roadmap: Challenges and Opportunities
As we move forward, several challenges and opportunities lie ahead in the study of black hole scattering events within the Scalar-Tensor theory of gravity:
Challenges
- Further understanding the effects of the extra scalar degree of freedom on the observables
- Exploring the implications of introducing mass for the scalar field on the waveform
- Investigating other potential interaction vertices and their contributions to the radiation
- Tackling the complexity of radiation integrals in scenarios beyond the massless case
Opportunities
- Utilizing advanced computational techniques to handle intricate calculations
- Extending the analysis to higher orders in perturbation theory, beyond 2PM
- Exploring the impact of additional parameters on the observed scattering event
- Connecting the theoretical predictions to experimental observations and potential gravitational wave detections
By addressing these challenges and capitalizing on the opportunities, we can gain deeper insights into the Scalar-Tensor theory of gravity and its manifestations in black hole scattering events. These advancements have the potential to enhance our understanding of fundamental physics and contribute to the broader field of gravitational physics.
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by jsendak | Jan 12, 2024 | GR & QC Articles
This study aims to investigate the strong gravitational lensing effects in
$f(T)$ gravity. We present the theoretical analytic expressions for the lensing
effects in $f(T)$ gravity, including deflection angle, magnification, and time
delay. On this basis, we also take the plasma lensing effect into
consideration. We compare the lensing effects between the General Relativity in
a vacuum environment and the $f(T)$ gravity in a plasma environment. From a
strongly lensed fast radio burst, the results indicate that in a plasma
environment, General Relativity and $f(T)$ gravity can generate
indistinguishable image positions, but the magnification and time delay on
these positions are significantly different, which can be distinguished by
current facilities in principle. Therefore, the discrepancies between
observational results and theoretical expectations can serve as clues for a
modified gravity theory and provide constraints on $f(T)$ gravity.
The study investigates the strong gravitational lensing effects in $f(T)$ gravity and presents theoretical analytic expressions for these effects, including deflection angle, magnification, and time delay. The plasma lensing effect is also taken into consideration. By comparing the lensing effects between General Relativity in a vacuum environment and $f(T)$ gravity in a plasma environment, the study finds that in a plasma environment, General Relativity and $f(T)$ gravity can generate indistinguishable image positions. However, the magnification and time delay on these positions are significantly different, which can be potentially distinguished by current facilities. This suggests that discrepancies between observational results and theoretical expectations can provide clues for a modified gravity theory and constraints on $f(T)$ gravity.
Future Roadmap
To further explore and validate the findings of this study, future research can focus on the following areas:
1. Experimental Verification
Experimental observations using advanced telescopes and facilities should be conducted to test the differences in magnification and time delay predicted by General Relativity and $f(T)$ gravity in a plasma environment. By comparing the observations with the theoretical expectations, researchers can gauge the validity of $f(T)$ gravity in describing strong gravitational lensing effects.
2. Improved Models
Developing more sophisticated models for $f(T)$ gravity and plasma lensing effects could enhance our understanding of the observed discrepancies. These models should consider additional factors that may influence the lensing effects, such as the density and composition of the plasma. Improvements to the theoretical analytic expressions presented in this study may also be necessary.
3. Theoretical Framework
A deeper theoretical analysis may uncover the underlying reasons for the significant differences in magnification and time delay between General Relativity and $f(T)$ gravity in a plasma environment. Exploring the theoretical framework of $f(T)$ gravity and its relation to plasma lensing could provide valuable insights into the nature of gravity and its behavior in various environments.
4. Constraints on $f(T)$ Gravity
Utilizing the discrepancies between observational results and theoretical expectations as constraints on $f(T)$ gravity can guide the development and modification of gravity theories. Further investigations should aim to establish more precise constraints and explore the range of applicability for $f(T)$ gravity as a potential alternative to General Relativity.
Challenges and Opportunities
While this research opens up new possibilities and directions for studying gravitational lensing in $f(T)$ gravity, several challenges and opportunities lie ahead:
- Data Collection: Obtaining sufficient and high-quality observational data, especially of strongly lensed fast radio bursts, will be crucial for testing the predictions of $f(T)$ gravity and comparing them with General Relativity.
- Technological Advancements: Advancements in telescope technology, data analysis algorithms, and computational power are needed to accurately measure the magnification and time delay of lensed images, as well as to differentiate between the effects of General Relativity and $f(T)$ gravity.
- Theoretical Complexity: The theoretical analysis of $f(T)$ gravity and plasma lensing is a complex task that requires advanced mathematical tools and computational methods. Overcoming these challenges will require interdisciplinary collaborations and expertise.
- Scientific Exploration: Further exploration of modified gravity theories, such as $f(T)$ gravity, can lead to breakthroughs in our understanding of the fundamental nature of gravity, expanding our knowledge of the Universe and its behavior under extreme conditions.
In conclusion, the study demonstrates that $f(T)$ gravity in a plasma environment can produce distinguishable differences in magnification and time delay compared to General Relativity. The observed discrepancies between theoretical expectations and observational results can serve as valuable clues for modified gravity theories and provide constraints on $f(T)$ gravity. To advance this field of research, future efforts should focus on experimental verification, improved models, deeper theoretical analysis, and utilizing discrepancies as constraints.
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by jsendak | Jan 12, 2024 | GR & QC Articles
Cosmological dynamics are investigated in detail through systematic
procedures by using the autonomous system analyses of gravitational field
equations in higher-order symmetric teleparallel equivalent of general
relativity. The explicit analyses of the late-time cosmic evolutions are
demonstrated for fundamental three types of models under the presence of
non-relativistic matter (i.e., dark matter and baryons) as well as radiation.
The stability of cosmological solutions is also explored by examining
non-hyperbolic critical points based on the center manifold theory. It is shown
that the acceleration of the universe can be achieved with the higher curvature
gravity. Three different models were considered for the study and dynamical
systems analysis technique is incorporated. The main finding of the present
analyses is that cosmological solutions in higher-order symmetric teleparallel
equivalent of general relativity can effectively fit observable datasets. This
is depicted by phase space portraits and qualitative evolution of the
cosmological models.
Future Roadmap for Cosmological Dynamics in Higher-order Symmetric Teleparallel Equivalent of General Relativity
In this article, the author examines the cosmological dynamics in detail through systematic procedures using the autonomous system analyses of gravitational field equations in higher-order symmetric teleparallel equivalent of general relativity. The explicit analyses focus on the late-time cosmic evolutions and the stability of cosmological solutions under the presence of non-relativistic matter and radiation.
The main conclusion of the study is that acceleration of the universe can be achieved with the higher curvature gravity, and cosmological solutions in higher-order symmetric teleparallel equivalent of general relativity can effectively fit observable datasets. The findings are supported by phase space portraits and qualitative evolution of the cosmological models.
Future Challenges
- Model refinement: Further refinement of the three different models studied will be necessary to improve the accuracy of fitting observable datasets. The incorporation of additional variables or adjusting existing parameters may be required.
- Data validation: The observational data used to validate the models should be carefully analyzed and verified for consistency and accuracy. Robust statistical methods should be employed to ensure reliable comparisons.
- Testing alternative theories: While higher-order symmetric teleparallel equivalent of general relativity shows promise, it is important to explore and test alternative theories to gain a comprehensive understanding of cosmological dynamics. This will involve comparing the predictions and outcomes of different theoretical frameworks.
- Computational challenges: The complexity of the analyses and simulations involved in investigating cosmological dynamics pose computational challenges. Advancements in computational power and algorithms will be crucial to overcome these hurdles.
Potential Opportunities
- Cosmological model validation: The ability to effectively fit observable datasets using higher-order symmetric teleparallel equivalent of general relativity opens up opportunities for the validation of cosmological models and theories.
- Understanding dark matter and acceleration: The achievement of universe acceleration through higher curvature gravity provides insights into the nature and behavior of dark matter. This can contribute to our understanding of the fundamental properties of the universe.
- Innovations in gravitational field equations: The systematic procedures and analyses used in this study can pave the way for innovations in gravitational field equations. This may lead to the development of new theoretical frameworks and models for cosmological dynamics.
- Interdisciplinary collaborations: Cosmological dynamics involve concepts from various disciplines such as physics, mathematics, and astronomy. The findings of this study can foster interdisciplinary collaborations and stimulate further research in these fields.
Overall, the findings of this study contribute to the understanding of cosmological dynamics in higher-order symmetric teleparallel equivalent of general relativity and present avenues for future research. Further refinement of the models, validation of data, testing of alternative theories, and advancements in computational techniques are important challenges to address. However, the opportunities for model validation, insights into dark matter and acceleration, innovations in gravitational field equations, and interdisciplinary collaborations hold great potential for advancing our understanding of the universe.
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by jsendak | Jan 12, 2024 | GR & QC Articles
Recent observational data from the Event Horizon Telescope (EHT)
collaboration provide convincing realistic evidence for the existence of black
hole rotation. From a phenomenological perspective, a recently proposed stable
rotating regular (SRR) black hole circumvents the theoretical flaws of the Kerr
solution. For the purpose of obtaining observational signatures of this black
hole, we study its gravitational lensing effect. In the strong field limit, we
calculate the deflection angle of light, the radius of the photon sphere, and
other observables. The observables include the relativistic image position,
separation, magnification, and time delays between different images. Then, by
modeling M87* and Sgr A* as the SRR black hole, we compute their observables
and evaluate the deviation of the observables from the Kerr case. In the weak
field limit, we calculate the light deflection angle of M87* and Sgr A* via the
Gauss-Bonnet theorem (GBT). With the growth of deviation parameter $e$, the
gravitational lensing effect in the weak field limit intensifies monotonically,
and the gravitational lensing effect in the strong field limit changes
dramatically only at high spins. Our research may contribute to distinguish
between SRR black holes from Kerr black holes under higher-precision
astronomical observations.
Future Roadmap:
Introduction
In recent years, the Event Horizon Telescope (EHT) collaboration has provided compelling evidence for the existence of black hole rotation. However, a new stable rotating regular (SRR) black hole has been proposed to overcome some theoretical flaws of the previous Kerr solution. This article aims to explore the gravitational lensing effects of the SRR black hole and differentiate it from the Kerr case.
Observables and Calculations
The study focuses on several observables that can be used to distinguish between the SRR black hole and the Kerr black hole. These observables include:
- Relativistic image position
- Separation between images
- Magnification of images
- Time delays between images
To calculate these observables, the deflection angle of light, the radius of the photon sphere, and other factors need to be determined in both the weak field limit and the strong field limit. In the weak field limit, the Gauss-Bonnet theorem (GBT) is used for light deflection angle calculations for M87* and Sgr A*.
Deviation Parameter and Gravitational Lensing
The article explains that the intensity of the gravitational lensing effect in the weak field limit increases with the growth of the deviation parameter $e$. On the other hand, in the strong field limit, significant changes in the gravitational lensing effect are only observed at high spins. This information can aid in distinguishing SRR black holes from Kerr black holes under higher-precision astronomical observations.
Conclusion
This research on the gravitational lensing effects of stable rotating regular black holes provides a potential method for differentiating them from previous Kerr black holes. By calculating various observables, including relativistic image positions, separations, magnifications, and time delays, it is possible to evaluate the deviation of the observables from the Kerr case. However, further astronomical observations and higher precision measurements are required to fully understand and confirm these distinctions.
Potential Challenges and Opportunities:
The road ahead presents some challenges and opportunities:
- Challenge: Obtaining higher-precision observations: Accurate measurements and observations will be crucial to identify the differences between SRR black holes and Kerr black holes.
- Challenge: Theoretical validation: The proposed SRR black hole must undergo further theoretical scrutiny to confirm its stability and resolve any potential flaws.
- Opportunity: Advancements in observational techniques: Technological advancements in observational tools and telescopes may enable researchers to obtain the necessary data to distinguish between these two types of black holes.
- Opportunity: New insights into black hole physics: Understanding the nature and characteristics of SRR black holes could provide new insights into the behavior of rotating black holes and the fundamental principles of general relativity.
With continued progress in observational capabilities and theoretical investigations, future studies can build upon this research to enhance our understanding of black hole rotation and potentially revolutionize our knowledge of astrophysics.
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