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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by jsendak | Feb 23, 2024 | GR & QC Articles
arXiv:2402.13360v1 Announce Type: new
Abstract: This study explores the behavior of compact stars within the framework of $f(R,L_m,T)$ gravity, focusing on the functional form $f(R,L_m,T) = R + alpha TL_m$. The modified Tolman-Oppenheimer-Volkoff (TOV) equations are derived and numerically solved for several values of the free parameter $alpha$ by considering both quark and hadronic matter — described by realistic equations of state (EoSs). Furthermore, the stellar structure equations are adapted for two different choices of the matter Lagrangian density (namely, $L_m= p$ and $L_m= -rho$), laying the groundwork for our numerical analysis. As expected, we recover the traditional TOV equations in General Relativity (GR) when $alpha rightarrow 0$. Remarkably, we found that the two choices for $L_m$ have appreciably different effects on the mass-radius diagrams. Results showcase the impact of $alpha$ on compact star properties, while final remarks summarize key findings and discuss implications, including compatibility with observational data from NGC 6397’s neutron star. Overall, this research enhances comprehension of $f(R,L_m,T)$ gravity’s effects on compact star internal structures, offering insights for future investigations.
This study examines the behavior of compact stars within the framework of $f(R,L_m,T)$ gravity, focusing specifically on the functional form $f(R,L_m,T) = R + alpha TL_m$. The modified Tolman-Oppenheimer-Volkoff (TOV) equations are derived and numerically solved for different values of the parameter $alpha$, considering both quark and hadronic matter with realistic equations of state. The stellar structure equations are adapted for two choices of the matter Lagrangian density, laying the foundation for the numerical analysis.
When $alpha$ approaches zero, the traditional TOV equations in General Relativity (GR) are recovered. However, it was discovered that the two choices for $L_m$ have significantly different effects on the mass-radius diagrams. This highlights the impact of $alpha$ on the properties of compact stars. The study concludes by summarizing the key findings and discussing their implications, including their compatibility with observational data from NGC 6397’s neutron star.
Overall, this research enhances our understanding of the effects of $f(R,L_m,T)$ gravity on the internal structures of compact stars. It provides insights that can contribute to future investigations in this field.
Roadmap for Future Investigations
To further explore the implications and potential applications of $f(R,L_m,T)$ gravity on compact stars, several avenues of research can be pursued:
1. Expansion to Other Functional Forms
While this study focuses on the specific functional form $f(R,L_m,T) = R + alpha TL_m$, there is potential for investigation into other functional forms. Different choices for $f(R,L_m,T)$ may yield interesting and diverse results, expanding our understanding of compact star behavior.
2. Exploration of Different Equations of State
Currently, the study considers realistic equations of state for both quark and hadronic matter. However, there is room for exploration of other equations of state. By incorporating different equations of state, we can gain a more comprehensive understanding of the behavior of compact stars under $f(R,L_m,T)$ gravity.
3. Inclusion of Additional Parameters
Expanding the analysis to include additional parameters beyond $alpha$ can provide a more nuanced understanding of the effects of $f(R,L_m,T)$ gravity on compact stars. By investigating how different parameters interact with each other and impact the properties of compact stars, we can uncover new insights into the behavior of these celestial objects.
4. Comparison with Observational Data
While this study discusses the compatibility of the findings with observational data from NGC 6397’s neutron star, it is important to expand this comparison to a wider range of observational data. By comparing the theoretical predictions with a larger dataset, we can validate the conclusions drawn and identify any discrepancies or areas for further investigation.
Challenges and Opportunities
Potential Challenges:
- Obtaining accurate and comprehensive observational data on compact stars for comparison with theoretical predictions can be challenging due to their extreme conditions and limited visibility.
- Numerically solving the modified TOV equations for various parameter values and choices of matter Lagrangian density may require significant computational resources and optimization.
- Exploring different functional forms and equations of state can lead to complex analyses, requiring careful interpretation and validation of results.
Potential Opportunities:
- The advancements in observational techniques and instruments provide opportunities for obtaining more precise data on compact stars, enabling more accurate validation of theoretical models.
- Ongoing advancements in computational power and numerical techniques allow for more efficient and faster solution of the modified TOV equations, facilitating the exploration of a broader parameter space.
- The diverse range of functional forms and equations of state available for investigation provides ample opportunities for uncovering novel insights into the behavior and properties of compact stars.
By addressing these challenges and capitalizing on the opportunities, future investigations into the effects of $f(R,L_m,T)$ gravity on compact star internal structures can continue to push the boundaries of our understanding and pave the way for further advancements in the field.
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by jsendak | Feb 22, 2024 | GR & QC Articles
arXiv:2402.12409v1 Announce Type: new
Abstract: The main objective of this paper is to investigate the impact of $f(mathcal{Q},mathcal{T})$ gravity on the geometry of anisotropic compact stellar objects, where $mathcal{Q}$ is non-metricity and $mathcal{T}$ is the trace of the energy-momentum tensor. In this perspective, we use the physically viable non-singular solutions to examine the configuration of static spherically symmetric structures. We consider a specific model of this theory to examine various physical quantities in the interior of the proposed compact stars. These quantities include fluid parameters, anisotropy, energy constraints, equation of state parameters, mass, compactness and redshift. The Tolman-Oppenheimer-Volkoff equation is used to examine the equilibrium state of stellar models, while the stability of the proposed compact stars is investigated through sound speed and adiabatic index methods. It is found that the proposed compact stars are viable and stable in the context of this theory.
The main objective of this paper is to investigate the impact of $f(mathcal{Q},mathcal{T})$ gravity on the geometry of anisotropic compact stellar objects. The authors focus on using physically viable non-singular solutions to study the configuration of static spherically symmetric structures. Specifically, they consider a specific model of $f(mathcal{Q},mathcal{T})$ gravity and examine various physical quantities in the interior of the compact stars.
The paper discusses the implications of $f(mathcal{Q},mathcal{T})$ gravity on fluid parameters, anisotropy, energy constraints, equation of state parameters, mass, compactness, and redshift of the proposed compact stars. The authors utilize the Tolman-Oppenheimer-Volkoff equation to analyze the equilibrium state of stellar models and investigate the stability of the proposed compact stars using sound speed and adiabatic index methods.
Future Roadmap
Potential Challenges:
- Theoretical Complexity: Further research may be required to fully understand the intricacies and complexities of $f(mathcal{Q},mathcal{T})$ gravity and its impact on compact stellar objects.
- Experimental Verification: Experimental tests or observations are necessary to validate the predictions and conclusions of this study.
- Generalizability: The authors focus on a specific model of $f(mathcal{Q},mathcal{T})$ gravity. Future studies could explore the generalizability of their findings by considering different models within this framework.
Potential Opportunities:
- Understanding Compact Stellar Objects: This study provides insights into the geometry and physical quantities of anisotropic compact stellar objects, which could contribute to our understanding of these astrophysical entities.
- Exploring Modified Gravity Theories: $f(mathcal{Q},mathcal{T})$ gravity is a modified theory of gravity. Further investigations into this theory may shed light on the nature of gravity itself and its implications in various astrophysical contexts.
- Advancing Stellar Structure Theory: The analysis of equilibrium states and stability of compact stars in the context of $f(mathcal{Q},mathcal{T})$ gravity can enhance our knowledge of stellar structure and the fundamental forces governing star formation and evolution.
In conclusion, this paper investigates the impact of $f(mathcal{Q},mathcal{T})$ gravity on anisotropic compact stellar objects and provides valuable insights into their geometry and physical quantities. While further research and experimental verification are needed, this study opens up opportunities for understanding compact stellar objects, exploring modified gravity theories, and advancing our knowledge of stellar structure.
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by jsendak | Feb 21, 2024 | GR & QC Articles
arXiv:2402.10916v1 Announce Type: new
Abstract: In this analysis, we study the dynamics of quantum oscillator fields within the context of a position-dependent mass (PDM) system situated in an Einstein-Maxwell space-time, incorporating a non-zero cosmological constant. The magnetic field is aligned along the symmetry axis direction. To analyze PDM quantum oscillator fields, we introduce a modification to the Klein-Gordon equation by substituting the four-momentum vector $p_{mu} to Big(p_{mu}+i,eta,X_{mu}+i,mathcal{F}_{mu}Big)$ into the Klein-Gordon equation, where the four-vector is defibed by $X_{mu}=(0, r, 0, 0)$, $mathcal{F}_{mu}=(0, mathcal{F}_r, 0, 0)$ with $mathcal{F}_r=frac{f'(r)}{4,f(r)}$, and $eta$ is the mass oscillator frequency. The radial wave equation for the relativistic modified Klein-Gordon equation is derived and subsequently solved for two distinct cases: (i) $f(r)=e^{frac{1}{2},alpha,r^2}$, and (ii) $f(r)=r^{beta}$, where $alpha geq 0, beta geq 0$. The resultant energy levels and wave functions for quantum oscillator fields are demonstrated to be influenced by both the cosmological constant and the geometrical topology parameter which breaks the degeneracy of the energy spectrum. Furthermore, we observed noteworthy modifications in the energy levels and wave functions when compared to the results derived in the flat space background.
Analysis of Quantum Oscillator Fields with Position-Dependent Mass
In this analysis, we examine the dynamics of quantum oscillator fields within the context of a position-dependent mass (PDM) system situated in an Einstein-Maxwell space-time, incorporating a non-zero cosmological constant. The magnetic field is aligned along the symmetry axis direction.
To analyze PDM quantum oscillator fields, we introduce a modification to the Klein-Gordon equation by substituting the four-momentum vector pμ → (pμ + iηXμ+ i𝓕μ) into the Klein-Gordon equation. Here, the four-vector is defined by Xμ = (0, r, 0, 0), 𝓕μ = (0, 𝓕r, 0, 0) with 𝓕r=f'(r) / (4f(r)), and η is the mass oscillator frequency.
Derivation and Solutions
The radial wave equation for the relativistic modified Klein-Gordon equation is derived and subsequently solved for two distinct cases:
- f(r) = e(1/2)αr²
- f(r) = rβ
In case (i), where f(r) = e(1/2)αr², and in case (ii), where f(r) = rβ, with α ≥ 0 and β ≥ 0, we obtain the resultant energy levels and wave functions for the quantum oscillator fields.
Influence of Cosmological Constant and Geometrical Topology Parameter
The energy levels and wave functions for quantum oscillator fields are demonstrated to be influenced by both the cosmological constant and the geometrical topology parameter, which breaks the degeneracy of the energy spectrum. Notably, there are modifications observed in the energy levels and wave functions when compared to the results derived in a flat space background.
Future Roadmap
Looking ahead, there are several potential challenges and opportunities on the horizon regarding the analysis of quantum oscillator fields with position-dependent mass:
- Further investigation: More extensive research is needed to explore different forms of position-dependent mass functions and their effects on quantum oscillator fields. This could involve considering more complex mass distributions or non-linear mass dependence.
- Experimental verification: Conducting experiments or simulations to validate the theoretical predictions and properties of quantum oscillator fields with position-dependent mass would provide valuable insights and potential applications in various fields, such as quantum computing or high-energy physics.
- Generalization of findings: Extending the analysis to higher-dimensional space-times or incorporating additional physical factors, such as magnetic fields, gravitational waves, or other forces, could enhance our understanding of the behavior of quantum oscillator fields with position-dependent mass in more complex scenarios.
- Applications: Exploring the potential practical applications of this analysis, such as in quantum technologies or novel materials with tailored physical properties, could lead to groundbreaking advancements in various fields.
- Interdisciplinary collaborations: Collaborations between physicists, mathematicians, and other scientists from different disciplines could foster new approaches and perspectives in studying quantum oscillator fields with position-dependent mass, leading to innovative breakthroughs.
Overall, the study of quantum oscillator fields with position-dependent mass presents an intriguing avenue for research and opens up new possibilities for understanding and manipulating quantum systems in diverse contexts.
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