Gravitational Collapse in Asymptotically Safe and Scale-Dependent Gravity: Exploring the Oppenheimer-Snyder Model

Core Concepts

This paper investigates the Oppenheimer-Snyder (OS) gravitational collapse model within the frameworks of both asymptotically safe gravity (ASG) and scale-dependent gravity (SDG), revealing distinct collapse behaviors and singularity characteristics depending on the chosen gravity theory.

Abstract

• Bibliographic Information: Hassannejad, R., Lambiase, G., Scardigli, F., & Shojai, F. (2024). Gravitational Collapse in Scale-Dependent Gravity. arXiv preprint arXiv:2410.15904v1.

• Research Objective: This paper aims to study the classical gravitational collapse of a spherically symmetric star within the frameworks of asymptotically safe gravity (ASG) and scale-dependent gravity (SDG), focusing on the Oppenheimer-Snyder (OS) model.

• Methodology: The authors employ a theoretical approach, utilizing the effective average action and the running Newton constant concepts from ASG and SDG. They model the collapsing star with a spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) metric for the interior and a spherically symmetric solution of AS/SD gravity for the exterior. The Israel junction conditions are applied to ensure a smooth transition between the interior and exterior geometries.

• Key Findings:

  • The collapse behavior differs significantly depending on the value of the ˜ω parameter, which characterizes the scale dependence of gravity.
  • For ˜ω > 0 (ASG), the metric is singularity-free, and the star's surface takes an infinite proper time to reach the center.
  • For ˜ω = 0 (Schwarzschild case), the collapse mirrors the classic OS model, with the star's surface hitting the central singularity in a finite proper time.
  • For ˜ω < 0 (SDG), the collapse also occurs in finite proper time, but the singularity is located at a finite positive radial coordinate, leading to a finite volume for the "forbidden region."

• Main Conclusions:

  • The study highlights the distinct characteristics of gravitational collapse in ASG and SDG compared to general relativity.
  • The presence or absence of singularities and the time taken for collapse are significantly influenced by the scale dependence of gravity.
  • The findings have implications for understanding the final stages of stellar evolution and the nature of black holes in modified theories of gravity.

• Significance: This research contributes to the ongoing exploration of modified gravity theories and their implications for astrophysical phenomena like gravitational collapse and black hole formation. It provides insights into the potential role of scale dependence in shaping the dynamics of gravity at high-energy scales.

• Limitations and Future Research: The study focuses on a simplified model of a spherically symmetric, homogeneous star. Future research could explore more realistic scenarios with deviations from spherical symmetry and varying matter distributions. Further investigation into the nature and implications of the finite-volume "forbidden region" in the SDG case is also warranted.

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Key Insights Distilled From

Gravitational Collapse in Scale-Dependent Gravity

by Ramin Hassan... at arxiv.org 10-22-2024

https://arxiv.org/pdf/2410.15904.pdf

Deeper Inquiries

How would the inclusion of angular momentum affect the collapse dynamics in ASG and SDG?

Incorporating angular momentum into the dynamics of gravitational collapse within the frameworks of Asymptotically Safe Gravity (ASG) and Scale-Dependent Gravity (SDG) introduces significant complexities and intriguing possibilities. Let's break down the potential implications:
1. Departure from Spherical Symmetry:

The inclusion of angular momentum inherently breaks the spherical symmetry that simplifies the Oppenheimer-Snyder (OS) model. We would need to transition from a spherically symmetric metric like (9) to a more general axisymmetric metric, such as the Kerr metric or its ASG/SDG counterparts.
2. Formation of an Ergosphere:

Rotating black holes, described by metrics like the Kerr metric, possess an ergosphere, a region outside the event horizon where spacetime is dragged along with the black hole's rotation. Investigating the existence and properties of an ergosphere in rotating ASG/SDG black holes would be crucial.
3. Impact on Horizon Structure:

Angular momentum modifies the structure of black hole horizons. Instead of a single event horizon, rotating black holes typically have an outer event horizon and an inner Cauchy horizon. The stability of these horizons in ASG/SDG, especially considering the potential for singularity avoidance, would be a key area of study.
4. Centrifugal Effects and Collapse Dynamics:

The centrifugal force arising from angular momentum would counteract the inward pull of gravity. This could potentially alter the collapse dynamics, potentially slowing down or even halting the collapse depending on the balance between gravity and centrifugal forces.
5. Implications for Singularity Resolution:

A fascinating question is whether the presence of angular momentum could modify the singularity resolution mechanisms proposed in ASG and SDG. Could rotation provide an additional repulsive force that further prevents singularity formation?
6. Challenges and Research Directions:

Finding analytical solutions for rotating black holes in ASG/SDG is likely to be highly challenging. Numerical simulations and approximations would be essential tools for investigating these scenarios.
Exploring the impact of angular momentum on the Hawking radiation and thermodynamics of ASG/SDG black holes would be another avenue for future research.
In summary, incorporating angular momentum into ASG and SDG models of gravitational collapse opens up a rich landscape of possibilities, with the potential to reveal novel insights into black hole physics and quantum gravity.

Could the finite volume "forbidden region" in SDG offer any insights into the information paradox?

The presence of a finite volume "forbidden region" in Scale-Dependent Gravity (SDG), as depicted in Figure 4, presents an intriguing aspect of black hole physics that might offer subtle clues regarding the information paradox. Here's a breakdown of potential connections:
1. Information Storage and Retrieval:

The information paradox stems from the apparent conflict between the principles of quantum mechanics (information conservation) and the classical picture of black hole evaporation.
The finite volume "forbidden region" in SDG could, in principle, serve as a reservoir for information. Unlike the point-like singularity in classical general relativity, this extended region might allow for more complex information storage mechanisms.
2. Quantum Gravity Effects:

SDG, as an approach to quantum gravity, suggests that the nature of spacetime and gravity is modified at high energy scales, such as those found near a black hole singularity.
The "forbidden region," characterized by strong gravity and potentially modified spacetime, could be a domain where quantum gravity effects become significant, potentially influencing information processing.
3. Horizon Remnants and Information Encoding:

Some proposed resolutions to the information paradox involve the idea of black hole remnants, objects left behind after evaporation that retain information.
The "forbidden region," if it persists in some form even after the black hole evaporates, could potentially act as a remnant, encoding information about the collapsed matter.
4. Challenges and Speculative Nature:

It's crucial to emphasize that these connections are highly speculative at this stage. The precise nature of the "forbidden region" in SDG and its implications for information storage and retrieval require further investigation.
Understanding how information could be encoded within this region and potentially accessed by external observers would be central to addressing the information paradox.
In conclusion, while the finite volume "forbidden region" in SDG doesn't provide a definitive solution to the information paradox, it introduces a novel structural feature that could potentially play a role in information storage and processing near black hole singularities. Further research is needed to explore these possibilities more concretely.

What are the observational signatures that could distinguish between gravitational collapse in general relativity, ASG, and SDG?

Differentiating between gravitational collapse scenarios predicted by General Relativity (GR), Asymptotically Safe Gravity (ASG), and Scale-Dependent Gravity (SDG) poses a significant observational challenge. However, subtle distinctions in the dynamics of collapse and the properties of the resulting objects could provide crucial clues. Here are some potential observational signatures:
1. Time Scales of Collapse:

GR: In classical GR, the collapse of a sufficiently massive object to a black hole occurs in a finite amount of proper time for an observer comoving with the collapsing matter.
ASG: For ASG with ˜ω > 0, the collapse to a singularity-free object might take an infinite amount of proper time, as suggested by the asymptotic behavior in equation (37).
SDG: SDG with ˜ω < 0 predicts a finite proper time collapse, similar to GR, but with the singularity located at a finite radius.
Observational Implication: Observing extremely slow or halted collapses of compact objects could hint at deviations from GR and potentially favor ASG-like scenarios.
2. Gravitational Wave Signatures:

GR: The precise waveforms of gravitational waves emitted during black hole mergers in GR are well-studied.
ASG/SDG: Deviations from GR in the strong gravity regime near merging compact objects in ASG or SDG could lead to subtle differences in the emitted gravitational wave signals.
Observational Implication: High-precision gravitational wave astronomy with future detectors might be able to detect these minute discrepancies, providing evidence for or against modified gravity theories.
3. Black Hole Shadows:

GR: The Event Horizon Telescope has provided images of black hole shadows, regions of darkness silhouetted against a bright background. The size and shape of these shadows are consistent with GR predictions.
ASG/SDG: The presence of modified gravity effects in ASG or SDG could alter the trajectories of photons near black holes, potentially leading to observable differences in the size, shape, or even the presence of multiple shadows.
Observational Implication: Continued observations and analysis of black hole shadows with increased resolution could reveal deviations from GR predictions.
4. Absence of Singularities:

ASG: A key feature of ASG is the potential avoidance of singularities.
Observational Implication: Directly observing the absence of a singularity, perhaps through the detection of specific radiation signatures or other unique phenomena associated with a singularity-free object, would be strong evidence in favor of ASG.
5. Quantum Gravity Effects:

Both ASG and SDG are approaches to quantum gravity.
Observational Implication: Observing any phenomena near black holes or other extreme gravity environments that cannot be explained by classical GR but are consistent with predictions from quantum gravity theories would be groundbreaking.
Challenges and Future Prospects:

Distinguishing between these subtle observational signatures will require extremely precise measurements and advanced data analysis techniques.
The next generation of telescopes, gravitational wave detectors, and other astronomical instruments will be crucial for pushing the boundaries of our observational capabilities and potentially uncovering evidence for modified gravity theories like ASG and SDG.