by jsendak | Feb 13, 2024 | GR & QC Articles
Critical phenomena in gravitational collapse are characterized by the emergence of surprising structure in solution space, namely the appearance of universal power-laws and periodicities near the threshold of collapse, and a universal discretely self-similar solution at the threshold itself. This seminal work spurred a comprehensive investigation of extreme spherical spacetimes in numerical relativity, with analogous results for numerous matter models. Recent research suggests that the generalization to less symmetric scenarios is subtle. In twist-free axisymmetric vacuum collapse for instance, numerical evidence suggests a breakdown of universality of solutions at the threshold of collapse. In this study, we explore gravitational collapse involving a massless complex scalar field minimally coupled to general relativity. We employ the pseudospectral code BAMPS to investigate a neighborhood of the spherically symmetric critical solution in phase space, focusing on aspherical departures from it. First, working in explicit spherical symmetry, we find strong evidence that the spacetime metric of the spherical critical solution of the complex scalar field agrees with that of the Choptuik solution. We then examine universality of the behavior of solutions near the threshold of collapse as the departure from spherical symmetry increases, comparing with recent investigations of the real scalar field. We present a series of well-tuned numerical results and document shifts of the power-law exponent and periods as a function of the degree of asphericity of the initial data. At sufficiently high asphericities we find that the center of collapse bifurcates, on the symmetry axis, but away from the origin. Finally we look for and evaluate evidence that in the highly aspherical setting the collapse is driven by gravitational waves.
Future Roadmap for Readers
This study explores gravitational collapse involving a massless complex scalar field minimally coupled to general relativity. The research aims to investigate the behavior of solutions near the threshold of collapse as the departure from spherical symmetry increases. The roadmap for readers is outlined below:
1. Understanding the background
Before diving into the specific research, it is important to grasp some key concepts. The article mentions critical phenomena in gravitational collapse characterized by universal power-laws and periodicities near the threshold of collapse. Readers should familiarize themselves with the basics of gravitational collapse, numerical relativity, and matter models.
2. Exploring the limitations of symmetry
The article highlights recent research suggesting a breakdown of universality of solutions in twist-free axisymmetric vacuum collapse. Readers should delve into the challenges faced when dealing with less symmetric scenarios in gravitational collapse.
3. Investigating a massless complex scalar field
The study focuses on gravitational collapse involving a massless complex scalar field. Readers should gain an understanding of this specific field and its role within general relativity.
4. Examining the numerical results
The study utilizes the pseudospectral code BAMPS to investigate a neighborhood of the spherically symmetric critical solution in phase space with aspherical departures from it. Readers should analyze the presented numerical results, which highlight shifts in power-law exponents and periods as a function of asphericity of the initial data.
5. Bifurcation of collapse and the role of gravitational waves
In highly aspherical settings, the collapse bifurcates on the symmetry axis, but away from the origin. The article suggests that gravitational waves may be driving this collapse. Readers should explore the evidence presented and evaluate the role of gravitational waves in the collapse process.
Challenges and Opportunities on the Horizon
- Challenge: The generalization of collapse to less symmetric scenarios is identified as a subtle task. Researchers will face difficulties in analyzing and understanding the behavior of solutions in these scenarios.
- Opportunity: This research provides an opportunity to deepen our understanding of gravitational collapse in scenarios with less symmetry. It opens avenues for further investigation and potential breakthroughs in numerical relativity.
- Challenge: Asphericity of initial data introduces complexities in the analysis. Researchers will need to address these challenges to accurately interpret the numerical results and draw meaningful conclusions.
- Opportunity: The exploration of aspherical departures from the spherically symmetric critical solution presents an opportunity to uncover new insights and patterns in gravitational collapse. This may expand our knowledge of the behavior of spacetime near the threshold of collapse.
- Challenge: Determining the role of gravitational waves in highly aspherical settings requires careful evaluation and analysis. Researchers will need to assess the evidence and potentially develop innovative techniques to study the influence of gravitational waves.
- Opportunity: If gravitational waves are indeed found to drive collapse in highly aspherical scenarios, it would mark a significant advancement in our understanding of the collapse process. This could have implications for astrophysics and the study of black holes.
Summary
This study investigates the behavior of solutions near the threshold of collapse in scenarios involving a massless complex scalar field and gravitational collapse. The research builds upon previous work on critical phenomena in gravitational collapse and examines the effects of asphericity and the potential role of gravitational waves. While challenges exist in generalizing collapse to less symmetric scenarios and analyzing aspherical departures, this research presents opportunities for expanding our knowledge and potentially making breakthroughs in numerical relativity and astrophysics.
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by jsendak | Feb 12, 2024 | GR & QC Articles
We propose an explicit spin-foam amplitude for Lorentzian gravity in three dimensions. The model is based on two main requirements: that it should be structurally similar to its well-known Euclidean analog, and that geometricity should be recovered in the semiclassical regime. To this end we introduce new coherent states for space-like 1-dimensional boundaries, derived from the continuous series of unitary $mathrm{SU}(1,1)$ representations. We show that the relevant objects in the amplitude can be written in terms of the defining representation of the group, just as so happens in the Euclidean case. We derive an expression for the semiclassical amplitude at large spins, showing that it relates to the Lorentzian Regge action.
Future Roadmap for Readers
Overview
In this article, we present an explicit spin-foam amplitude for Lorentzian gravity in three dimensions. Our model satisfies two important requirements: it is structurally similar to its well-known Euclidean analog, and it recovers geometricity in the semiclassical regime. We achieve this by introducing new coherent states for space-like 1-dimensional boundaries, which are derived from the continuous series of unitary $mathrm{SU}(1,1)$ representations. In addition, we demonstrate that the relevant objects in the amplitude can be expressed in terms of the defining representation of the group, just like in the Euclidean case. Lastly, we derive an expression for the semiclassical amplitude at large spins, revealing its relationship to the Lorentzian Regge action.
Roadmap
- Introduction: We provide an overview of the article, discussing the motivation behind our research and the goals we aim to achieve.
- Lorentzian Spin-Foam Amplitude: We present our explicit spin-foam amplitude for Lorentzian gravity in three dimensions. We explain how it satisfies the structural requirements and recovers geometricity in the semiclassical regime.
- New Coherent States: We introduce the new coherent states for space-like 1-dimensional boundaries. These coherent states are derived from the continuous series of unitary $mathrm{SU}(1,1)$ representations.
- Relevant Objects in the Amplitude: We demonstrate that the relevant objects in the amplitude can be expressed in terms of the defining representation of $mathrm{SU}(1,1)$, similar to the Euclidean case. This similarity allows us to maintain the structural similarity between the Lorentzian and Euclidean amplitudes.
- Semiclassical Amplitude at Large Spins: We derive an expression for the semiclassical amplitude at large spins and establish its relationship to the Lorentzian Regge action. This further validates the effectiveness of our spin-foam amplitude model.
Challenges and Opportunities
While our proposed spin-foam amplitude for Lorentzian gravity in three dimensions shows significant promise, there are challenges and opportunities that lie ahead:
- Validation and Testing: The model needs to be thoroughly tested and validated through simulations or comparisons with existing theories and experimental data. This will help ensure its accuracy and reliability.
- Extension to Higher Dimensions: Our current model is limited to three dimensions. Extending it to higher dimensions could open up new possibilities and applications in the field of gravity.
- Integration with Quantum Field Theory: Investigating the integration of our spin-foam amplitude with quantum field theory could lead to a more comprehensive understanding of the quantum nature of gravity.
- Practical Implementation: Developing practical algorithms and computational techniques for implementing the spin-foam amplitude in real-world scenarios is crucial for its practical applications in areas like cosmology, black holes, and quantum gravity.
Conclusion
Our explicit spin-foam amplitude for Lorentzian gravity in three dimensions, which satisfies structural requirements and recovers geometricity in the semiclassical regime, holds great potential for advancing our understanding of gravity at the quantum level. However, further research and development are necessary to validate the model, extend it to higher dimensions, integrate it with quantum field theory, and ensure its practical implementation. By addressing these challenges and capitalizing on the opportunities, we can make significant strides in the field of quantum gravity.
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by jsendak | Feb 9, 2024 | GR & QC Articles
Black hole superradiance has proven being very valuable in several realms of gravitational physics, and holds a promising discovery potential. In this paper, we show how it can sheed light on a long standing problem in physics, the quest for magnetic monopoles in the Universe. Placing them in the interior of primordial rotating black holes, which act as natural amplifiers, we show that massive charged bosonic fields in their vicinity exhibit a superradiant instability which surpasses significantly that of neutral Kerr black holes. Strikingly, this is true for black holes containing an order-one number of magnetic monopoles, or merely a single one, and possessing either low, moderate or large values of angular momentum. In particular, the instability is drastically faster than the radiative decay time of charged pions, thus making it physically relevant. Furthermore, our analysis identifies the most unstable modes as a class of monopole spheroidal harmonics, that we dub north and south monopole modes, whose morphology is markedly different from the usual superradiantly unstable modes since they extend along the rotational axis. We conclude by discussing implications of our results for primordial magnetic black holes, and their observational signatures as sources of cosmic rays and high-frequency gravitational waves.
Black hole superradiance has been proven to be valuable in various areas of gravitational physics and offers significant potential for discovery. In this paper, we focus on its application to the long-standing challenge of finding magnetic monopoles in the Universe.
We propose that primordial rotating black holes could serve as natural amplifiers for magnetic monopoles placed within their interiors. This amplification leads to a superradiant instability in the vicinity of these black holes, which is even more pronounced than that observed in neutral Kerr black holes. This instability is relevant for black holes containing just one or a small number of magnetic monopoles, regardless of their level of angular momentum.
An interesting finding is that the superradiant instability occurs at a much faster rate than the radiative decay time of charged pions, making it physically relevant. Additionally, our analysis reveals the existence of a specific class of monopole spheroidal harmonics known as north and south monopole modes. These modes differ from the usual superradiantly unstable modes as they extend along the rotational axis of the black hole.
In conclusion, our research has significant implications for understanding primordial magnetic black holes and their potential role as sources of cosmic rays and high-frequency gravitational waves. By exploring the phenomenon of black hole superradiance and its application to magnetic monopoles, we have opened up new avenues for investigation and future discoveries in gravitational physics.
Roadmap for Readers
- Introduction to black hole superradiance and its relevance in gravitational physics
- Discussion of the long-standing problem of finding magnetic monopoles in the Universe
- Explanation of the proposed use of primordial rotating black holes as amplifiers for magnetic monopoles
- Presentation of the superradiant instability observed in the vicinity of these black holes
- Comparison of the instability in black holes with different numbers of magnetic monopoles and levels of angular momentum
- Analysis of the faster rate of the superradiant instability compared to the decay time of charged pions
- Description of the unique monopole spheroidal harmonics known as north and south monopole modes
- Discussion of the implications for primordial magnetic black holes and their potential observational signatures as sources of cosmic rays and high-frequency gravitational waves
- Summary of the key findings and their significance in advancing our understanding of gravitational physics
Potential Challenges and Opportunities
While our research opens up exciting possibilities for further exploration, there are several challenges that need to be addressed:
- Experimental verification: The proposed phenomenon needs to be empirically tested in order to validate its existence.
- Data collection: Gathering observational data on primordial magnetic black holes and their characteristics poses technological and logistical challenges.
- Theoretical refinement: Further theoretical analysis is required to fully understand the underlying mechanisms and implications of the observed superradiant instability.
- Interdisciplinary collaboration: Collaboration between researchers from diverse fields such as astrophysics, particle physics, and gravitational wave astronomy is crucial for comprehensive investigations.
Despite these challenges, the opportunities presented by this research are immense:
- Potential discovery of magnetic monopoles: This research offers a new avenue for detecting elusive magnetic monopoles in the Universe.
- Advancement of gravitational physics: The study of black hole superradiance and its application to magnetic monopoles can significantly contribute to our understanding of gravitational phenomena.
- Expanded knowledge of primordial black holes: Investigating the role of primordial rotating black holes in amplifying magnetic monopoles can shed light on the formation and evolution of these mysterious objects.
- New observational tools: The identification of primordial magnetic black holes as potential sources of cosmic rays and high-frequency gravitational waves opens up new possibilities for detecting and studying these phenomena.
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by jsendak | Feb 8, 2024 | GR & QC Articles
K-essence theories are usually studied in the framework of one scalar field $phi$. Namely, the Lagrangian of K-essence is the function of scalar field $phi$ and its covariant derivative. However, in this paper, we explore a two-field pure K-essence, i.e. the corresponding Lagrangian is the function of covariant derivatives of two scalar fields without the dependency of scalar fields themselves. That is why we call it pure K-essence. The novelty of this K-essence is that its Lagrangian contains the quotient term of the kinetic energies from the two scalar fields. This results in the presence of many interesting features, for example, the equation of state can be arbitrarily small and arbitrarily large. As a comparison, the range for equation of state of quintessence is from $-1$ to $+1$. Interestingly, this novel K-essence can play the role of inflation field, dark matter and dark energy. Finally, the absence of the scalar fields themselves in the equations of motion makes the study considerable simple such that even the exact black hole solutions can be found.
K-essence theories are typically studied using a single scalar field, $phi$, where the Lagrangian of K-essence is a function of $phi$ and its covariant derivative. However, in this paper, we investigate a two-field pure K-essence, where the Lagrangian depends on the covariant derivatives of two scalar fields without any direct dependence on the scalar fields themselves. Therefore, we refer to this as pure K-essence.
The main novelty of this pure K-essence lies in its Lagrangian, which includes a quotient term of the kinetic energies from the two scalar fields. This leads to the presence of various interesting features, such as an equation of state that can be arbitrarily small or arbitrarily large. In contrast, the equation of state range for quintessence, another type of K-essence, is limited to $-1$ to $+1$.
What makes this pure K-essence particularly intriguing is its ability to serve as an inflation field, dark matter, and dark energy. These are fundamental components in understanding the expansion and structure formation of the universe.
Furthermore, the absence of the scalar fields themselves in the equations of motion simplifies the study considerably. In fact, it allows for the discovery of exact black hole solutions within this framework.
Future Roadmap
Challenges
- Validation and further exploration of the theoretical framework: The novel concept of pure K-essence with its unique Lagrangian requires rigorous testing and validation against known observational and experimental data.
- Understanding the physical implications: Investigating the implications of a pure K-essence as an inflation field, dark matter, and dark energy in more detail is necessary to fully understand its role in the universe.
- Experimental verification: Conducting experiments and observations to test the predictions and behavior of pure K-essence is crucial in confirming its existence and properties.
Opportunities
- Expanded theoretical framework: Building upon the concept of pure K-essence opens up new possibilities for studying the dynamics of scalar fields with more complex Lagrangians.
- Application in cosmology: The ability of pure K-essence to serve as multiple fundamental components offers exciting opportunities for advancing our understanding of the universe’s evolution and structure formation.
- New solutions and insights: The simplicity of the equations of motion in pure K-essence theory may lead to further discoveries, such as exact solutions and insights into gravity and black hole physics.
In conclusion, the exploration of a two-field pure K-essence with its unique Lagrangian presents fascinating opportunities for advancing our knowledge in cosmology, dark matter, and black hole physics. However, the challenges of validation, understanding the physical implications, and experimental verification remain crucial in fully grasping the potential of this novel theory.
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by jsendak | Feb 7, 2024 | GR & QC Articles
We investigate the shadow cast of black holes immersed in a dark matter halo. We use the M87* shadow data obtained by the EHT collaboration to constrain two parameters ($M,a$) of dark matter halo surrounding a black hole with mass $M_{rm bh}$. For $age10.8M$, we find the favored region (shadow bound), while the disfavored region is found for $a<10.8M$ when imposing the EHT results. This shadow bound is much less than the observation bound of galaxies ($age 10^4 M$).
Examination of the conclusions drawn from the research on the shadow cast of black holes immersed in a dark matter halo reveals several potential challenges and opportunities on the horizon. Based on the M87* shadow data obtained by the EHT collaboration, two parameters ($M$ and $a$) of the dark matter halo surrounding a black hole with mass $M_{rm bh}$ are constrained.
Conclusions:
- A favored region, known as the shadow bound, is found for values of $a$ greater than or equal to .8M$. This indicates that black holes immersed in a dark matter halo are likely to have a shadow within this parameter range.
- A disfavored region is found for values of $a$ less than .8M$. This suggests that black holes with lower values of $a$ may not have a well-defined shadow, implying a weaker influence of the dark matter halo or other unknown factors.
Future Roadmap:
Looking ahead, there are several potential challenges and opportunities in further exploring and understanding black holes immersed in dark matter halos:
- Refining Shadow Boundaries: Researchers can continue to investigate and refine the boundaries of the favored region (shadow bound) for the parameter $a$. This may involve more precise measurements and observations to narrow down the range where black holes are likely to have well-defined shadows.
- Exploring Sub-Shadow Region: Further investigation is needed to understand the disfavored region for $a$ values less than .8M$. Researchers can explore whether there are sub-shadow regions or alternative phenomena that arise in this parameter range, shedding light on the behavior of black holes in the presence of a dark matter halo.
- Dark Matter Halo Properties: The study highlights the importance of understanding the properties of dark matter halos surrounding black holes. Future research can focus on characterizing these halos in more detail, such as their density profiles, distribution, and potential interactions with black holes.
- Galactic-Scale Impact: Investigating the influence of dark matter halos on black holes at a larger scale is an intriguing avenue for future exploration. Researchers can study how different galactic environments and variations in dark matter halos affect the behavior and shadows of black holes, leading to a deeper understanding of the connection between dark matter and black hole physics.
Challenges and Opportunities:
While there are exciting opportunities for further research, several challenges must be considered:
- Data Limitations: The current conclusions are based on the M87* shadow data obtained by the EHT collaboration. Expanding the dataset to include more black holes immersed in different dark matter halos would enhance our understanding of these systems, but obtaining such data poses observational challenges.
- Modeling Complex Interactions: Dark matter halos and their interaction with black holes involve complex physical processes. Developing accurate models and simulations to capture these interactions presents a significant challenge. Collaborative efforts between astrophysicists, cosmologists, and specialists in computational modeling will be instrumental in addressing this challenge.
- Multidisciplinary Collaboration: Understanding black holes immersed in dark matter halos requires expertise from various fields, including astrophysics, particle physics, and cosmology. Encouraging multidisciplinary collaboration can lead to novel insights and advances in this complex research domain.
In conclusion, the research on black holes immersed in dark matter halos has provided valuable insights into the nature and properties of these systems. However, much work remains to be done to refine our understanding, explore alternative scenarios, and overcome the challenges involved. With continued research and collaboration, the field holds great potential for unraveling the mysteries of black holes and their relationships with dark matter.
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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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