by jsendak | Jan 21, 2024 | GR & QC Articles
Two novel topological black hole exact solutions with unusual shapes of
horizons in the simplest holographic axions model, the four-dimensional
Einstein-Maxwell-axions theory, are constructed. We draw embedding diagrams in
various situations to display unusual shapes of novel black holes. To
understand their thermodynamics from the quasi-local aspect, we re-derive the
unified first law and the Misner-Sharp mass from the Einstein equations for the
spacetime as a warped product $M2 times Mco2$. The Ricci scalar $Rhat$ of
the sub-manifold $Mco2$ can be a non-constant. We further improve the
thermodynamics method based on the unified first law. Such a method simplifies
constructing solutions and hints at generalization to higher dimensions.
Moreover, we apply the unified first law to discuss black hole thermodynamics.
Examine the conclusions of the following text and outline a future roadmap for readers, indicating potential challenges and opportunities on the horizon.
Two novel topological black hole exact solutions with unusual shapes of horizons have been constructed in the simplest holographic axions model, specifically in the four-dimensional Einstein-Maxwell-axions theory. The article presents embedding diagrams in various situations to display the unusual shapes of these novel black holes. Additionally, the thermodynamics of these black holes is explored from a quasi-local aspect, involving the re-derivation of the unified first law and the Misner-Sharp mass from the Einstein equations for the spacetime as a warped product $M2 times Mco2$. Notably, it is observed that the Ricci scalar $Rhat$ of the sub-manifold $Mco2$ can be non-constant. Furthermore, an improved thermodynamics method is proposed based on the unified first law, demonstrating its potential to simplify the construction of solutions and suggesting its applicability to higher dimensions. Lastly, the unified first law is applied to discuss black hole thermodynamics.
Future Roadmap
As we look to the future, there are several potential challenges and opportunities on the horizon. Here is a suggested roadmap for readers:
- Further Study of Novel Black Hole Solutions: Researchers should conduct further study and exploration of the constructed novel black hole solutions. Analyzing their properties, behavior, and implications could provide valuable insights into the nature of black holes and their role in the holographic axions model.
- Investigation of Unusual Horizon Shapes: The unusual shapes of the black hole horizons presented in this article warrant further investigation. Researchers can delve deeper into understanding the factors influencing these shapes and their significance in the context of black hole physics and the holographic axions model. Exploring the connection between horizon shapes and other physical properties could be a promising avenue of research.
- Refinement of Thermodynamics Method: The proposed improved thermodynamics method based on the unified first law presents an opportunity for refinement and enhancement. Researchers can fine-tune and optimize the method to make it even more effective in constructing solutions and analyzing black hole thermodynamics. Additionally, applying this method to other models and dimensions could provide valuable comparisons and insights.
- Generalization to Higher Dimensions: The hint at generalization to higher dimensions opens up a new dimension of research. Investigating the applicability and implications of the unified first law and the constructed solutions in higher-dimensional spacetimes could contribute to the understanding of black holes in a broader context.
- Exploration of Non-constant Ricci Scalar: The observation that the Ricci scalar $Rhat$ of the sub-manifold $Mco2$ can be non-constant raises intriguing questions. Future research should aim to understand the implications and consequences of this non-constancy, exploring its relationship with other geometric and physical properties. Investigating whether this phenomenon exists in other models or scenarios could shed further light on its significance.
- Application to Other Areas: Building upon the insights gained from studying these novel black hole solutions and the improved thermodynamics method, researchers can explore potential applications in other areas of physics. Investigating whether similar techniques and concepts can be applied to different phenomena or theories could open up new avenues of research and discovery.
In conclusion, this article presents two novel black hole solutions with unusual horizon shapes, along with an improved thermodynamics method based on the unified first law. The roadmap outlined above outlines potential future directions for research, including further studying the black hole solutions, refining the thermodynamics method, exploring higher dimensions and non-constant Ricci scalars, and seeking applications in other physics domains.
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by jsendak | Jan 21, 2024 | GR & QC Articles
We discuss gauge theories of scale invariance beyond the Standard Model (SM)
and Einstein gravity. A consequence of gauging this symmetry is that their
underlying 4D geometry is non-metric ($nabla_mu g_{alphabeta}not=0$).
Examples of such theories are Weyl’s {it original} quadratic gravity theory
and its Palatini version. These theories have spontaneous breaking of the
gauged scale symmetry to Einstein gravity. All mass scales have a geometric
origin: the Planck scale ($M_p$), cosmological constant ($Lambda$) and the
mass of the Weyl gauge boson ($omega_mu$) of scale symmetry are proportional
to a scalar field vev that has an origin in the (geometric) $tilde R^2$ term
in the action. With $omega_mu$ of non-metric geometry origin, the SM Higgs
field also has a similar origin, generated by Weyl boson fusion in the early
Universe. This appears as a microscopic realisation of “matter creation from
geometry” discussed in the thermodynamics of open systems applied to cosmology.
Unlike in local scale invariant theories (no $omega_mu$ present) with an
underlying pseudo-Riemannian geometry, in our case: 1) there are no ghosts and
no additional fields beyond the SM and underlying Weyl or Palatini geometry, 2)
the cosmological constant is positive and is small because gravity is weak, 3)
the Weyl or Palatini connection shares the Weyl (gauge) symmetry of the action,
and: 4) there exists a non-trivial, conserved Weyl current of this symmetry. An
intuitive picture of non-metricity and its relation to mass generation is also
provided from a solid state physics perspective where it is common and is
associated with point defects (metric anomalies) of the crystalline structure.
Gauge Theories of Scale Invariance Beyond the Standard Model
In this article, we explore gauge theories of scale invariance beyond the Standard Model (SM) and Einstein gravity. These theories have a non-metric 4D geometry, meaning that the connection between the metric tensor and covariant derivative is non-zero.
Examples of Non-Metric Gauge Theories
Two examples of these theories are Weyl’s original quadratic gravity theory and its Palatini version. In these theories, the gauged scale symmetry is spontaneously broken, resulting in Einstein gravity. The mass scales in these theories, such as the Planck scale (Mp), cosmological constant (Λ), and the mass of the Weyl gauge boson (ωμ), are proportional to a scalar field vev originating from the geometric R^2 term in the action.
Origin of SM Higgs Field
In addition to the non-metricity originating from ωμ, the Standard Model Higgs field also has a similar origin. It is generated through Weyl boson fusion in the early Universe, providing a microscopic realization of “matter creation from geometry” discussed in thermodynamics of open systems applied to cosmology.
Key Features of Non-Metric Gauge Theories
Unlike local scale invariant theories without ωμ, the theories discussed here have several key features:
- No ghosts or additional fields beyond the SM and underlying Weyl or Palatini geometry.
- The cosmological constant is positive and small due to the weak gravity.
- The Weyl or Palatini connection shares the Weyl (gauge) symmetry of the action.
- There exists a non-trivial, conserved Weyl current associated with this symmetry.
Understanding Non-Metricity from a Solid State Physics Perspective
An intuitive understanding of non-metricity and its relation to mass generation can be gained from a solid state physics perspective. Non-metricity is common in solid state physics and is associated with point defects (metric anomalies) in the crystalline structure.
Future Roadmap for Readers
As our understanding of gauge theories of scale invariance beyond the Standard Model and Einstein gravity continues to evolve, several challenges and opportunities lie ahead:
- Further Theoretical Developments: Researchers can explore and develop new theoretical frameworks for understanding non-metric gauge theories and their implications for fundamental physics.
- Experimental Validation: Experimental tests and observations are needed to validate the predictions and implications of these gauge theories. This could involve particle physics experiments, cosmological observations, and precision measurements.
- Interdisciplinary Collaboration: Collaboration between physicists and solid-state researchers can lead to a deeper understanding of the connection between non-metricity and mass generation, potentially uncovering new phenomena and applications in both fields.
- Practical Applications: Insights from non-metric gauge theories could have practical applications beyond fundamental physics, such as in materials science, condensed matter physics, and quantum computing.
In summary, the study of gauge theories of scale invariance beyond the Standard Model and Einstein gravity opens up exciting possibilities for advancing our understanding of fundamental physics. While there are challenges to overcome, the potential for theoretical breakthroughs, experimental discoveries, interdisciplinary collaboration, and practical applications makes this field ripe with opportunities.
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by jsendak | Jan 21, 2024 | GR & QC Articles
We study the statistics of scalar perturbations in models of inflation with
small and rapid oscillations in the inflaton potential (resonant
non-Gaussianity). We do so by deriving the wavefunction
$Psi[zeta(boldsymbol{x})]$ non-perturbatively in $zeta$, but at first order
in the amplitude of the oscillations. The expression of the wavefunction of the
universe (WFU) is explicit and does not require solving partial differential
equations. One finds qualitative deviations from perturbation theory for $
|zeta| gtrsim alpha^{-2}$, where $alpha gg 1$ is the number of
oscillations per Hubble time. Notably, the WFU exhibits distinct behaviours for
negative and positive values of $zeta$ (troughs and peaks respectively). While
corrections for $zeta <0$ remain relatively small, of the order of the
oscillation amplitude, positive $zeta$ yields substantial effects, growing
exponentially as $e^{pialpha/2}$ in the limit of large $zeta$. This
indicates that even minute oscillations give large effects on the tail of the
distribution.
Text:
We study the statistics of scalar perturbations in models of inflation with small and rapid oscillations in the inflaton potential (resonant non-Gaussianity). We do so by deriving the wavefunction Ψ[ζ(x)] non-perturbatively in ζ, but at first order in the amplitude of the oscillations. The expression of the wavefunction of the universe (WFU) is explicit and does not require solving partial differential equations. One finds qualitative deviations from perturbation theory for |ζ| ≳ α⁻², where α ≫ 1 is the number of oscillations per Hubble time. Notably, the WFU exhibits distinct behaviors for negative and positive values of ζ (troughs and peaks respectively). While corrections for ζ < 0 remain relatively small, of the order of the oscillation amplitude, positive ζ yields substantial effects, growing exponentially as e^(πα/2) in the limit of large ζ. This indicates that even minute oscillations give large effects on the tail of the distribution.
Conclusions:
- Scalar perturbations in models of inflation with small and rapid oscillations in the inflaton potential exhibit qualitative deviations from perturbation theory for |ζ| ≳ α⁻².
- The wavefunction of the universe (WFU) has explicit expression and does not require solving partial differential equations.
- The WFU exhibits distinct behaviors for negative and positive values of ζ, with troughs and peaks respectively.
- Corrections for negative ζ are relatively small compared to positive ζ.
- Positive ζ yields substantial effects, growing exponentially as e^(πα/2) in the limit of large ζ.
- Even minute oscillations have large effects on the tail of the distribution.
Future Roadmap:
The study of scalar perturbations in models of inflation with small and rapid oscillations in the inflaton potential opens up new directions for research. Here are some potential challenges and opportunities on the horizon:
1. Further Investigation of Non-Perturbative Analysis:
The non-perturbative analysis of the wavefunction Ψ[ζ(x)] provides valuable insights into the statistics of scalar perturbations. Future research should focus on refining and expanding this analysis. By studying higher orders in the amplitude of the oscillations, a more comprehensive understanding of the effects of rapid oscillations can be gained.
2. Exploring the Physical Implications:
The distinct behaviors of the wavefunction of the universe for negative and positive values of ζ have important physical implications. Further investigation is needed to understand the underlying mechanisms that give rise to these behaviors and their consequences for the evolution of the universe. This could lead to new insights into the nature of inflation and its implications for cosmology.
3. Experimental Validation:
Experimental validation of the theoretical predictions is crucial to confirm the findings of this study. Future experiments focusing on measuring and characterizing scalar perturbations in models with small and rapid oscillations can provide valuable data to compare with the theoretical predictions. This could involve observations from cosmological probes or laboratory experiments that simulate inflationary scenarios.
4. Implications for Cosmological Observations:
The substantial effects of positive ζ on the tail of the distribution have implications for cosmological observations. Future research should investigate the impact of these effects on observables such as the cosmic microwave background radiation and large-scale structure formation. This could lead to new ways of interpreting observational data and refining our understanding of the early universe.
5. Exploring Generalizations:
The study focused on models of inflation with small and rapid oscillations in the inflaton potential. It would be interesting to explore the applicability of the non-perturbative analysis to other inflationary models or even beyond inflationary cosmology. Investigating the effects of different potential shapes or additional fields could provide valuable insights into the broader implications of the findings.
6. Theoretical Developments:
Building upon the explicit expression of the wavefunction of the universe obtained in this study, further theoretical developments can be pursued. This could involve exploring connections with other areas of physics, such as quantum gravity or string theory. Additionally, investigations into possible connections between resonant non-Gaussianity and other cosmological phenomena, such as primordial black holes or gravitational waves, could yield interesting results.
Overall, the study of scalar perturbations in models of inflation with small and rapid oscillations in the inflaton potential has opened up exciting avenues for future research. By further investigating the non-perturbative analysis, exploring the physical implications, validating the theoretical predictions through experiments, studying the impact on cosmological observations, exploring generalizations, and pursuing theoretical developments, we can deepen our understanding of inflationary cosmology and its implications for the early universe.
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by jsendak | Jan 21, 2024 | GR & QC Articles
The Cosmic microwave background (CMB) anisotropies predicted by two
cosmological models are compared, one of them is the standard model of general
relativity with cold dark matter and cosmological constant, whereas the second
model is based on a consistent vector-tensor theory of gravitation explaining
solar system and cosmological observations. It is proved that the resulting
differences — between the anisotropies of both models — are due to the
so-called late integrated Sachs Wolfe effect and, consequently, cross
correlations between maps of CMB temperatures and tracers of the dark matter
distribution could be used in future to select one of the above models. The
role of reionization is analysed in detail.
Examining the Conclusions of the Text
The article compares the predictions of two cosmological models: the standard model of general relativity with cold dark matter and a cosmological constant, and a model based on a vector-tensor theory of gravitation. The comparison focuses on the anisotropies of the Cosmic Microwave Background (CMB).
It is demonstrated that the differences in anisotropies between the two models arise from the late integrated Sachs-Wolfe effect. This effect can be understood as the interaction between CMB photons and the changing gravitational potential of the matter distribution in the universe. By analyzing cross-correlations between maps of CMB temperatures and tracers of dark matter distribution, it may be possible to distinguish between the two cosmological models.
The role of reionization, the process through which neutral hydrogen in the early universe becomes ionized, is also examined in detail. Reionization has a significant impact on the CMB anisotropies and is an important factor to consider when studying cosmological models.
Future Roadmap: Challenges and Opportunities
Roadmap for Readers:
- Understanding the standard model of general relativity with cold dark matter and a cosmological constant as one of the compared cosmological models.
- Exploring the vector-tensor theory of gravitation as an alternative model and its explanations for solar system and cosmological observations.
- Learning about the late integrated Sachs-Wolfe effect and its role in creating differences in CMB anisotropies between the two models.
- Investigating how cross-correlations between CMB temperature maps and tracers of dark matter distribution can be utilized to select one of the models.
- Examining the importance of reionization and its impact on CMB anisotropies in relation to the cosmological models.
Potential Challenges:
- Understanding the complexities of general relativity and the vector-tensor theory of gravitation.
- Grasping the mathematical concepts related to the late integrated Sachs-Wolfe effect and cross-correlations analysis.
- Keeping up with advancements and updates in observational techniques for mapping CMB temperatures.
- Staying informed about current research on reionization and its effects on the CMB anisotropies.
Potential Opportunities:
- Contributing to the selection of a more accurate cosmological model through analysis of cross-correlations between CMB temperature maps and dark matter tracers.
- Exploring the potential implications of verifying one model over the other for our understanding of the universe’s composition and expansion.
- Participating in ongoing research and discussions surrounding reionization and its impact on the CMB.
- Engaging with the scientific community and academic institutions to stay updated on advancements in cosmology and gravitational theories.
Conclusion:
By studying the differences in CMB anisotropies between the standard model of general relativity with cold dark matter and a cosmological constant, and a vector-tensor theory of gravitation, researchers aim to make progress in selecting the most accurate cosmological model. The late integrated Sachs-Wolfe effect and cross-correlations analysis between CMB temperature maps and dark matter tracers play crucial roles in this endeavor. Additionally, understanding the impact of reionization on the CMB will contribute to further advancements in our understanding of the universe. While challenges exist in comprehending complex theories and keeping up with cutting-edge research, opportunities for contributing to cosmological knowledge and engaging with the scientific community abound.
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by jsendak | Jan 21, 2024 | GR & QC Articles
We investigate symmetric Metric-Affine Theories of Gravity with a Lagrangian
containing all operators of dimension up to four that are relevant to free
propagation in flat space. Complementing recent work in the antisymmetric case,
we derive the conditions for the existence of a single massive particle with
good properties, in addition to the graviton.
Future Roadmap – Symmetric Metric-Affine Theories of Gravity
Future Roadmap – Symmetric Metric-Affine Theories of Gravity
In this article, we have examined the conclusions of our investigation into symmetric Metric-Affine Theories of Gravity with a Lagrangian that contains relevant operators of dimension up to four for free propagation in flat space. Building upon recent work in the antisymmetric case, we have derived conditions for the existence of a single massive particle in addition to the graviton with good properties.
Potential Challenges on the Horizon
- Theoretical Complexity: One potential challenge is dealing with the theoretical complexity involved in studying and understanding Metric-Affine Theories of Gravity. As we delve deeper into the subject, it may become more intricate, requiring advanced mathematical tools and techniques.
- Empirical Validation: Another challenge lies in the empirical validation of the derived conditions and predictions. Conducting experiments and gathering observational data to support the existence of a single massive particle and its properties can be a time-consuming and resource-intensive process.
- Integration with Existing Theories: Integrating the findings of symmetric Metric-Affine Theories of Gravity with other established theories, such as General Relativity, could present challenges in terms of consistency and compatibility.
Potential Opportunities on the Horizon
- Advancing Fundamental Understanding: Exploring symmetric Metric-Affine Theories of Gravity can contribute to advancing our fundamental understanding of the nature of gravity and the universe at large.
- Extension of Theoretical Frameworks: The derived conditions and properties of the single massive particle could enhance existing theoretical frameworks by providing new perspectives and insights into the behavior of gravitational interactions.
- Potential Technological Applications: The discoveries and advancements in gravitational theories can potentially lead to technological applications, such as improved space navigation systems, advanced propulsion methods, or better gravitational wave detection technologies.
Conclusion: The study of symmetric Metric-Affine Theories of Gravity has provided us with insights into the conditions for the existence of a single massive particle alongside the graviton. While challenges related to theoretical complexity, empirical validation, and integration with existing theories lie ahead, the opportunities for advancing our understanding, extending theoretical frameworks, and potential technological applications are promising. Further research and collaboration are required to fully explore and unlock the potential of these discoveries.
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by jsendak | Jan 21, 2024 | GR & QC Articles
We investigate quasitopological black holes in $(2+1)$ dimensions in the
context of electromagnetic-generalized-quasitopological-gravities (EM-GQT). For
three different families of geometries of quasitopological nature, we study the
causal structure and their response to a probe scalar field. To linear order,
we verify that the scalar field evolves stably, decaying in different towers of
quasinormal modes. The studied black holes are either charged geometries
(regular and singular) or a regular Ba~nados-Teitelboim-Zanelli (BTZ)-like
black hole, both coming from the EM-GQT theory characterized by nonminimal
coupling parameters between gravity and a background scalar field. We calculate
the quasinormal modes applying different numerical methods with convergent
results between them. The oscillations demonstrate a very peculiar structure
for charged black holes: in the intermediate and near extremal cases, a
particular scaling arises, similar to that of the rotating BTZ geometry, with
the modes being proportional to the distance between horizons. For the single
horizon black hole solution, we identify the presence of different quasinormal
families by analyzing the features of that spectrum. In all three considered
geometries, no instabilities were found.
Based on our investigation, we have concluded that the quasitopological black holes in $(2+1)$ dimensions in the context of electromagnetic-generalized-quasitopological-gravities (EM-GQT) exhibit stable evolution of a probe scalar field. We have studied three different families of quasitopological geometries and have found that the scalar field decays in different towers of quasinormal modes.
The black holes we have examined can be classified as either charged geometries (regular and singular) or a regular Bañados-Teitelboim-Zanelli (BTZ)-like black hole. These black holes are derived from the EM-GQT theory, which includes nonminimal coupling parameters between gravity and a background scalar field.
In our calculations of the quasinormal modes, we have employed various numerical methods, all yielding convergent results. The oscillations of the modes in charged black holes exhibit a unique structure. In the intermediate and near extremal cases, a scaling proportional to the distance between horizons emerges, similar to that observed in the rotating BTZ geometry.
For the single horizon black hole solution, we have identified the presence of different quasinormal families by analyzing the characteristics of the spectrum. Importantly, we did not find any instabilities in any of the three considered geometries.
Future Roadmap
Challenges:
- Further investigation is needed to understand the causal structure and response of other fields, such as electromagnetic fields, to these quasitopological black holes in EM-GQT theory. The study of other probe fields may reveal additional insights and properties.
- Exploring the thermodynamic properties of these black holes can provide valuable information about their entropy, temperature, and thermodynamic stability. This analysis could involve studying thermodynamic quantities and phase transitions.
- Investigating the stability of these black holes under perturbations beyond linear order could uncover additional behavior and help to determine their long-term evolution.
Opportunities:
- The peculiar scaling observed in the oscillations of charged black holes could lead to new understandings of their underlying physical mechanisms. Further exploration of this scaling effect and its implications may offer insights into the connection between charge and geometry.
- The identification of different quasinormal families in the single horizon black hole solution presents an opportunity for studying the distinct characteristics and dynamics of these families. This information could contribute to a deeper understanding of black hole spectra in general.
- Extending the study to higher dimensions and different theories of gravity could provide valuable comparisons and insights into the behavior of quasitopological black holes across different contexts. Such investigations could include theories with additional matter fields or modified gravity theories.
In conclusion, the examination of quasitopological black holes in $(2+1)$ dimensions in the context of electromagnetic-generalized-quasitopological-gravities (EM-GQT) has revealed stable evolution and unique characteristics. While there are still challenges to address and opportunities to explore, this research lays the foundation for further expanding our understanding of these intriguing black hole solutions.
Reference:
Author(s): [Author names]
Journal: [Journal name]
Published: [Publication date]
DOI: [DOI number]
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