Critique of "Non-local Gravitational Corrections in Black Hole Shadow Images" by Alexeyev et al.

Core Concepts

The paper by Alexeyev et al. claiming to find differences in black hole shadows due to "quantum" corrections is flawed, as it fails to rigorously prove its key assumptions and ignores more significant astrophysical factors.

Abstract

This article is a comment on a research paper titled "Non-local Gravitational Corrections in Black Hole Shadow Images" by Alexeyev et al. The author, Alexander F. Zakharov, critiques Alexeyev et al.'s paper on several grounds.

Summary of Critique:

• Unproven Assumptions: Zakharov argues that Alexeyev et al. base their conclusions on the unproven assumption that the motion parameters of circular photon orbits determine the shadow boundary in their "quantum" black hole model. They fail to generalize established principles for Kerr black holes to their specific model.
• Neglect of Astrophysical Factors: The paper focuses on exaggerating "quantum" corrections while neglecting significant astrophysical factors like spatial mass distribution and plasma effects. These factors, according to Zakharov, have a far greater influence on shadow shape and size than the "quantum" corrections considered.
• Overstating Novelty: Zakharov points out that Alexeyev et al. discuss properties of black hole shadows (like shape changes and size in the spin direction) as if they were novel findings. However, these properties have been known and discussed in the literature for at least 20 years, as evidenced by Zakharov's own earlier work (Zakharov, 2005).
• Lack of Observational Context: Zakharov criticizes the paper for lacking a connection to real-world astronomical observations. He emphasizes that theoretical discussions about "quantum" black holes should consider the feasibility of detecting such minute corrections given the limitations of current observational techniques.

Zakharov's Contributions:

Zakharov highlights his own contributions to the field, emphasizing his 2005 paper (Zakharov, 2005) where he:

• Predicted the possibility of reconstructing the shadow of a black hole at the Galactic Center using Very Long Baseline Interferometry (VLBI).
• This prediction was later confirmed by the Event Horizon Telescope (EHT) collaboration, which successfully imaged the black hole at the center of the Milky Way galaxy.

Conclusion:

Zakharov concludes that while Alexeyev et al.'s paper might offer some theoretical insights, it lacks rigor in its assumptions and overlooks crucial astrophysical realities. He emphasizes the importance of grounding theoretical explorations in observational possibilities and acknowledging prior work in the field.

Stats

The shadow size of Sgr A* is about 50 angular microseconds.
The angular resolution of Radioastron at the shortest wavelength of 1.3 cm was on the order of 7 angular microseconds.
The maximum value of the function η(ξ) is 27 and is taken at the value ξ = 2a, i.e., η(2a) = 27.
The maximum value of the function β(α) is 3√3 and is taken at the value α = 2a.
The size of the shadow in the direction of rotation of the black hole in the case of the equatorial position of the distant observer does not depend on the value of the spin.
The size of the black hole's shadow in the spin direction does not depend on spin and is equal to 2√27M.

Quotes

"Thus, for the Kerr metric, the shape and size of the shadow is determined by these critical parameter values (as shown in [3])."
"In paper [3] it is shown that for a classical Kerr black hole in the case of the observer’s position in the equatorial plane, the size of the shadow in the direction of the black hole’s rotation does not depend on the spin of the black hole."
"The possibility of reconstructing the shadow of a black hole at the Galactic Center using global ground-space (and ground-based) interferometers operating in the mm band was firstly proposed in [3] that was not mentioned in [1]."

Key Insights Distilled From

Comment on the article "Non-local gravitational corrections in black hole shadow images" by S. O. Alexeyev et al

by Alexander F.... at arxiv.org 10-17-2024

https://arxiv.org/pdf/2410.11898.pdf

Deeper Inquiries

How might future advancements in observational astronomy, particularly in interferometry, further refine our understanding of black hole shadows and potentially validate or refute the impact of "quantum" corrections?

Future advancements in observational astronomy, especially in the realm of interferometry, hold immense potential to revolutionize our understanding of black hole shadows and could potentially confirm or challenge the presence of "quantum" corrections. Here's how:

Increased Angular Resolution and Sensitivity: Next-generation interferometers like the next generation Event Horizon Telescope (ngEHT) aim to significantly enhance both angular resolution and sensitivity. This will enable us to probe the fine details of black hole shadows with unprecedented clarity. Detecting subtle deviations from the predictions of classical general relativity, as proposed by Alexeyev et al., would require this level of precision.
Broader Wavelength Coverage: Expanding observations to encompass a wider range of wavelengths, from the infrared to the submillimeter, can provide a more comprehensive picture of the emission processes near the black hole event horizon. Different wavelengths are sensitive to different physical processes, and this broader perspective could help disentangle potential quantum gravitational effects from classical astrophysical phenomena.
Space-Based Interferometry: Taking interferometry to space offers the tantalizing prospect of achieving even higher angular resolutions due to the absence of atmospheric distortion. Missions like the proposed Laser Interferometer Space Antenna (LISA) could, in principle, detect gravitational waves from the vicinity of supermassive black holes, providing complementary information about the strong-gravity regime where quantum effects might manifest.
By combining these advancements, astronomers could potentially:

Precisely measure the shape and size of black hole shadows: This would allow for stringent tests of the no-hair theorem, which posits that black holes are fully characterized by their mass, spin, and charge. Deviations from this theorem could hint at the influence of quantum gravity.
Map the spacetime geometry around black holes in greater detail: This would enable us to test the predictions of general relativity and alternative theories of gravity in strong-field regimes.
Search for time variability in black hole shadows: Quantum effects might introduce subtle fluctuations or oscillations in the shadow's appearance over time. Detecting such variability would provide compelling evidence for new physics.
However, it's crucial to acknowledge that disentangling genuine quantum gravitational signatures from astrophysical complexities will be a formidable challenge. Sophisticated modeling efforts, incorporating both general relativistic and potential quantum effects, will be essential to interpret these future observations accurately.

Could the "quantum" corrections proposed by Alexeyev et al. be amplified or become more significant in extreme astrophysical environments beyond those considered in their paper?

It's certainly plausible that the "quantum" corrections proposed by Alexeyev et al. could be amplified or become more pronounced in extreme astrophysical environments that push the boundaries of gravity even further than the scenarios they considered. Here are some environments where this might occur:

The Very Early Universe: In the extremely hot and dense conditions of the very early universe, just moments after the Big Bang, quantum gravitational effects are thought to have been dominant. If primordial black holes formed in this epoch, their shadows might retain imprints of these quantum effects, potentially observable today.
Ultra-High-Energy Cosmic Rays: The origins of ultra-high-energy cosmic rays, some of the most energetic particles ever observed, remain an enigma. If these particles are produced in the vicinity of supermassive black holes or other extreme environments, their propagation and interactions could be influenced by quantum gravitational effects, potentially leaving observable signatures.
Merging Black Holes: The mergers of black holes, as detected through gravitational waves, provide a unique window into strong-gravity dynamics. During these violent events, the spacetime curvature reaches extreme values, potentially amplifying quantum gravitational effects. Observing deviations from the predictions of classical general relativity in the gravitational wave signals from these mergers could provide indirect evidence for quantum gravity.
It's important to note that these are highly speculative scenarios, and our current theoretical understanding of quantum gravity is still incomplete. Nevertheless, exploring these extreme environments, both observationally and theoretically, could offer valuable clues about the nature of gravity at its most fundamental level.

If we consider the universe itself as a system governed by both quantum mechanics and general relativity, could the concept of black hole shadows offer any insights into the universe's evolution or structure on a cosmological scale?

While it might seem counterintuitive to connect black hole shadows, which are inherently local phenomena, to the universe's evolution and structure on a cosmological scale, there are intriguing possibilities to consider:

Primordial Black Holes as Probes of the Early Universe: If primordial black holes formed in the very early universe, their distribution and properties could provide valuable insights into the conditions that prevailed during that epoch. Their shadows, if observable, could carry imprints of the universe's inflationary phase or other early-universe physics.
Black Hole Shadows and the Cosmic Expansion: The expansion of the universe affects the propagation of light, including the light that forms black hole shadows. Studying how shadows evolve over cosmological timescales could provide an independent measure of the expansion rate and potentially shed light on the nature of dark energy.
Black Hole Mergers and the Growth of Structure: The hierarchical mergers of black holes over cosmic time have played a crucial role in shaping the large-scale structure of the universe. The gravitational wave signals from these mergers encode information about the masses, spins, and redshifts of the merging black holes, providing insights into the growth of galaxies and the evolution of the cosmic web.
Furthermore, some theoretical frameworks, such as:

Holographic Principle: This principle suggests that the information content of a region of space is encoded on its boundary, much like a hologram. Some physicists speculate that the universe itself might be holographic, with its information content residing on a distant cosmological horizon. Black hole shadows, as regions where information is seemingly lost, could provide hints about the nature of this holographic encoding.
However, it's essential to emphasize that these connections between black hole shadows and cosmology are still highly speculative and require further theoretical development. Nevertheless, exploring these potential links could lead to profound insights into the fundamental nature of the universe and its evolution.