by jsendak | May 30, 2024 | GR & QC Articles
arXiv:2405.18496v1 Announce Type: new
Abstract: Gravitational wave observations of black hole-neutron star binaries, particularly those where the black hole has a lower mass compared to other observed systems, have the potential to place strong constraints on modifications to general relativity that arise at small curvature length scales. Here we study the dynamics of black hole-neutron star mergers in shift-symmetric Einstein-scalar-Gauss-Bonnet gravity, a representative example of such a theory, by numerically evolving the full equations of motion. We consider quasi-circular binaries with different mass-ratios that are consistent with recent gravitational wave observations, including cases with and without tidal disruption of the star, and quantify the impact of varying the coupling controlling deviations from general relativity on the gravitational wave signal and scalar radiation. We find that the main effect on the late inspiral is the accelerated frequency evolution compared to general relativity, and that–even considering Gauss-Bonnet coupling values approaching those where the theory breaks down–the impact on the merger gravitational wave signal is mild, predominately manifesting as a small change in the amplitude of the ringdown. We compare our results to current post-Newtonian calculations and find consistency throughout the inspiral.
Future Roadmap: Challenges and Opportunities in Gravitational Wave Observations of Black Hole-Neutron Star Binaries
Gravitational wave observations offer a unique opportunity to study the dynamics of black hole-neutron star binaries and potentially place constraints on modifications to general relativity. In this study, we specifically focus on the dynamics of these binaries in shift-symmetric Einstein-scalar-Gauss-Bonnet gravity, a representative example of a theory that deviates from general relativity at small curvature length scales.
Current Status
We start by considering quasi-circular binaries with different mass-ratios, consistent with recent gravitational wave observations. Our analysis includes both cases with and without tidal disruption of the neutron star. By numerically evolving the full equations of motion, we investigate the impact of varying the coupling controlling deviations from general relativity on the gravitational wave signal and scalar radiation.
Our findings reveal that the main effect on the late inspiral is an accelerated frequency evolution compared to general relativity. However, even when approaching Gauss-Bonnet coupling values that exceed the theory’s validity, the impact on the merger gravitational wave signal remains mild. It primarily manifests as a small change in the amplitude of the ringdown phase. Furthermore, when comparing our results to current post-Newtonian calculations, we find consistency throughout the inspiral process.
Roadmap for the Future
Despite the promising results obtained from our study, there are still several challenges and opportunities on the horizon in the field of gravitational wave observations of black hole-neutron star binaries. Here is a roadmap for future research:
- Expanding the Parameter Space: Our study focused on quasi-circular binaries with specific mass-ratios. Future research should explore a wider range of mass ratios to investigate how these systems behave under different conditions.
- Investigating Tidal Effects: We considered both cases with and without tidal disruption of the neutron star. Further investigation into the impact of tidal effects on the gravitational wave signal is necessary to better understand the behavior of black hole-neutron star binaries.
- Exploring Other Modified Theories: Our study focused on shift-symmetric Einstein-scalar-Gauss-Bonnet gravity. Future research should explore other modified theories of gravity to ascertain the impact of different theoretical frameworks on the dynamics of black hole-neutron star binaries.
- Improving Numerical Simulations: Although we have conducted numerical simulations to study these binaries, there is always room for improvement. Enhancing the accuracy and efficiency of these simulations will provide more reliable results and a deeper understanding of the gravitational wave signals.
- Comparison with Observations: As gravitational wave detectors become more sensitive, it is crucial to compare our theoretical predictions with actual observational data. This will allow us to validate our simulations and potentially discover new phenomena or deviations from general relativity.
In conclusion, gravitational wave observations of black hole-neutron star binaries offer an exciting opportunity to probe modifications to general relativity. While our study provides valuable insights into the dynamics of these systems in Einstein-scalar-Gauss-Bonnet gravity, there are still challenges and numerous opportunities for future research. By expanding the parameter space, investigating tidal effects, exploring other modified theories, improving numerical simulations, and comparing with observations, we can continue to advance our understanding of the universe and potentially uncover new physics.
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by jsendak | May 29, 2024 | GR & QC Articles
arXiv:2405.17592v1 Announce Type: new
Abstract: Relative motion effects have long been known to “contaminate” the observations. In fact, when looking back to the history of astronomy, one finds a number of examples where relative motions have led to a gross misinterpretation of reality. Using relativistic cosmological perturbation theory it was shown that observers living inside bulk-flow domains that expand slightly slower than their surroundings, can have the illusion of cosmic acceleration, while the host universe is actually decelerating. This claim was originally based on studies of a perturbed tilted Einstein-de Sitter model, primarily for mathematical simplicity. Nevertheless, nothing really changed when the background universe was replaced by a Friedmann cosmology with nonzero pressure and spatial curvature. This raised the possibility that the peculiar-motion effect on the deceleration parameter, as measured locally by the bulk-flow observers, may be generic and independent of the specifics of the host universe. Here, we investigate this possibility, by extending the earlier studies to perturbed Bianchi cosmologies. We find that the picture remains unchanged, unless the Bianchi background has unrealistically high anisotropy. The peculiar-motion effect on the deceleration parameter, as measured by the relatively moving observers, is essentially the same with that reported earlier in a perturbed Einstein-de Sitter universe and in the rest of its Friedmann counterparts.
Examining the Conclusions
The article discusses the influence of relative motion on observations in astronomy and how it can lead to a misinterpretation of reality. The researchers used relativistic cosmological perturbation theory to demonstrate that observers inside bulk-flow domains that expand slightly slower than their surroundings can perceive cosmic acceleration, even when the host universe is actually decelerating. This claim was initially based on studying a perturbed tilted Einstein-de Sitter model, but it was found that similar effects occur in a Friedmann cosmology with non-zero pressure and spatial curvature. The authors now aim to determine whether this peculiar-motion effect on the deceleration parameter is generic across different cosmological scenarios by studying perturbed Bianchi cosmologies. The early findings suggest that the peculiar-motion effect remains consistent unless the Bianchi background exhibits extremely high anisotropy.
Future Roadmap: Challenges and Opportunities
The research introduces several challenges and opportunities for further exploration in the field of cosmology.
1. Extending the Study to Other Cosmological Models
The authors suggest that the peculiar-motion effect on the deceleration parameter may be independent of the specifics of the host universe. While the study has been extended to perturbed Bianchi cosmologies, further research is needed to investigate the effect in various other cosmological models. This will help determine the universality of the peculiar-motion effect and its implications for observational cosmology.
2. Realistic Anisotropy in Bianchi Backgrounds
The current findings indicate that the peculiar-motion effect on the deceleration parameter remains consistent unless the Bianchi background exhibits unrealistically high anisotropy. Future studies should focus on analyzing perturbed Bianchi cosmologies with levels of anisotropy closer to those expected in realistic scenarios. This will provide valuable insights into the possible impact of anisotropy on the peculiar-motion effect and its implications for understanding cosmic acceleration.
3. Comparison with Observational Data
While the current study demonstrates the theoretical aspects of the peculiar-motion effect, a crucial next step is to compare the findings with observational data. This will involve analyzing data from surveys and observations to evaluate whether the peculiar-motion effect can explain any disparities between the observed and predicted cosmic acceleration. Such comparisons will provide empirical evidence to validate or refine the theoretical conclusions.
4. Implications for Dark Energy
The peculiar-motion effect raises questions about the role of dark energy in cosmic acceleration. Understanding the extent to which this effect contributes to the perceived acceleration can have significant implications for our understanding of the nature of dark energy. Further research should explore the connection between the peculiar-motion effect and dark energy, potentially shedding light on the underlying mechanisms driving cosmic acceleration.
5. Refining Relativistic Cosmological Perturbation Theory
The current study utilizes relativistic cosmological perturbation theory to investigate the peculiar-motion effect. As future research builds upon these findings, there is an opportunity to refine and expand this theory. This will enhance our understanding of the underlying physics and mathematical frameworks needed to accurately model and analyze the observations affected by relative motions.
In conclusion, the study’s findings indicate that the peculiar-motion effect on the deceleration parameter is likely to be a consistent phenomenon across different cosmological scenarios, with some caveats related to anisotropy. The future roadmap outlined above will address these caveats and explore the implications and applications of the peculiar-motion effect in observational cosmology.
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by jsendak | May 28, 2024 | GR & QC Articles
arXiv:2405.15798v1 Announce Type: new
Abstract: Holographic dark energy models have proven to be a very interesting way to study various aspects of late-time acceleration of the universe. In this work we extensively study HDE models with the Granda-Oliveros cutoff with an ansatz based approach. We consider the Tsallis, Barrow and PLEC HDE models in this regard and consdier simple power law, emergent universe, intermediate and logamediate forms of for the universe. Studying various cosmologically interesting parameters alongside the thermodynamical aspects in these models, we show that the Logamediate models are the best fit out of the other possibilites, followed by the emergent universe model, intermediate model and the simple power law models at the very last in terms of feasibility.
The Future of Holographic Dark Energy Models
In recent years, holographic dark energy (HDE) models have emerged as a fascinating framework for understanding the late-time acceleration of the universe. These models offer unique insights into various cosmological aspects and provide new possibilities for studying the universe. In this work, we extensively examine HDE models with the Granda-Oliveros cutoff using an ansatz-based approach.
Models Considered
We consider three different HDE models: Tsallis, Barrow, and PLEC. These models provide distinct perspectives and insights into the nature of dark energy. By exploring these models, we can gain a deeper understanding of the universe’s accelerated expansion.
Forms of the Universe
To study the feasibility of HDE models, we examine four different forms of the universe: simple power law, emergent universe, intermediate, and logamediate. Each form offers unique characteristics and implications for the late-time acceleration.
Key Findings
After extensive analysis and studying several cosmologically interesting parameters, we have determined the feasibility of each HDE model and form of the universe.
- The Logamediate model shows the best fit among all possibilities, indicating its potential as a promising framework for understanding the late-time acceleration of the universe.
- The Emergent Universe model demonstrates strong feasibility and offers valuable insights into the universe’s expansion.
- The Intermediate model presents an interesting alternative and warrants further investigation to fully comprehend its implications.
- The Simple Power Law models are the least feasible among the examined possibilities and require additional refinements or alternative explanations.
Future Challenges and Opportunities
While this study sheds light on the potential of HDE models and provides valuable insights, there are several challenges and opportunities that should be taken into consideration for future research.
Challenges
- Data Constraints: Obtaining accurate and precise observational data is crucial for validating and refining HDE models. Overcoming limitations in observational techniques and expanding data collection efforts will be a challenge.
- Theoretical Refinements: Further theoretical developments are necessary to improve our understanding of HDE models and explore their implications in greater detail. Refining the underlying assumptions and incorporating more complex dynamics will require interdisciplinary efforts.
- Consistency with Other Frameworks: Comparing HDE models with alternative frameworks, such as quintessence or modified gravity theories, will be essential for understanding their compatibility and distinguishing unique features.
Opportunities
- Expanded Observational Data: Advancements in observational techniques and upcoming missions, such as the James Webb Space Telescope, will provide a wealth of data to refine and validate HDE models.
- Interdisciplinary Collaborations: Engaging researchers from various fields like cosmology, theoretical physics, and mathematics will foster a holistic understanding of HDE models and facilitate innovative approaches.
- Mathematical Innovations: Exploring alternative mathematical frameworks and computational techniques can lead to novel insights and potentially unearth new aspects of HDE models.
In conclusion, HDE models with the Granda-Oliveros cutoff offer an intriguing avenue for studying the late-time acceleration of the universe. By examining different HDE models and forms of the universe, we have identified the Logamediate model as the most promising, followed by the Emergent Universe model, the Intermediate model, and the Simple Power Law models. Overcoming challenges in data constraints, theoretical refinements, and consistency with other frameworks will be crucial for the future exploration of HDE models. However, the opportunities presented by expanded observational data, interdisciplinary collaborations, and mathematical innovations provide exciting prospects for unravelling the mysteries of dark energy and the accelerated expansion of the universe.
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by jsendak | May 27, 2024 | GR & QC Articles
arXiv:2405.15035v1 Announce Type: new
Abstract: Mathematicians have been proposing for sometimes that Monge-Amp`ere equation, a nonlinear generalization of the Poisson equation, where trace of the Hessian is replaced by its determinant, provides an alternative non-relativistic description of gravity. Monge-Amp`ere equation is affine invariant, has rich geometric properties, connects to optimal transport theory, and remains bounded at short distances. Monge-Amp`ere gravity, that uses a slightly different form of the Monge-Amp`ere equation, naturally emerges through the application of large-deviation principle to a Brownian system of indistinguishable and independent particles. In this work we provide a physical formulation of this mathematical model, study its theoretical viability and confront it with observations. We show that Monge-Amp`ere gravity cannot replace the Newtonian gravity as it does not withstand the solar-system test. We then show that Monge-Amp`ere gravity can describe a scalar field, often evoked in modified theories of gravity such as Galileons. We show that Monge-Amp`ere gravity, as a nonlinear model of a new scalar field, is screened at short distances, and behaves differently from Newtonian gravity above galactic scales but approaches it asymptotically. Finally, we write a relativistic Lagrangian for Monge-Amp`ere gravity in flat space time, which is the field equation of a sum of the Lagrangians of all Galileons. We also show how the Monge-Amp`ere equation can be obtained from the fully covariant Lagrangian of quartic Galileon in the static limit. The connection between optimal transport theory and modified theories of gravity with second-order field equations, unravelled here, remains a promising domain to further explore.
Future Roadmap for Readers: Challenges and Opportunities
Introduction
In this article, we examine the conclusions of a study on Monge-Amp`ere gravity, a non-relativistic description of gravity based on the Monge-Amp`ere equation. We outline a future roadmap for readers, highlighting potential challenges and opportunities on the horizon.
Overview of Monge-Amp`ere Equation
The Monge-Amp`ere equation is a nonlinear generalization of the Poisson equation, where the trace of the Hessian is replaced by its determinant. This equation is affine invariant, has rich geometric properties, and connects to optimal transport theory. It also remains bounded at short distances.
Emergence of Monge-Amp`ere Gravity
The study explores how Monge-Amp`ere gravity naturally emerges through the application of a large-deviation principle to a Brownian system of indistinguishable and independent particles. A physical formulation of this mathematical model is provided, and its theoretical viability is examined and compared to observations.
Limitations of Monge-Amp`ere Gravity
The study finds that Monge-Amp`ere gravity cannot replace Newtonian gravity, as it does not withstand the solar-system test. However, it is shown that Monge-Amp`ere gravity can still describe a scalar field, which is often considered in modified theories of gravity such as Galileons.
Behavior of Monge-Amp`ere Gravity
It is demonstrated that Monge-Amp`ere gravity, as a nonlinear model of a new scalar field, is screened at short distances and behaves differently from Newtonian gravity above galactic scales. However, it still approaches Newtonian gravity asymptotically.
Relativistic Formulation and Connection to Galileons
A relativistic Lagrangian for Monge-Amp`ere gravity in flat spacetime is derived, which represents the field equation of a sum of the Lagrangians of all Galileons. Furthermore, it is shown how the Monge-Amp`ere equation can be obtained from the fully covariant Lagrangian of quartic Galileon in the static limit.
Promising Domain for Further Exploration
The connection between optimal transport theory and modified theories of gravity with second-order field equations, as unraveled in this study, remains a promising domain for further exploration. There are potential challenges and opportunities to investigate the implications and applications of Monge-Amp`ere gravity in various contexts.
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by jsendak | May 24, 2024 | GR & QC Articles
arXiv:2405.12987v1 Announce Type: new
Abstract: It has been claimed in cite{1}, that the idea proposed in cite{2} has certain mistakes based on arguments of energy conditions and others. Additionally, some of the key arguments of the paper are criticized. Here we demonstrate that the results obtained in cite{2} are correct and that there is no violation of any energy condition. The statements claimed in cite{1} are based on three things: 1). Misinterpretation of the metric solution. 2). Language issues related to the physical quantities obtained in cite{1}, where the authors make wrong interpretations about certain results over the geometry proposed in cite{2}. 3). Non-rigorous evaluations of the vacuum condition defined via the result over the Ricci tensor $R_{munu}=0$
Article Title: Examining the Conclusions of cite{1}
In the paper cite{1}, it was claimed that the idea presented in cite{2} contains certain mistakes regarding energy conditions and other arguments. However, we aim to demonstrate in this article that the results obtained in cite{2} are indeed correct, and there is no violation of any energy condition. We will address the criticisms raised in cite{1} and provide a thorough analysis of the key arguments.
1. Misinterpretation of the Metric Solution
The first claim in cite{1} revolves around the misinterpretation of the metric solution proposed in cite{2}. We will carefully examine the metric solution and provide a comprehensive explanation of its implications. By clarifying any misunderstandings, we can showcase the accuracy of the results obtained in cite{2}.
2. Language Issues and Incorrect Interpretations
The second point raised in cite{1} pertains to language issues and wrong interpretations of certain physical quantities derived in cite{1} in relation to the geometry proposed in cite{2}. We will analyze the language used in both papers and provide a clear understanding of the correct interpretations of the relevant results. By addressing these language issues, we can ensure that the conclusions drawn in cite{2} are accurately represented.
3. Non-rigorous Evaluations of the Vacuum Condition
The third criticism put forth in cite{1} involves non-rigorous evaluations of the vacuum condition defined by the result over the Ricci tensor, $R_{munu}=0$. We will re-evaluate the vacuum condition rigorously and provide a comprehensive analysis to ascertain its validity. By conducting a rigorous evaluation, we can confirm the accuracy of the vacuum condition defined in cite{2}.
Future Roadmap for Readers
As readers navigate through this article, they can expect to gain a deeper understanding of the conclusions drawn in cite{1} and the counterarguments presented here. The following roadmap outlines the key points to consider:
- Introduction to the claims made in cite{1} and the purpose of this article.
- Thorough analysis of the metric solution proposed in cite{2} to address the misinterpretation claim.
- Examination of language issues and incorrect interpretations of physical quantities in cite{1} relating to the geometry in cite{2}.
- Rigorous evaluation of the vacuum condition defined by $R_{munu}=0$ as criticized in cite{1}.
- Comparison and synthesis of the evidence presented to conclude the validity of the results in cite{2}.
- Summary of the key findings and reaffirmation of the accuracy of the results obtained in cite{2}.
Challenges and Opportunities on the Horizon
While examining the conclusions of cite{1} and presenting a future roadmap, we anticipate potential challenges and opportunities that might arise:
- Challenges: The main challenge is the intricate nature of the topic, which requires a careful analysis of the arguments and counterarguments. The language issues could pose difficulties in accurately interpreting the findings. Additionally, addressing the non-rigorous evaluations may involve complex mathematical calculations.
- Opportunities: By thoroughly examining the claims made in cite{1} and providing compelling counterarguments, this article contributes to the advancement of knowledge in the field. It offers an opportunity to clarify misconceptions and promote a more comprehensive understanding of the results presented in cite{2}. Moreover, this article can facilitate productive discussions among researchers, leading to further insights and breakthroughs in the subject matter.
Note: This article is a response to the claims made in cite{1} and should be read in conjunction with cite{2} to fully comprehend the arguments and counterarguments presented.
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by jsendak | May 22, 2024 | GR & QC Articles
arXiv:2405.12249v1 Announce Type: new
Abstract: We give an alternate proof of one of the results given in [16] showing that initial data sets with boundary for the Einstein equations $(M, g, k)$ satisfying the dominant energy condition can be conformally deformed to the strict dominant energy condition, while preserving the character of the boundary (minimal, future trapped, or past trapped) while changing the area of the boundary and ADM energy of the initial data set by an arbitrarily small amount. The proof relies on solving an equation that looks like the equation for spacetime harmonic functions studied in [7], but with a Neumann boundary condition and non-zero right hand side, which we refer to as a spacetime Poisson equation. One advantage of this method of proof is that the conformal deformation is explicitly constructed as a solution to a PDE, as opposed to only knowing the solution exists via an application of the implicit function theorem as in [16]. We restrict ourselves to the physically relevant case of a $3$-manifold $M$, though the proof can be generalized to higher dimensions.
Future Roadmap: Challenges and Opportunities
Introduction
In this article, we examine an alternate proof of a result presented in a previous work. The result shows that initial data sets with boundaries for the Einstein equations can be conformally deformed while satisfying the dominant energy condition. The proof relies on solving a spacetime Poisson equation with a Neumann boundary condition, and the conformal deformation is explicitly constructed as a solution to a PDE. In this roadmap, we outline potential challenges and opportunities on the horizon.
Potential Challenges
- Mathematical Complexity: The proof relies on solving a spacetime Poisson equation with specific boundary conditions. The mathematics involved in solving such equations can be complex and require expertise in partial differential equations.
- Generalization to Higher Dimensions: The proof presented in this article focuses on the physically relevant case of a 3-manifold. Generalizing the proof to higher dimensions may introduce additional challenges, as the equations and techniques involved can become more intricate.
Potential Opportunities
- Improved Understanding of Einstein Equations: The alternate proof presented in this article offers a new perspective on conformal deformations within the context of the Einstein equations. This can potentially enhance our understanding of the mathematical properties of these equations and their solutions.
- Enhanced Applications: By explicitly constructing the conformal deformation as a solution to a PDE, the proof offers a practical approach for applying conformal deformations in various domains ranging from physics to geometry. This can lead to potential advancements in fields such as general relativity, astrophysics, and differential geometry.
- Further Developments in Spacetime Harmonic Functions: The proof involves solving an equation related to spacetime harmonic functions. This opens up possibilities for further research and developments in the theory and applications of these functions.
Conclusion
In conclusion, the alternate proof presented in this article offers a promising approach for conformal deformations of initial data sets with boundaries in the context of the Einstein equations. While the proof brings forth challenges in terms of mathematical complexity and generalization to higher dimensions, it also presents opportunities for improved understanding of the Einstein equations, enhanced applications, and further developments in spacetime harmonic functions. This roadmap provides a glimpse into the potential challenges and opportunities that lie ahead for readers interested in this area of research.
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