аналитика - Theoretical Physics - # Celestial Holography

Logarithmic Corrections to the Entropy of Flat Space Cosmologies: A One-Loop Calculation from Celestial Holography

Q: How do these findings about logarithmic corrections to entropy in 3D flat space cosmologies inform our understanding of black hole thermodynamics in higher dimensions?

While these findings specifically address 3D flat space cosmologies, their implications for black hole thermodynamics in higher dimensions are not directly evident. Here's why: Dimensional Dependence: The simplicity of 3D gravity, lacking propagating gravitons, makes it a useful toy model. However, this simplicity also means that direct extrapolations to higher dimensions, where gravity is significantly more complex, are not always straightforward. The logarithmic corrections found in this 3D model might not directly translate to similar corrections in higher-dimensional black hole entropy. Asymptotic Flatness vs. AdS/CFT: The study focuses on asymptotically flat spacetimes, while much of our understanding of black hole thermodynamics stems from the AdS/CFT correspondence, which relates black holes in Anti-de Sitter (AdS) space to conformal field theories (CFTs) on the boundary. The AdS/CFT framework provides powerful tools for studying black hole entropy, but its applicability to asymptotically flat spacetimes is still under investigation. Universality of Logarithmic Corrections: Despite these caveats, the presence of logarithmic corrections to entropy in this 3D model hints at a potentially universal feature of quantum gravity. Logarithmic corrections are often associated with quantum effects and could provide valuable insights into the microscopic degrees of freedom responsible for black hole entropy. Further research is needed to determine if similar logarithmic corrections arise in higher-dimensional asymptotically flat spacetimes and if they can be connected to the microscopic origin of black hole entropy.

Q: Could the presence of these logarithmic corrections be an artifact of the specific duality used, or do they point to a more fundamental aspect of quantum gravity in asymptotically flat spacetimes?

It's difficult to definitively claim whether these logarithmic corrections are purely artifacts of the specific celestial holography duality used or represent a more fundamental aspect of quantum gravity in asymptotically flat spacetimes. Here's a balanced perspective: Arguments for a Duality Artifact: Specific Model: The corrections arise within a particular 1D celestial holographic dual theory, which itself is an effective description of a simplified 3D gravity model. It's possible that these corrections are specific to the chosen model and might not persist in more general settings. Alternative Dualities: Other holographic dualities, such as those based on 2D Liouville-like theories, might lead to different results for logarithmic corrections. Comparing results from different dualities could help disentangle model-dependent features from more fundamental ones. Arguments for a Fundamental Aspect: Universality of Logarithmic Corrections: Logarithmic corrections to black hole entropy are believed to be universal features of quantum gravity, appearing in various approaches and models. Their presence in this celestial holographic model, even if specific to the model, could still hint at a deeper connection to the quantum nature of gravity. Quantum Fluctuations: The authors attribute the logarithmic corrections to one-loop effects in the path integral, suggesting they arise from quantum fluctuations of the gravitational field. This connection to quantum fluctuations strengthens the argument for a more fundamental origin. Further research is crucial to determine the robustness of these logarithmic corrections across different holographic dualities and their potential connection to the underlying quantum structure of spacetime.

Q: If we consider the universe as a holographic system, what are the implications of these findings for the concept of cosmic entropy and the ultimate fate of the universe?

Considering the universe as a holographic system is a fascinating idea, but directly applying these findings to cosmic entropy and the universe's fate requires caution. Here's why: Cosmological Constant: The study focuses on asymptotically flat spacetimes with zero cosmological constant, while our universe is observed to have a positive cosmological constant, leading to an accelerating expansion. This difference in cosmological constant significantly impacts the large-scale structure and evolution of the universe, making direct comparisons challenging. Global vs. Local Entropy: The findings address the entropy of specific solutions (flat space cosmologies) within 3D gravity. Applying these results to the entire universe, which is vastly more complex and dynamic, requires careful consideration of global entropy contributions from various sources beyond these specific solutions. Speculative Nature: The holographic principle itself, while a compelling idea, remains a conjecture. Connecting specific holographic models to our universe's global properties and ultimate fate involves a high degree of speculation. However, these findings do raise intriguing questions about cosmic entropy: Quantum Corrections to Cosmic Entropy: If the holographic principle holds, could quantum gravitational effects, like those leading to logarithmic corrections in this model, contribute to the universe's total entropy? Entropy Bounds and the Universe's Fate: Holographic entropy bounds suggest limits on the maximum entropy within a given region. Could understanding quantum corrections to entropy in holographic models shed light on the universe's ultimate fate, particularly in scenarios like the "heat death" where entropy reaches a maximum? While these questions remain open, exploring holographic models and their implications for entropy could provide valuable insights into the universe's fundamental nature and evolution.

Основные понятия

This paper calculates the quantum corrections to the entropy of three-dimensional flat space cosmologies using a novel celestial holographic duality, revealing previously unknown logarithmic corrections arising from one-loop effects in the dual theory.

Аннотация

Bibliographic Information: Bhattacharjee, A., Menon, S., & Saha, M. (2024). Logarithmic corrections to entropy of 3D cosmological solutions from celestial dual. arXiv preprint arXiv:2411.05605.
Research Objective: This study aims to compute the logarithmic corrections to the entropy of three-dimensional Flat Space Cosmologies (FSCs) using a celestial holographic description.
Methodology: The authors employ a one-dimensional Schwarzian-like theory proposed as a dual to 3D gravity in asymptotically flat spacetimes. They quantize this dual theory using coadjoint orbit techniques, focusing on the symplectic structure of the BMS3 orbit. This allows them to calculate the one-loop partition function of the theory.
Key Findings: The research reveals that the one-loop partition function of the celestial dual theory contributes novel logarithmic corrections to the entropy of FSCs. These corrections were not accounted for in previous semiclassical analyses.
Main Conclusions: The study demonstrates the significance of considering quantum corrections in celestial holography. The calculated logarithmic corrections to FSC entropy highlight the potential of this approach to provide a more complete understanding of quantum gravity in asymptotically flat spacetimes.
Significance: This work advances the understanding of celestial holography and its application to flat spacetimes. The findings have implications for the study of black hole thermodynamics and the AdS/CFT correspondence in lower dimensions.
Limitations and Future Research: The analysis focuses on the large charge regime of FSCs. Further research could explore the validity of these corrections in other regimes and investigate the connection between these corrections and bulk fluctuations in the gravitational theory.

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Статистика

The Bekenstein-Hawking entropy of a black hole is given by S = A/4G, where A is the area of the event horizon and G is Newton's constant.
In three-dimensional gravity, the central charge of the asymptotic symmetry algebra is related to Newton's constant by c = 3l/2G, where l is the AdS radius.
The entropy of a three-dimensional flat space cosmology is given by S = 2π√(M|J|), where M is the mass and J is the angular momentum.

Цитаты

"Both the area law of entropy and its logarithmic corrections are universal features of gravitational theories [34–38]."
"The main goal of this paper is to extend the analysis of [27] in finding the logarithmic corrections to the entropy of FSC solutions from the celestial side."
"Our analysis results in novel logarithmic corrections to the entropy of FSC solutions, which come from the one-loop partition function."

Ключевые выводы из

Logarithmic corrections to entropy of 3D cosmological solutions from celestial dual

by Arindam Bhat... в arxiv.org 11-11-2024

https://arxiv.org/pdf/2411.05605.pdf

Logarithmic corrections to entropy of 3D cosmological solutions from celestial dual

Дополнительные вопросы

How do these findings about logarithmic corrections to entropy in 3D flat space cosmologies inform our understanding of black hole thermodynamics in higher dimensions?

While these findings specifically address 3D flat space cosmologies, their implications for black hole thermodynamics in higher dimensions are not directly evident. Here's why:

Dimensional Dependence: The simplicity of 3D gravity, lacking propagating gravitons, makes it a useful toy model. However, this simplicity also means that direct extrapolations to higher dimensions, where gravity is significantly more complex, are not always straightforward. The logarithmic corrections found in this 3D model might not directly translate to similar corrections in higher-dimensional black hole entropy.

Asymptotic Flatness vs. AdS/CFT: The study focuses on asymptotically flat spacetimes, while much of our understanding of black hole thermodynamics stems from the AdS/CFT correspondence, which relates black holes in Anti-de Sitter (AdS) space to conformal field theories (CFTs) on the boundary. The AdS/CFT framework provides powerful tools for studying black hole entropy, but its applicability to asymptotically flat spacetimes is still under investigation.

Universality of Logarithmic Corrections: Despite these caveats, the presence of logarithmic corrections to entropy in this 3D model hints at a potentially universal feature of quantum gravity. Logarithmic corrections are often associated with quantum effects and could provide valuable insights into the microscopic degrees of freedom responsible for black hole entropy.
Further research is needed to determine if similar logarithmic corrections arise in higher-dimensional asymptotically flat spacetimes and if they can be connected to the microscopic origin of black hole entropy.

Could the presence of these logarithmic corrections be an artifact of the specific duality used, or do they point to a more fundamental aspect of quantum gravity in asymptotically flat spacetimes?

It's difficult to definitively claim whether these logarithmic corrections are purely artifacts of the specific celestial holography duality used or represent a more fundamental aspect of quantum gravity in asymptotically flat spacetimes. Here's a balanced perspective:
Arguments for a Duality Artifact:

Specific Model: The corrections arise within a particular 1D celestial holographic dual theory, which itself is an effective description of a simplified 3D gravity model. It's possible that these corrections are specific to the chosen model and might not persist in more general settings.

Alternative Dualities: Other holographic dualities, such as those based on 2D Liouville-like theories, might lead to different results for logarithmic corrections. Comparing results from different dualities could help disentangle model-dependent features from more fundamental ones.
Arguments for a Fundamental Aspect:

Universality of Logarithmic Corrections: Logarithmic corrections to black hole entropy are believed to be universal features of quantum gravity, appearing in various approaches and models. Their presence in this celestial holographic model, even if specific to the model, could still hint at a deeper connection to the quantum nature of gravity.

Quantum Fluctuations: The authors attribute the logarithmic corrections to one-loop effects in the path integral, suggesting they arise from quantum fluctuations of the gravitational field. This connection to quantum fluctuations strengthens the argument for a more fundamental origin.
Further research is crucial to determine the robustness of these logarithmic corrections across different holographic dualities and their potential connection to the underlying quantum structure of spacetime.

If we consider the universe as a holographic system, what are the implications of these findings for the concept of cosmic entropy and the ultimate fate of the universe?

Considering the universe as a holographic system is a fascinating idea, but directly applying these findings to cosmic entropy and the universe's fate requires caution. Here's why:

Cosmological Constant: The study focuses on asymptotically flat spacetimes with zero cosmological constant, while our universe is observed to have a positive cosmological constant, leading to an accelerating expansion. This difference in cosmological constant significantly impacts the large-scale structure and evolution of the universe, making direct comparisons challenging.

Global vs. Local Entropy: The findings address the entropy of specific solutions (flat space cosmologies) within 3D gravity. Applying these results to the entire universe, which is vastly more complex and dynamic, requires careful consideration of global entropy contributions from various sources beyond these specific solutions.

Speculative Nature: The holographic principle itself, while a compelling idea, remains a conjecture. Connecting specific holographic models to our universe's global properties and ultimate fate involves a high degree of speculation.
However, these findings do raise intriguing questions about cosmic entropy:

Quantum Corrections to Cosmic Entropy: If the holographic principle holds, could quantum gravitational effects, like those leading to logarithmic corrections in this model, contribute to the universe's total entropy?

Entropy Bounds and the Universe's Fate: Holographic entropy bounds suggest limits on the maximum entropy within a given region. Could understanding quantum corrections to entropy in holographic models shed light on the universe's ultimate fate, particularly in scenarios like the "heat death" where entropy reaches a maximum?
While these questions remain open, exploring holographic models and their implications for entropy could provide valuable insights into the universe's fundamental nature and evolution.