⚛️ high-energy theory

Multi-Boundary Spinning $AdS_5$ Black Holes, Strongly Coupled Plasma Balls and a dual locally de Sitter spacetime

This paper constructs a new family of exact spinning black hole solutions in five-dimensional anti-de Sitter space that are dual to strongly coupled spinning plasma balls on Minkowski spacetime, revealing a novel UV region in the bulk that is locally a three-dimensional de Sitter spacetime times a real line.

Original authors: Andrés Anabalón, Guillermo Buckle, Annelies Fullgraff, Marcelo Oyarzo

Published 2026-09-21

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CC BY 4.0

Original authors: Andrés Anabalón, Guillermo Buckle, Annelies Fullgraff, Marcelo Oyarzo

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the extreme heat of particle colliders, where atoms are smashed together to recreate the conditions of the early universe, a strange substance emerges. This is the quark-gluon plasma, a state of matter so hot that protons and neutrons melt into a soup of their constituent parts. For years, physicists have known that this plasma behaves like a near-perfect fluid, flowing with almost no friction. More recently, experiments have revealed that this fluid can spin with unimaginable speed, creating vortices so intense that they polarize particles within the soup. Understanding how such a fluid behaves when it rotates at speeds approaching the speed of light has been a major challenge, because the mathematics of such extreme rotation often breaks down, leading to predictions of physical impossibilities.

To solve this, a team of researchers has turned to a powerful theoretical tool known as holography. This approach allows scientists to study complex, four-dimensional systems by mapping them onto a simpler, five-dimensional gravitational model. In this framework, the swirling plasma is represented by a spinning black hole. By constructing a new, exact mathematical description of such a black hole in five dimensions, the researchers have found a way to describe the rotating plasma without the usual mathematical breakdowns. Their work reveals that the plasma does not simply stop or explode as it reaches the speed of light; instead, the geometry of the space it inhabits changes in a surprising way, creating a second, distinct region of space that acts as a natural boundary for the fluid.

The researchers began by modeling a spinning black hole in a universe with a negative cosmological constant, a setting that naturally curves space in a way that helps contain the system. They sought a solution that would match the behavior of a rigidly rotating fluid on a flat, four-dimensional surface, much like the spacetime we experience. As they built their model, they discovered that the usual coordinates used to describe the black hole were insufficient. The rotation of the fluid introduces a factor known as the Lorentz factor, which measures how time and space distort as an object moves faster. In their new solution, this factor acts as a genuine coordinate, a new dimension that can be explored just like distance or time.

As the researchers followed the path of this new coordinate, they found that the space does not end abruptly when the fluid reaches the speed of light. Instead, the geometry smoothly transitions into a second, separate asymptotic region. In the first region, which corresponds to the flat space where the plasma lives, the fluid spins faster and faster as it moves outward. At a specific critical radius, the speed of light is reached, and the Lorentz factor becomes infinite. Rather than hitting a wall or a singularity, the space opens up into a new realm. This second region is shaped like a three-dimensional space that expands over time, known as de Sitter space, stretched out along a line. It is a completely different kind of universe from the flat one where the plasma started, yet the two regions are connected continuously.

This dual structure offers a profound insight into the nature of the spinning plasma. In the first region, the fluid behaves as a perfect, rotating disk. However, as it approaches the speed of light, the description of the fluid changes. In the second, de Sitter region, the energy and pressure of the fluid do not vanish or become infinite; instead, they rearrange themselves into an anisotropic fluid. This means the fluid exerts different pressures in different directions, but it remains well-behaved and stable. The researchers calculated the energy and pressure in this new region and confirmed that they satisfy the fundamental physical conditions required for matter to exist, ensuring that the model is physically realistic.

The study also clarifies what happens to the black hole itself. The solution describes a black hole with a single event horizon, beyond which nothing can escape. The surface of this horizon is not compact like a sphere but extends infinitely in certain directions, making it a planar structure. The temperature of this black hole is determined by its rotation and mass, and the area of the horizon provides a measure of the entropy of the system. Crucially, the researchers showed that their model contains no closed timelike curves, which are paths through time that would allow an object to return to its own past, a feature that would violate causality. They also demonstrated that the space is free of singularities outside the horizon, meaning the geometry is smooth and predictable everywhere except at the very center of the black hole.

One of the most striking aspects of this work is how it resolves a long-standing issue with rotating fluids. In previous attempts to describe a fluid spinning at the speed of light, the mathematics suggested that the system would become singular or undefined. By using the holographic approach, the researchers showed that the system naturally evolves into a new geometric phase. The transition is seamless, and the fluid in the new region continues to obey the laws of physics. This suggests that the ultrarelativistic limit of a spinning plasma is not a point of failure but a gateway to a different kind of spacetime structure.

The researchers also explored the limits of their solution. They found that if the rotation were to stop, the model would revert to a standard, non-rotating black hole, confirming that their new solution is a genuine extension of known physics. They investigated whether the space could be extended further into regions where the mathematical coordinates become negative, finding that such extensions lead to singularities unless specific conditions are met. They also noted that while their model describes a fluid that spins up to the speed of light, real-world plasma balls in particle colliders likely end before reaching that limit. Their model provides a framework where a boundary can be placed at a finite point to mimic this physical cutoff, offering a way to connect the ideal mathematical model with the reality of experimental data.

Ultimately, this work provides a new, exact description of a spinning black hole that serves as a dual to a rotating plasma. It reveals that the space surrounding such a black hole is not a simple, single region but a complex structure with two distinct boundaries. One boundary is the familiar flat space where the plasma rotates, and the other is an expanding de Sitter space where the fluid takes on a new, anisotropic form. This discovery deepens our understanding of how gravity and quantum fluids interact at the most extreme limits, showing that even when matter spins at the very edge of physical possibility, the universe finds a way to remain consistent and whole. The results suggest that the holographic principle is a robust tool for exploring these frontiers, offering a clear path to understanding the behavior of matter under conditions that cannot be replicated in a laboratory.

Technical Summary: Multi-Boundary Spinning AdS $_5$ Black Holes and Dual Locally de Sitter Spacetime

Problem Statement
The paper addresses the theoretical description of strongly coupled, rotating fluids in four dimensions, specifically motivated by the observation of high vorticities in the quark–gluon plasma (QGP) produced in heavy-ion collisions. While relativistic hydrodynamics successfully describes the large-scale evolution of such plasmas, a fundamental theoretical framework for strongly coupled rotating fluids remains incomplete. Previous holographic approaches typically model rotating plasmas using asymptotically Anti-de Sitter (AdS) black holes dual to fluids on a flat Minkowski boundary. However, a rigidly rotating fluid in Minkowski space encounters a physical singularity at the "speed-of-light" cylinder ( $w = \Omega_0^{-1}$ ), where the local Lorentz factor $\gamma$ diverges. The authors seek to extend recent four-dimensional constructions to five dimensions to investigate whether holography can provide a regular description of the ultrarelativistic limit of such spinning plasma balls, potentially revealing new asymptotic structures in the bulk spacetime.

Methodology
The authors employ the gauge/gravity duality within five-dimensional General Relativity with a negative cosmological constant ( $\Lambda = -6/L^2$ ).

Construction of Solutions: They construct a new family of exact, spinning black hole solutions in the coordinate patch $(t, \phi, z, r, y)$ . The metric is derived by extending recent four-dimensional solutions, utilizing a specific ansatz that allows for a non-trivial dependence on two non-compact radial coordinates, $r$ and $y$ .
Geometric Analysis: The global structure of the spacetime is analyzed by examining the curvature invariants (Kretschmann scalar), the behavior of the Riemann tensor in an orthonormal frame, and the existence of horizons and closed timelike curves (CTCs). The authors identify the event horizon via the zeros of a specific function $F(r)$ and analyze the analytic extension of the spacetime into regions where $r^2 < 0$ .
Holographic Renormalization: To extract the dual field theory data, the authors perform holographic renormalization on two distinct asymptotic boundaries: the standard $r \to \infty$ region and a new $y \to \infty$ region. They utilize the standard counterterm action (including the Gibbons-Hawking-York term and curvature corrections) to compute the renormalized energy-momentum tensor $\langle T_{ij} \rangle$ .
Fluid Dynamics Interpretation: The resulting energy-momentum tensors are compared against the kinematic requirements of a rigidly rotating perfect fluid in four dimensions, specifically checking for conformal invariance (tracelessness), conservation laws, and the equation of state $P = \rho/3$ .

Key Contributions and Results

Two-Boundary Structure: The primary result is the discovery that the constructed AdS $_5$ spacetime possesses two independent, coexisting asymptotic regions that join continuously.
- Region 1 ( $r \to \infty$ ): This boundary corresponds to the standard flat Minkowski spacetime. The dual energy-momentum tensor here describes a conformal perfect fluid in rigid rotation with constant angular velocity $\Omega_0$ . The pressure scales as $P \propto \gamma^4$ , consistent with hydrodynamic expectations for a conformal fluid.
- Region 2 ( $y \to \infty$ ): This region defines a new asymptotic boundary. The induced metric on this boundary is locally a three-dimensional de Sitter spacetime ( $dS_3$ ) times the real line ( $\mathbb{R}$ ). The coordinate $y$ in the bulk is identified with the boundary Lorentz factor $\gamma$ . As $y \to \infty$ , the system reaches the ultrarelativistic limit ( $\gamma \to \infty$ ).
Dual Fluid in de Sitter Space: The authors compute the dual energy-momentum tensor at the $y \to \infty$ boundary. They find that it describes an anisotropic, traceless fluid that satisfies both the weak and strong energy conditions. Unlike the isotropic fluid in the Minkowski region, this fluid exhibits different pressures along the $z$ , $r$ , and $\phi$ directions, yet remains regular.
Resolution of the Speed-of-Light Singularity: In the standard Minkowski description, the fluid pressure diverges as the radial distance approaches the speed-of-light cylinder ( $w \to \Omega_0^{-1}$ ). In this new solution, the divergence of the Lorentz factor ( $\gamma \to \infty$ ) does not lead to a singularity in the bulk geometry or the dual description. Instead, it corresponds to the transition to the second asymptotic region ( $y \to \infty$ ). The paper claims that holography provides a regular description of the ultrarelativistic limit of the spinning plasma, mapping the "edge" of the plasma disk to a new conformal boundary with $dS_3 \times \mathbb{R}$ geometry.
Geometric Properties:
- The spacetime is free of curvature singularities outside the event horizon (for $r^2 + y^2 > 0$ ).
- The solution admits a closed conformal Killing–Yano tensor, ensuring the separability of the geodesic equations (a Carter-like constant exists).
- The absence of closed timelike curves (CTCs) imposes a constraint on the mass parameter: $mL^2 > -1$ .
- The static limit ( $\alpha \to 0$ ) recovers the standard planar Schwarzschild-AdS black hole.

Significance and Claims
The paper claims to provide a novel holographic framework for understanding the ultrarelativistic limit of strongly coupled rotating fluids. By constructing a regular bulk geometry that connects a flat Minkowski boundary to a locally de Sitter boundary, the authors demonstrate that the "speed-of-light" divergence of a rotating plasma can be interpreted as a transition to a new asymptotic region rather than a physical singularity.

The authors note that while previous models of plasma balls (e.g., in RHIC contexts) typically end before reaching the speed of light, the current model utilizes a conformal boundary at infinity. They explicitly state that achieving a realistic description where the plasma ball ends at a finite value of the Lorentz factor would require introducing a physical boundary (rather than a conformal one) at a finite value of $y$ . They propose that a holographic description of CFTs with boundaries, as suggested in reference [20], provides a natural framework to pursue for this purpose. The work extends the understanding of multi-boundary AdS spacetimes and suggests that the ultrarelativistic limit of spinning D3-branes (in the context of string theory limits) naturally generates a curved brane with a de Sitter region.

The authors remain modest regarding the immediate phenomenological application, acknowledging that while the model captures the finite extent of the plasma ball in the limit, a more realistic description of a plasma ball with a physical boundary would require further work. They also identify future directions, including the study of charged versions of these solutions to explore supersymmetric limits and the stability of the $r^2 < 0$ region.

Technical Summary: Multi-Boundary Spinning AdS5_55​ Black Holes and Dual Locally de Sitter Spacetime

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Technical Summary: Multi-Boundary Spinning AdS $_5$ Black Holes and Dual Locally de Sitter Spacetime