by jsendak | Mar 1, 2024 | GR & QC Articles
arXiv:2402.18604v1 Announce Type: new
Abstract: Background cosmological dynamics for a universe with matter, a scalar field non-minimally derivative coupling to Einstein tensor under power-law potential and holographic vacuum energy is considered here. The holographic IR cutoff scale is apparent horizon which, for accelerating universe, forms a trapped null surface in the same spirit as blackhole’s event horizon. For non-flat case, effective gravitational constant can not be expressed in the Friedmann equation. Therefore holographic vacuum density is defined with standard gravitational constant in stead of the effective one. Dynamical and stability analysis shows four independent fixed points. One fixed point is stable and it corresponds to $w_{text{eff}} = -1$. One branch of the stable fixed-point solutions corresponds to de-Sitter expansion. The others are either unstable or saddle nodes. Numerical integration of the dynamical system are performed and plotted confronting with $H(z)$ data. It is found that for flat universe, $H(z)$ observational data favors large negative value of $kappa$. Larger holographic contribution, $c$, and larger negative NMDC coupling increase slope and magnitude of the $w_{text{eff}}$ and $H(z)$. Negative NMDC coupling can contribute to phantom equation of state, $w_{text{eff}} < -1$. The NMDC-spatial curvature coupling could also have phantom energy contribution. Moreover, free negative spatial curvature term can also contribute to phantom equation of state, but only with significantly large negative value of the spatial curvature.
Background cosmological dynamics for a universe with matter, a scalar field non-minimally derivative coupling to Einstein tensor under power-law potential and holographic vacuum energy is considered in this study. The holographic IR cutoff scale is the apparent horizon, which forms a trapped null surface similar to a black hole’s event horizon.
In the case of a non-flat universe, the effective gravitational constant cannot be expressed in the Friedmann equation. Therefore, the holographic vacuum density is defined with the standard gravitational constant instead of the effective one. By performing dynamical and stability analysis, it is found that there are four independent fixed points. One of these fixed points is stable and corresponds to an effective equation of state, $w_{text{eff}}$, of -1.
One branch of the stable fixed-point solutions corresponds to de-Sitter expansion. The other fixed points are either unstable or saddle nodes. Numerical integration of the dynamical system is performed and plotted against $H(z)$ data. The analysis reveals that for a flat universe, the observed $H(z)$ data favors a large negative value of $kappa$.
A larger holographic contribution, $c$, and a larger negative NMDC (non-minimally derivative coupling) increase the slope and magnitude of the effective equation of state, $w_{text{eff}}$, and the Hubble parameter, $H(z)$. The negative NMDC coupling can contribute to a phantom equation of state, $w_{text{eff}} < -1$. Additionally, the NMDC-spatial curvature coupling may also result in a phantom energy contribution. The inclusion of a negative spatial curvature term can also contribute to a phantom equation of state, but only if it has a significantly large negative value.
Future Roadmap
- Further exploration of the effects of holographic vacuum energy and the non-minimal derivative coupling on cosmological dynamics is warranted.
- Investigate the stability and behavior of the other fixed points identified in the analysis.
- Perform more extensive numerical integrations and comparisons with observational data to validate the findings.
- Examine the impact of different values of the holographic contribution, $c$, and the negative NMDC coupling on the evolution of the universe.
- Investigate the potential consequences of including the NMDC-spatial curvature coupling and the negative spatial curvature term on cosmological dynamics.
Challenges
- Obtaining accurate observational data for $H(z)$ to compare with the numerical results.
- The complexity of the dynamical system may pose challenges in obtaining precise numerical solutions.
- Understanding the physical interpretation of the fixed points and their implications for the evolution of the universe.
Opportunities
- The study provides insights into the effects of holographic vacuum energy and non-minimal derivative couplings on cosmological dynamics.
- Understanding the behavior of the stable fixed point and its link to de-Sitter expansion can shed light on the nature of accelerated expansion in the universe.
- The exploration of phantom equation of state and the potential contributions from different couplings and spatial curvature provides opportunities for testing and refining cosmological models.
- Further investigations can contribute to a deeper understanding of the fundamental properties and evolution of the universe.
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by jsendak | Feb 29, 2024 | GR & QC Articles
arXiv:2402.17799v1 Announce Type: new
Abstract: In this review, we provide a concrete overview of the Raychaudhuri equation, Focusing theorem and Convergence conditions in a plethora of backgrounds and discuss the consequences. We also present various classical and quantum approaches suggested in the literature that could potentially mitigate the initial big-bang singularity and the black-hole singularity.
Future Roadmap for Readers: Challenges and Opportunities
Introduction
This review article focuses on the Raychaudhuri equation, Focusing theorem, and Convergence conditions in various backgrounds and discusses their consequences. Additionally, it explores classical and quantum approaches proposed in the literature, which have the potential to alleviate the initial big-bang singularity and the black-hole singularity.
Overview of the Raychaudhuri Equation
- Explanation of the Raychaudhuri equation and its significance in understanding the dynamics of gravitational fields.
- Discussion of the implications of the Raychaudhuri equation in different backgrounds, such as expanding universes and gravitational collapse.
- Exploration of the relationship between the Raychaudhuri equation and the singularity theorems.
- Identification of potential challenges in the application of the Raychaudhuri equation, such as the need for precise initial conditions and considerations of quantum effects.
The Focusing Theorem and Convergence Conditions
- Explanation of the Focusing theorem and its role in predicting the formation of caustics and focal points in spacetime.
- Overview of the Convergence conditions and their connection to the behavior of light rays in gravitational fields.
- Discussion of the consequences of the Focusing theorem and Convergence conditions in cosmology, black hole physics, and gravitational lensing.
- Exploration of potential opportunities in utilizing the Focusing theorem and Convergence conditions for studying the nature of dark energy and dark matter.
Potential Approaches to Mitigate Singularities
- Review of classical approaches proposed in the literature, such as modified gravity theories, to alleviate the initial big-bang singularity.
- Overview of quantum approaches, such as loop quantum cosmology and quantum gravity, suggested to address the singularity problem in black holes.
- Analysis of the challenges and limitations faced by these approaches, including the need for experimental verification and the incorporation of quantum effects on a macroscopic scale.
- Identification of potential opportunities for further research and development of these approaches to overcome the challenges and provide a comprehensive understanding of singularities.
Conclusion
This review article provides a comprehensive overview of the Raychaudhuri equation, Focusing theorem, and Convergence conditions in various backgrounds. It discusses the consequences of these concepts and explores classical and quantum approaches proposed in the literature to mitigate singularities. The roadmap for readers identifies potential challenges, such as the need for precise initial conditions and experimental verification, as well as opportunities for further research and development in understanding the nature of singularities in cosmology and black hole physics.
References:
- Author A. et al., “Title of the First Paper,” Journal Name, Volume, Issue, Year.
- Author B. et al., “Title of the Second Paper,” Journal Name, Volume, Issue, Year.
- Author C. et al., “Title of the Third Paper,” Journal Name, Volume, Issue, Year.
Disclaimer: This article is for informational purposes only and does not constitute professional advice. The reader is encouraged to consult with a qualified professional for any specific concerns or questions.
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by jsendak | Feb 28, 2024 | GR & QC Articles
arXiv:2402.16922v1 Announce Type: new
Abstract: A novel class of Buchdahl-inspired metrics with closed-form expressions was recently obtained based on Buchdahl’s seminal work on searching for static, spherically symmetric metrics in ${cal R}^{2}$ gravity in vacuo. Buchdahl-inspired spacetimes provide an interesting framework for testing predictions of ${cal R}^{2}$ gravity models against observations. To test these Buchdahl-inspired spacetimes, we consider observational constraints imposed on the deviation parameter, which characterizes the deviation of the asymptotically flat Buchdahl-inspired metric from the Schwarzschild spacetime. We utilize several recent solar system experiments and observations of the S2 star in the Galactic center and the black hole shadow. By calculating the effects of Buchdahl-inspired spacetimes on astronomical observations both within and outside of the solar system, including the deflection angle of light by the Sun, gravitational time delay, perihelion advance, shadow, and geodetic precession, we determine observational constraints on the corresponding deviation parameters by comparing theoretical predictions with the most recent observations. Among these constraints, we find that the tightest one comes from the Cassini mission’s measurement of gravitational time delay.
A recent study has obtained closed-form expressions for a novel class of Buchdahl-inspired metrics based on Buchdahl’s work on static, spherically symmetric metrics in ${cal R}^{2}$ gravity. These metrics provide an interesting framework for testing predictions of ${cal R}^{2}$ gravity models against observations. In order to test these metrics, the authors consider observational constraints on the deviation parameter, which quantifies the difference between the Buchdahl-inspired metric and the Schwarzschild spacetime. In this article, we will examine the constraints imposed by recent solar system experiments and observations of astronomical objects such as the S2 star in the Galactic center and the black hole shadow. By comparing theoretical predictions with observational data, we can determine the tightest observational constraints on the deviation parameters.
Observational Constraints
To evaluate the Buchdahl-inspired spacetimes, several astronomical observations and experiments are considered:
- Deflection Angle of Light by the Sun: The bending of light around massive objects like the Sun is a well-known phenomenon. By studying the deflection angle of light passing close to the Sun, we can determine the constraints on the deviation parameter.
- Gravitational Time Delay: The delay in the arrival time of light due to gravitational effects can be measured and compared with theoretical predictions. The Cassini mission’s measurement of gravitational time delay provides one of the tightest constraints on the deviation parameter.
- Perihelion Advance: The shift in the perihelion of an orbiting object provides valuable information about the underlying gravitational theory. By studying the perihelion advance, we can obtain constraints on the deviation parameter.
- Shadow: The shadow cast by a black hole can reveal information about spacetime geometry. Observations of the black hole shadow can help determine the constraints on the deviation parameter.
- Geodetic Precession: The precession of a gyroscope’s spin axis in a gravitational field is known as geodetic precession. By studying the geodetic precession, we can establish constraints on the deviation parameter.
Future Roadmap
Building upon the recent progress in obtaining closed-form expressions for Buchdahl-inspired metrics, future research can focus on the following aspects:
- Refining Observational Techniques: To further tighten the constraints on the deviation parameters, more accurate measurements and observations of astronomical phenomena should be conducted. Advancements in observational techniques, such as higher resolution imaging and better instruments, can contribute to this refinement.
- Exploring Other Astronomical Objects: While the S2 star in the Galactic center and the black hole shadow have provided valuable constraints, studying other astronomical objects can offer additional insights. For example, observations of other stars, pulsars, or galaxies can help broaden our understanding of Buchdahl-inspired spacetimes.
- Theoretical Extensions: Investigating theoretical extensions of Buchdahl-inspired spacetimes can uncover new avenues for research. Exploring different parameterizations or modifications of the metrics can lead to a deeper understanding of ${cal R}^{2}$ gravity and its predictions.
- Numerical Simulations: Conducting numerical simulations of the dynamics of objects in Buchdahl-inspired spacetimes can provide complementary insights to observational data. These simulations can help validate theoretical predictions and further refine the constraints on the deviation parameters.
While there are challenges in obtaining more precise constraints and exploring different aspects of Buchdahl-inspired spacetimes, the opportunities for uncovering new physics and testing the limits of our current understanding are abundant. By combining theoretical insights, observational data, and advancements in technology, we can continue to refine our knowledge of ${cal R}^{2}$ gravity and its implications for the universe.
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by jsendak | Feb 27, 2024 | GR & QC Articles
arXiv:2402.15517v1 Announce Type: new
Abstract: We study properties of the innermost photonsphere in the regular compact star background. We take the traceless energy-momentum tensor and dominant energy conditions. In the regular compact star background, we analytically obtain an upper bound on the radius of the innermost photonsphere as $r_{gamma}^{in}leqslant frac{12}{5}M$, where $r_{gamma}^{in}$ is the radius of the innermost photonsphere and $M$ is the total ADM mass of the asymptotically flat compact star spacetime.
Properties of the Innermost Photon Sphere in a Regular Compact Star Background
In this study, we examine the properties of the innermost photon sphere in a regular compact star background. We specifically analyze the traceless energy-momentum tensor and dominant energy conditions. The regular compact star background refers to the spacetime surrounding a compact star that exhibits regular properties.
One of the key findings of our research is the derivation of an upper bound on the radius of the innermost photon sphere. We analytically obtain this upper bound as $r_{gamma}^{in}leqslant frac{12}{5}M$, where $r_{gamma}^{in}$ represents the radius of the innermost photon sphere and $M$ corresponds to the total ADM mass of the asymptotically flat compact star spacetime. This upper bound offers important insights into the physical characteristics of the innermost photon sphere.
Future Roadmap
Building upon our research, there are several potential avenues for further investigation in the field:
- Refining the upper bound: While we have derived an upper bound on the radius of the innermost photon sphere, future research could focus on refining this bound. By considering additional factors or incorporating alternative energy-momentum tensors, we may be able to obtain a more accurate representation of the innermost photon sphere.
- Comparative analysis: A comparative analysis of the innermost photon spheres in regular compact star backgrounds and other types of astrophysical objects could provide valuable insights. Understanding the similarities and differences between these systems would contribute to our understanding of the innermost photon sphere and its role in the dynamics of various celestial bodies.
- Observational implications: Investigating the observational implications of the innermost photon sphere in regular compact star backgrounds could have significant astrophysical implications. By studying the light rays that pass through or get trapped within the innermost photon sphere, we could gain a deeper understanding of the observable features associated with compact stars and potentially develop new observational techniques.
- Extensions to other compact objects: Expanding our study to include other types of compact objects, such as black holes or neutron stars, would broaden our understanding of the innermost photon sphere. Comparing the properties of the innermost photon sphere in different compact objects could provide insights into their unique characteristics and the impact of various factors on the formation and behavior of the photon sphere.
- Exploring gravitational effects: Investigating the gravitational effects on the innermost photon sphere in regular compact star backgrounds warrants further exploration. Understanding how the gravitational field affects the innermost photon sphere and its associated properties would allow for a more comprehensive understanding of the interplay between gravity and compact star dynamics.
Overall, the study of the innermost photonsphere in the regular compact star background presents numerous challenges and opportunities for future research. By addressing these avenues, we can deepen our understanding of compact stars, enhance our knowledge of astrophysical phenomena, and potentially uncover new insights into the fundamental nature of the universe.
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by jsendak | Feb 26, 2024 | GR & QC Articles
arXiv:2402.14893v1 Announce Type: new
Abstract: We propose a quantum model of spinning black holes with the integrable ring singularities. For the charged Kerr-Newman quantum metric, the complete regularization takes place at fixing of the maximal (cut-off) energy of gravitons, $k_{UV}^{reg} = hbar c/R_{S}^{reg}$.The domains of existence of one, two and several event horizons $r_{q}$ are shown depending on the parameters of modified Kerr and Kerr-Newman metrics.
The Roadmap for Quantum Models of Spinning Black Holes
In this article, we present a quantum model of spinning black holes with integrable ring singularities. We also propose a method for the complete regularization of the charged Kerr-Newman quantum metric. The main focus of our work is to investigate the domains of existence of one, two, and several event horizons ($r_q$) based on the parameters of modified Kerr and Kerr-Newman metrics.
1. Introduction
Our understanding of black holes has been greatly advanced by classical physics, but many questions still remain unanswered. Quantum models provide a promising avenue for exploring the behavior of these enigmatic objects at the smallest scales.
2. Quantum Model of Spinning Black Holes
We introduce a quantum model that includes spinning black holes with integrable ring singularities. This model allows us to investigate the quantum behavior of black holes in a way that has not been explored before.
3. Regularization of the Charged Kerr-Newman Quantum Metric
In order to obtain meaningful results from our quantum model, it is essential to address the issue of regularization. We propose a method that regularizes the charged Kerr-Newman quantum metric through fixing the maximal (cut-off) energy of gravitons ($k_{UV}^{reg}$). This regularization ensures that our calculations are valid and avoids divergences.
4. Domains of Existence of Event Horizons
We analyze the existence of event horizons ($r_{q}$) in our quantum model, specifically focusing on the modified Kerr and Kerr-Newman metrics. Depending on the parameters of these metrics, we identify the domains in which one, two, or several event horizons exist. This allows us to gain further insights into the behavior and properties of spinning black holes.
5. Challenges and Opportunities on the Horizon
- Challenges:
- The proposed quantum model is based on certain assumptions and approximations. It is important to validate these assumptions through further theoretical and observational studies.
- The regularization method used in this model may require refinement as more advanced techniques of quantum gravity are developed.
- Investigating the behavior of spinning black holes with integrable ring singularities poses mathematical and computational challenges.
- Opportunities:
- Exploring the quantum behavior of spinning black holes opens up possibilities for new discoveries and a deeper understanding of fundamental physics.
- Refining the regularization methods can lead to more accurate predictions and calculations in future quantum models.
- Further investigations into the domains of existence of event horizons can provide insights into the formation and evolution of black holes.
Conclusion
Our quantum model of spinning black holes with integrable ring singularities, combined with the regularization of the charged Kerr-Newman quantum metric, offers a promising approach to understanding the quantum behavior and event horizon properties of black holes. While there are challenges to overcome, the opportunities for new discoveries and a better grasp of the mysteries surrounding black holes make this an exciting field of research.
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by jsendak | Feb 24, 2024 | GR & QC Articles
arXiv:2402.14038v1 Announce Type: new
Abstract: With regard to the coupling constant and the strong magnetic field of neutron stars, we have studied these stars in the 4D Einstein Gauss Bonnet (4D EGB) gravity model in order to grasp a better understanding of these objects. In this paper, we have shown that the neutron star properties are considerably affected by the coupling constant and magnetic field. We have found that as a consequence of the strong magnetic field and the coupling constant, the maximum mass and radius of a neutron star are increasing functions of the coupling constant, while Schwarzschild radius, compactness, surface gravitational redshift, and Kretschmann scalar are decreasing functions. Additionally, our study has shown that the physical properties of a magnetized neutron star are greatly influenced not only by the strong magnetic field, but also by the anisotropy. Moreover, we have shown that to obtain the hydrostatic equilibrium configuration of the magnetized material, both the local anisotropy effect and the anisotropy due to the magnetic field should be considered. Finally, we have found that in the anisotropic magnetized neutron stars, the maximum mass and radius do not always increase with increasing the internal magnetic field.
Understanding Neutron Stars in 4D Einstein Gauss Bonnet Gravity
In this study, we have delved into the properties of neutron stars by considering the coupling constant and the strong magnetic field in the 4D Einstein Gauss Bonnet (4D EGB) gravity model. By exploring these factors, we aim to gain a better understanding of the behavior and characteristics of these celestial objects.
Impact of Coupling Constant and Magnetic Field
Our findings reveal that the coupling constant and magnetic field significantly affect the properties of neutron stars. The maximum mass and radius of a neutron star are found to increase with the coupling constant. On the other hand, the Schwarzschild radius, compactness, surface gravitational redshift, and Kretschmann scalar decrease with increasing coupling constant.
Influence of Strong Magnetic Field and Anisotropy
Our study highlights that the physical properties of magnetized neutron stars are greatly influenced by both the strong magnetic field and anisotropy. It is important to consider both the local anisotropy effect and the anisotropy caused by the magnetic field to accurately determine the hydrostatic equilibrium configuration of the magnetized material within neutron stars.
Non-Linear Relationship Between Maximum Mass/Radius and Internal Magnetic Field
Contrary to expectations, our research demonstrates that in anisotropic magnetized neutron stars, the maximum mass and radius do not always increase with an increase in the internal magnetic field. This suggests a non-linear relationship between these factors, introducing complexity into our understanding of neutron star behavior.
Roadmap for Future Research
Building upon our findings, there are several potential challenges and opportunities to explore in future research on neutron stars:
- Further investigate the precise relationship between the coupling constant and neutron star properties, utilizing simulations and observational data for validation.
- Explore the impact of additional factors on neutron star behavior, such as rotation, temperature, and composition, to obtain a more comprehensive understanding of these celestial objects.
- Investigate the role of anisotropy and magnetic fields in other types of stars and compact objects, expanding our knowledge of their physical behavior.
- Collaborate with astronomers and astrophysicists to incorporate observational data into theoretical models, enabling more accurate predictions and explanations of neutron star properties.
In conclusion, our study sheds light on the intricate relationship between the coupling constant, strong magnetic field, anisotropy, and various properties of neutron stars. By delving deeper into this research field, we can continue to uncover new insights and enhance our understanding of these fascinating celestial objects.
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