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 6, 2024 | GR & QC Articles
We propose a novel cosmological framework within the $f(R,T)$ type modified gravity theory, incorporating a non-minimally coupled with the higher order of the Ricci scalar ($R$) as well as the trace of the energy-momentum tensor ($T$). Therefore, our well-motivated chosen $f(R,T)$ expression is $ R + R^m + 2 lambda T^n$, where $lambda$, $m$, and $n$ are arbitrary constants. Taking a constant jerk parameter ($j$), we derive expressions for the deceleration parameter ($q$) and the Hubble parameter ($H$) as functions of the redshift $z$. We constrained our model with the recent Observational Hubble Dataset (OHD), $Pantheon$, and $ Pantheon $ + OHD datasets by using the analysis of Markov Chain Monte Carlo (MCMC). Our model shows early deceleration followed by late-time acceleration, with the transition occurring in the redshift range $1.10 leq z_{tr} leq 1.15$. Our findings suggest that this higher-order model of $f(R,T)$ gravity theory can efficiently provide a dark energy model for addressing the current scenario of cosmic acceleration.
We propose a novel cosmological framework within the $f(R,T)$ type modified gravity theory. This framework incorporates a non-minimally coupled higher order of the Ricci scalar ($R$) as well as the trace of the energy-momentum tensor ($T$). Our chosen $f(R,T)$ expression is $ R + R^m + 2 lambda T^n$, where $lambda$, $m$, and $n$ are arbitrary constants.
By taking a constant jerk parameter ($j$), we have derived expressions for the deceleration parameter ($q$) and the Hubble parameter ($H$) as functions of the redshift $z$. We have constrained our model using the recent Observational Hubble Dataset (OHD), $Pantheon$, and $Pantheon + OHD$ datasets through the analysis of Markov Chain Monte Carlo (MCMC).
Our results show that our model exhibits early deceleration followed by late-time acceleration, with the transition occurring in the redshift range .10 leq z_{tr} leq 1.15$. This suggests that our higher-order model of $f(R,T)$ gravity theory can effectively provide a dark energy model to address the current scenario of cosmic acceleration.
Future Roadmap
Challenges
- Data Accuracy: One challenge that researchers may face is ensuring the accuracy and reliability of the observational data used to constrain and validate our proposed model. It is important to continue improving observational techniques and minimizing systematic errors in order to obtain more precise results.
- Theoretical Development: Further theoretical development and analysis may be required to fully understand and interpret the implications of our proposed framework within the $f(R,T)$ modified gravity theory. This includes exploring potential connections with other cosmological models and addressing any limitations or assumptions made in our current model.
Opportunities
- Further Testing: Our model can be further tested and validated using future observations and surveys, such as those planned by upcoming space missions or ground-based observatories. These additional data points can help refine and improve our understanding of the cosmological framework and its predictions.
- Extensions and Modifications: Researchers have the opportunity to extend and modify our proposed $f(R,T)$ gravity theory framework to explore alternative models and incorporate additional physical factors. This can help address other open questions in cosmology, such as the nature of dark matter or the existence of primordial gravitational waves.
In conclusion, our study presents a promising cosmological framework within the $f(R,T)$ modified gravity theory. The use of observational data and MCMC analysis supports the viability of our model in providing a dark energy explanation for the current cosmic acceleration scenario. However, further research, including improvements in data accuracy and theoretical development, is necessary to fully understand and explore the potential of this framework.
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by jsendak | Jan 15, 2024 | GR & QC Articles
We investigate gravitational waves in the $f(Q)$ gravity, i.e., a geometric
theory of gravity described by a non-metric compatible connection, free from
torsion and curvature, known as symmetric-teleparallel gravity. We show that
$f(Q)$ gravity exhibits only two massless and tensor modes. Their polarizations
are transverse with helicity equal to two, exactly reproducing the plus and
cross tensor modes typical of General Relativity. In order to analyze these
gravitational waves, we first obtain the deviation equation of two trajectories
followed by nearby freely falling point-like particles and we find it to
coincide with the geodesic deviation of General Relativity. This is because the
energy-momentum tensor of matter and field equations are Levi-Civita
covariantly conserved and, therefore, free structure-less particles follow,
also in $f(Q)$ gravity, the General Relativity geodesics. Equivalently, it is
possible to show that the curves are solutions of a force equation, where an
extra force term of geometric origin, due to non-metricity, modifies the
autoparallel curves with respect to the non-metric connection. In summary,
gravitational waves produced in non-metricity-based $f(Q)$ gravity behave as
those in torsion-based $f(T)$ gravity and it is not possible to distinguish
them from those of General Relativity only by wave polarization measurements.
This shows that the situation is different with respect to the curvature-based
$f(R)$ gravity where an additional scalar mode is always present for $f(R)neq
R$.
The Future Roadmap for Gravitational Waves in $f(Q)$ Gravity
Introduction
In this article, we explore the behavior of gravitational waves in $f(Q)$ gravity, a geometric theory of gravity described by a non-metric compatible connection known as symmetric-teleparallel gravity. We analyze the properties of these waves and compare them to gravitational waves in General Relativity.
Two Massless and Tensor Modes
Our findings reveal that $f(Q)$ gravity exhibits only two massless and tensor modes. These modes have transverse polarizations with helicity equal to two, which is consistent with the plus and cross tensor modes observed in General Relativity.
Geodesic Deviation and Trajectory Analysis
To further study these gravitational waves, we examine the deviation equation of two nearby freely falling point-like particles. Surprisingly, we discover that this deviation equation coincides with the geodesic deviation observed in General Relativity. This suggests that free particles without any structure follow the geodesics of General Relativity even in $f(Q)$ gravity.
Force Equation and Geometric Origin
Alternatively, we can interpret the particle trajectories as solutions of a force equation. In this equation, an extra force term of geometric origin arises due to non-metricity. This modification to the autoparallel curves introduced by the non-metric connection showcases how non-metricity affects the behavior of gravitational waves in $f(Q)$ gravity.
Comparison with Torsion and Curvature-Based Gravity Theories
We compare the behavior of gravitational waves in $f(Q)$ gravity to torsion-based $f(T)$ gravity and curvature-based $f(R)$ gravity. Our analysis reveals that gravitational waves in $f(Q)$ gravity behave similarly to those in $f(T)$ gravity, where wave polarization measurements alone cannot distinguish them from waves in General Relativity. However, this differs from gravitational waves in $f(R)$ gravity, where an additional scalar mode is always present for $f(R)neq R$.
Conclusion and Future Challenges
This research demonstrates the similarity between gravitational waves in $f(Q)$ gravity and General Relativity. The absence of additional modes and the reproduction of the plus and cross tensor modes suggest that $f(Q)$ gravity may provide a consistent framework for describing gravitational waves. However, further investigation is needed to fully understand the implications and potential differences of gravitational wave behavior in $f(Q)$ gravity compared to General Relativity. Continued research in this area may uncover new challenges and opportunities, ultimately shaping the future of gravitational wave study.
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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 7, 2024 | GR & QC Articles
The Teleparallel Theory is equivalent to General Relativity, but whereas in
the latter gravity has to do with curvature, in the former gravity is described
by torsion. As is well known, there is in the literature a host of alternative
theories of gravity, among them the so called extended theories, in which
additional terms are added to the action, such as for example in the $f(R)$ and
$f(T)$ gravities, where $R$ is the Ricci scalar and $T$ is the scalar torsion,
respectively. One of the ways to probe alternative gravity is via compact
objects. In fact, there is in the literature a series of papers on compact
objects in $f(R)$ and $f(T)$ gravity. In particular, there are several papers
that consider $f(T) = T + xi T^2$, where $xi$ is a real constant. In this
paper, we generalise such extension considering compact stars in $f (T ) = T +
xi T^beta$ gravity, where $xi$ and $beta$ are real constants and looking
out for the implications in their maximum masses and compactness in comparison
to the General Relativity. Also, we are led to constrain the $beta$ parameter
to positive integers which is a restriction not imposed by cosmology.
Exploring Compact Objects in Extended Theories of Gravity
In recent years, there has been a surge of interest in alternative theories of gravity that go beyond General Relativity. These extended theories introduce additional terms to the action, offering new ways to describe gravity. One such theory is the Teleparallel Theory, where gravity is described by torsion rather than curvature.
Among the various extended theories, $f(R)$ and $f(T)$ gravities have gained significant attention. These theories involve adding extra terms to the action, involving the Ricci scalar $R$ and scalar torsion $T$, respectively.
A promising avenue for probing alternative gravity theories is through the study of compact objects. Compact stars, in particular, have been extensively explored in the context of $f(R)$ and $f(T)$ gravity. One specific extension that has been investigated is $f(T) = T + xi T^2$, with $xi$ being a real constant.
In this paper, we aim to generalize this extension by considering compact stars in $f(T) = T + xi T^beta$ gravity. Here, $xi$ and $beta$ are real constants that allow us to explore the implications on the maximum masses and compactness of these objects in comparison to General Relativity.
An interesting aspect that arises from our investigation is the restriction imposed on the $beta$ parameter. We find that it must be constrained to positive integers, which is not a restriction enforced by cosmology.
Roadmap for Future Research:
- Further investigate and refine the generalized extension $f(T) = T + xi T^beta$ gravity theory.
- Explore the implications of different values of $beta$ on the maximum masses and compactness of compact stars in $f(T)$ gravity.
- Compare the results obtained in $f(T)$ gravity with those predicted by General Relativity to identify any deviations.
- Consider the implications of the restricted $beta$ parameter on the overall consistency and validity of the theory.
- Extend the study to other compact objects, such as neutron stars, to gain a more comprehensive understanding of the behavior of $f(T)$ gravity.
Challenges and Opportunities:
While this research presents exciting opportunities to explore alternative theories of gravity and their implications on compact objects, there are several challenges to overcome:
- The complexity of the mathematical formalism involved in $f(T)$ theories requires careful analysis and numerical calculations.
- Validating the predictions of $f(T)$ gravity through observational data from compact objects poses a significant challenge due to the limited availability of precise measurements.
- Ensuring consistency with cosmological observations and constraints while studying compact stars in $f(T)$ gravity is essential to assess the viability of the theory.
In conclusion, the investigation of compact objects in extended theories of gravity, specifically $f(T) = T + xi T^beta$ gravity, offers new avenues for understanding the nature of gravity. By exploring the implications on maximum masses and compactness, we can gain insights into deviations from General Relativity. However, addressing challenges related to mathematical complexity, observational validation, and cosmological consistency will be crucial for advancing our understanding of alternative gravity theories.
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