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Grey Galaxies in $AdS_5$
by Kabir Bajaj, Vipul Kumar, Shiraz Minwalla, Jyotirmoy Mukherjee, Asikur Rahaman
Submission summary
| Authors (as registered SciPost users): | Jyotirmoy Mukherjee |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2412.06904v2 (pdf) |
| Date submitted: | Nov. 5, 2025, 10:22 a.m. |
| Submitted by: | Jyotirmoy Mukherjee |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
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| Approach: | Theoretical |
Abstract
It has recently been conjectured \cite{Kim:2023sig} that the end point of the rotational superradiant instability of black holes in $AdS_4$ is a Grey Galaxy: an $\omega=1$ black hole sitting at the centre of $AdS_4$, surrounded by a large disk of rapidly rotating gravitons and other bulk fields. In this paper we study Grey Galaxies in $AdS_5$. In this case, the rotational group is of rank 2, and so has two distinct angular velocities $\omega_1$ and $\omega_2$. We demonstrate that $AdS_5$ hosts two qualitatively distinct Grey Galaxy phases: the first with either $\omega_1\approx 1$ or $\omega_2\approx 1$, and the second with both angular velocities $\approx 1$. We use these results to present a conjecture for a part of the phase diagram of ${\cal N}=4$ Yang-Mills (as a function of energy and the two angular momenta) that displays several phase transitions between regular black holes and various Grey Galaxy phases. We present an explicit gravitational construction of the phases in which $\omega_1$ and $\omega_2$ are both parametrically close to unity, and demonstrate that the corresponding boundary stress tensor is the sum of two pieces. The first is the stress tensor of the central black hole. The second - the contribution of the bulk gas - takes the form of the stress tensor of an equilibrated boundary conformal fluid, rotating at the given angular speeds $\omega_i$. We also briefly comment on the structure of Grey Galaxies in $AdS_D$ for $D > 5$.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
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Report
A major accomplishment is the calculation of the stress tensor due to the excited gas in the bulk, located at large radii. This is done in the rank 4 case where both angular velocities are near criticality. The gas is shown to be effectively chiral in this limit. The stress tensor in this limit is improved with a subleading piece that ensures conservation. In this way one seems to connect to hydrodynamics in equilibrium a certain form for the partition function at high temperatures. This works surprisingly well, even if the gas is not necessarily high temperature.
Subsequently, the leading back reaction of the AdS geometry from the gas stress tensor is examined. Here is used a clever observation that the global patch of AdS$_5$ reduces to AdS$_5$ in the Poincare patch in their rank 4 critical limit. This leads to the complete bulk solution for rank 4 AdS$_5$ Grey Galaxies. Is is restricted to the bulk matter being a single massless scalar field, but they also conjecture a form for the full Grey Galaxy.
One limitation of the paper, is that while the phases and phase diagram are purported to hold for AdS$5 \times S^5$, all calculations and analysis are done assuming they are uniform on $S^5$. In Sec. 1.6 it is stated that non-uniform or localised solutions on $S^5$ are not studied. Strictly speaking this makes it unclear how much of their results are actually dual to the thermodynamics of N=4 SYM theory, and the authors precisely emphasise the connection N=4 SYM theory in the conclusions. The authors mention this fact in the conclusions.
This paper clearly has novel and very interesting results that are important for the community. It is well written and presented. Therefore, I recommend it for publication since it is an excellent paper of high quality. However, I did find a minor mistake in the formulas plus a minor comment. For this reason I ask for a minor revision.
Requested changes
(1) I found one mistake in formulas that seems to have propagated. In equations (6.31), (G.20) and (G.21) the two terms in the parenthesis are actually the same term. Instead, as is clear from (G.20), one should interchange $\omega_1$ and $\omega_2$ in the two terms, ensuring symmetry in $\omega_1 \leftrightarrow \omega_2$.
(2) The status of the improved bulk stress tensor in the end of section 5 is somewhat unclear to me. The authors have good arguments, and I can follow their logic. But is it clear why one would expect their conjectured perfect fluid form to work? Could there be competing higher derivative corrections at the subleading order? How much of this result is a self-consistent conjecture, and how much is proven? This would be nice to clarify, if possible.
Recommendation
Ask for minor revision
Report
Requested changes
Please find in the attached file "RefereeReport_GreyGalaxiesAdS5.pdf" a list of 3 comments that are to be viewed as "food for thought", in the sense that the authors might find them useful to eventually enhance three discussions.
Recommendation
Ask for minor revision