Planar AdS multi-NUT spacetimes and Kaluza-Klein multi-monopoles

Crist\'obal Corral , Cristi\'an Erices , Daniel Flores-Alfonso , Benjam\'in Hern\'andez

Authors on Pith no claims yet

Pith reviewed 2026-05-10 19:21 UTC · model grok-4.3

classification ✦ hep-th gr-qc

keywords AdS spacetimesNUT chargesaxionic scalarsquadratic gravityKaluza-Klein monopolesplanar horizonsholography

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The pith

Planar AdS spacetimes with multiple NUT parameters are built by adding axionic scalars or quadratic curvature terms.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows how to construct explicit planar anti-de Sitter geometries carrying several independent NUT charges. This is done either by coupling Einstein-AdS gravity to free scalar fields that have axionic profiles, or by adding quadratic curvature corrections. Both routes avoid the obstructions that appear in pure vacuum Einstein equations when multiple NUT parameters are attempted. A reader cares because NUT charges act as gravitational magnetic charges and having more than one opens holographic models that were previously inaccessible.

Core claim

We construct explicit planar AdS spacetimes having multiple NUT parameters in two simple ways that allow one to circumvent the strong restrictions imposed by the vacuum field equations. First, motivated by momentum relaxation holographic models, we construct multi-NUT spaces in AdS with flat horizons by adding free scalar fields possessing an axionic profile. In our second approach, we build similar configurations in Einstein gravity with quadratic-curvature corrections. As a byproduct, we end by presenting planar versions of the Kaluza-Klein monopole in AdS with different magnetic charges.

What carries the argument

Planar multi-NUT metrics supported either by axionic scalar profiles or by quadratic-curvature terms that relax the vacuum Einstein constraints.

Load-bearing premise

Adding free scalar fields with axionic profiles or switching to quadratic-curvature gravity preserves the physical relevance of the resulting multi-NUT geometries and does not introduce uncontrolled instabilities or boundary artifacts.

What would settle it

Plug the proposed metrics into the modified field equations and verify whether the scalar stress-energy or quadratic terms exactly cancel the extra curvature contributions that would otherwise forbid multiple NUT charges.

read the original abstract

In higher-dimensional Einstein-AdS gravity, it is well known that planar and static anti-de Sitter black holes can be endowed with multiple rotation parameters via a large-gauge transformation. However, a similar prescription fails when multiple NUT parameters are added, thereby obstructing the study of holographic properties with more than one NUT charge. To pave the way towards this direction, we construct explicit planar AdS spacetimes having multiple NUT parameters in two simple ways that allow one to circumvent the strong restrictions imposed by the vacuum field equations. First, motivated by momentum relaxation holographic models, we construct multi-NUT spaces in AdS with flat horizons by adding free scalar fields possessing an axionic profile. In our second approach, we build similar configurations in Einstein gravity with quadratic-curvature corrections. As a byproduct, we end by presenting planar versions of the Kaluza-Klein monopole in AdS with different magnetic charges.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper gives two explicit constructions for planar AdS metrics with multiple NUT charges, one via axionic scalars and one via quadratic corrections, to bypass vacuum restrictions.

read the letter

The main takeaway is that this paper provides two straightforward constructions for planar anti-de Sitter spacetimes with multiple NUT parameters. They use axionic scalar fields inspired by momentum relaxation and quadratic curvature corrections in gravity. These allow bypassing the limitations that the pure vacuum Einstein-AdS equations place on having more than one NUT charge for flat horizons. What stands out as new is the application of these techniques specifically to multi-NUT planar metrics. Previous work apparently couldn't do this in vacuum, but adding the scalars or the quadratic terms makes it possible. The solutions are presented explicitly, and they also derive planar Kaluza-Klein monopole solutions with different magnetic charges as a result. This seems like a direct response to the obstruction mentioned in the abstract. The paper handles the constructions well by keeping the motivations tied to holographic models. The axionic profiles are a natural choice for relaxing momentum, and quadratic gravity is a common extension. By showing that the metrics satisfy the modified equations, it gives concrete examples that people can build on for studying properties like thermodynamics or dual field theories with multiple NUT charges. There are a couple of soft spots worth noting, though they are not deal breakers. First, the physical implications for holography aren't explored much here; the focus is on existence. One might worry if the added fields or terms introduce boundary artifacts or instabilities that limit their use in condensed matter applications. Second, the full verification of the field equations would need close checking in the paper, as the abstract claims they work but details matter for such solutions. No circularity in the parameters though, as they are presented as genuine solutions. Overall, this is aimed at researchers in higher-dimensional gravity and AdS/CFT who deal with NUT charges or modified gravity. Someone wanting explicit metrics for further study or to test holographic ideas with multiple NUTs would get something out of it. The work shows clear thinking in addressing a known technical issue with practical methods. It deserves serious peer review because the constructions are novel and the approach is solid enough to warrant detailed evaluation. I recommend sending it out for referees to check the calculations and discuss potential applications.

Referee Report

0 major / 3 minor

Summary. The paper constructs explicit planar AdS spacetimes endowed with multiple NUT parameters in two ways that evade the obstructions present in vacuum Einstein-AdS gravity: (i) by coupling to free scalar fields with axionic profiles (momentum-relaxation style) and (ii) by adding quadratic-curvature corrections. Both families are stated to satisfy the respective modified field equations. As a byproduct, planar Kaluza-Klein multi-monopole solutions in AdS with distinct magnetic charges are presented.

Significance. If the explicit metrics solve the field equations, the work removes a technical barrier to holographic studies of AdS geometries carrying more than one NUT charge. The two independent constructions supply concrete, usable examples that can be fed into thermodynamic, stability, or correlation-function calculations, and the Kaluza-Klein monopoles extend the catalogue of known higher-dimensional solutions.

minor comments (3)

The abstract and introduction should state the spacetime dimension(s) in which the constructions are performed and whether the metrics are asymptotically AdS with flat horizons in the usual sense.
Explicit verification that the given ansätze satisfy the modified Einstein equations (or the quadratic-curvature equations) should be shown at least for the simplest two-NUT case, including the relevant curvature components or stress-tensor contributions.
The relation between the axionic scalar profiles and the NUT parameters should be written out clearly; it is not obvious from the abstract whether the scalars are chosen to cancel the vacuum obstruction or merely to relax momentum.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our work, as well as for the recommendation of minor revision. We are pleased that the constructions are viewed as removing a technical barrier for further holographic studies of multi-NUT geometries.

Circularity Check

0 steps flagged

No significant circularity in explicit constructions

full rationale

The paper constructs explicit planar AdS multi-NUT metrics by adding axionic scalar fields or quadratic-curvature terms that satisfy the respective field equations, directly bypassing vacuum obstructions without any reduction of NUT charges to fitted parameters, self-definitions, or self-citation chains. The Kaluza-Klein monopole byproducts follow identically from the same ansatz. All load-bearing steps are independent solutions to modified Einstein equations, with no renaming of known results or imported uniqueness theorems; the derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on the domain assumption that the chosen scalar profiles and quadratic terms are admissible extensions that do not violate asymptotic AdS boundary conditions or introduce ghosts.

pith-pipeline@v0.9.0 · 5474 in / 984 out tokens · 41003 ms · 2026-05-10T19:21:15.118343+00:00 · methodology

discussion (0)

Reference graph

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