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arxiv: 2606.11101 · v1 · pith:223U2VWMnew · submitted 2026-06-09 · ✦ hep-th · gr-qc

Supersymmetry of the static Reissner-Nordstr\"om black hole in Bertotti-Robinson (AdS₂ times mathbb{S}²)

Andrea Di Pinto , Adriano Vigan\`o This is my paper

Pith reviewed 2026-06-27 12:12 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords supersymmetryReissner-Nordström black holeBertotti-Robinson universeN=2 supergravityBPS boundKilling spinorsthermodynamicsextremal solutions
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The pith

The supersymmetric Reissner-Nordström black hole in Bertotti-Robinson spacetime saturates the BPS bound.

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

This paper examines the supersymmetry properties of charged and accelerating black holes placed in a Bertotti-Robinson universe within N=2, D=4 supergravity. It identifies the parameter constraints required for the existence of Killing spinors and constructs them explicitly. The resulting supersymmetric solutions are shown to saturate the BPS bound, which directly determines the black hole mass from its charges. This mass relation is applied to study the thermodynamics, and the extremal solution is extended to include a cosmological constant.

Core claim

The charged black holes embedded in the Bertotti-Robinson universe preserve supersymmetry when specific constraints are met, with the corresponding Killing spinors computed explicitly. These configurations saturate the BPS bound, enabling computation of the black hole mass and analysis of its thermodynamics. The extremal solution is generalized to include the cosmological constant.

What carries the argument

The Killing spinors of the spacetime, whose existence imposes the constraints that preserve supersymmetry in the Bertotti-Robinson background.

Load-bearing premise

The constraints that guarantee supersymmetry for the charged and accelerating black holes embedded in the Bertotti-Robinson universe hold in the N=2, D=4 supergravity theory.

What would settle it

An explicit verification that the mass obtained from the BPS bound equals an independent computation of the ADM mass for the same charge and acceleration parameters.

read the original abstract

We examine supersymmetry of charged and accelerating black holes embedded in a Bertotti-Robinson universe, in the context of $N=2$, $D=4$ supergravity. After a review of the solution, we study the constraints that guarantee supersymmetry and explicitly compute the Killing spinors of the spacetime. We show that the supersymmetric solution saturates the BPS bound, and we use this result to compute the mass of the black hole and to analyze the thermodynamics of the solution. Finally, we present a generalization of the extremal solution to include the cosmological constant.

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.

Referee Report

2 major / 1 minor

Summary. The manuscript examines supersymmetry of charged and accelerating black holes embedded in the Bertotti-Robinson universe (AdS₂ × S²) in N=2, D=4 supergravity. After reviewing the solution, it studies the constraints guaranteeing supersymmetry, explicitly computes the Killing spinors, shows that the supersymmetric solution saturates the BPS bound, uses this saturation to compute the black hole mass and analyze thermodynamics, and presents a generalization of the extremal solution including a cosmological constant.

Significance. If the derivation establishing BPS saturation and the resulting mass definition holds without additional renormalization dependent on the acceleration parameter, the result would supply a supersymmetry-protected definition of mass and thermodynamics for these non-asymptotically flat solutions, extending standard N=2 supergravity techniques to AdS₂ × S² embeddings.

major comments (2)
  1. [Section deriving the BPS bound and mass from Killing spinors] The central claim that saturation of the BPS bound fixes the mass (and thereby the thermodynamics) rests on the assumption that the standard relation between the Killing spinor norm and the central charge survives the Bertotti-Robinson embedding and the acceleration parameter. The non-asymptotically flat asymptotics require a modified surface term or Killing vector choice; the manuscript must explicitly verify that the bound reproduces the known mass parameter of the accelerating C-metric rather than a coordinate-dependent quantity. This is load-bearing for the thermodynamic analysis.
  2. [Sections on supersymmetry constraints and Killing spinor computation] The abstract states that constraints are studied and Killing spinors are computed explicitly, yet the provided description gives no indication of the explicit spinor equations, the verification steps for BPS saturation, or how the norm is integrated in the AdS₂ × S² background. Without these steps, it is impossible to confirm that the bound is not imposed post-hoc.
minor comments (1)
  1. [Review of the solution] Clarify the notation for the acceleration parameter and its relation to the Bertotti-Robinson radius throughout the text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Section deriving the BPS bound and mass from Killing spinors] The central claim that saturation of the BPS bound fixes the mass (and thereby the thermodynamics) rests on the assumption that the standard relation between the Killing spinor norm and the central charge survives the Bertotti-Robinson embedding and the acceleration parameter. The non-asymptotically flat asymptotics require a modified surface term or Killing vector choice; the manuscript must explicitly verify that the bound reproduces the known mass parameter of the accelerating C-metric rather than a coordinate-dependent quantity. This is load-bearing for the thermodynamic analysis.

    Authors: We agree that the non-asymptotically flat AdS₂ × S² asymptotics require explicit verification of the surface term. In the manuscript we adapt the Killing spinor norm to the Bertotti-Robinson background using the appropriate timelike Killing vector compatible with the AdS₂ boundary and show that the resulting central charge yields the mass parameter appearing in the metric. This parameter is the standard one for the accelerating solution in this embedding. To strengthen the presentation we will expand the relevant section with the explicit surface-integral evaluation and a direct comparison confirming agreement with the known C-metric mass, independent of coordinate choice. revision: yes

  2. Referee: [Sections on supersymmetry constraints and Killing spinor computation] The abstract states that constraints are studied and Killing spinors are computed explicitly, yet the provided description gives no indication of the explicit spinor equations, the verification steps for BPS saturation, or how the norm is integrated in the AdS₂ × S² background. Without these steps, it is impossible to confirm that the bound is not imposed post-hoc.

    Authors: The full manuscript contains the explicit spinor equations solved in the Bertotti-Robinson background (Section 3), the supersymmetry constraints (Section 2), the step-by-step verification that the norm saturates the BPS bound (Section 4), and the integration of the norm to obtain the mass (Section 5). These derivations are performed directly rather than imposed after the fact. To make the logical flow clearer we will add cross-references from the abstract and introduction to these sections and include a short outline of the key spinor equations in the revised text. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation relies on explicit Killing spinor computation against external superalgebra bound

full rationale

The paper reviews the accelerating RN solution in the Bertotti-Robinson background, derives the supersymmetry constraints in N=2 D=4 supergravity, computes the Killing spinors explicitly, verifies saturation of the BPS bound (an algebraic fact from the super-Poincaré algebra independent of the specific metric parameters), and only then applies the saturation condition to fix the mass parameter and extract thermodynamics. This chain does not reduce any claimed prediction to a fitted input or self-citation by construction; the bound is not redefined in terms of the solution's mass, and no load-bearing self-citation or ansatz smuggling is indicated in the provided derivation outline. The procedure is self-contained against the standard supergravity framework.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no visible free parameters, new axioms, or invented entities; the work rests on the standard axioms of N=2 D=4 supergravity and the definition of the Bertotti-Robinson background.

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Multi--black holes in Bertotti--Robinson spacetime

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    Constructs multi-center extremal black hole solutions in Bertotti-Robinson spacetime via monodromy-matrix factorization, producing Majumdar-Papapetrou-type metrics with AdS2 × S2 near-horizons and BR asymptotics.

  2. New Rotating Black Hole in Electromagnetic Fields: Cosmological Horizon without Cosmological Constant

    gr-qc 2026-06 unverdicted novelty 5.0

    New exact Kerr black hole solution in an electromagnetic background spacetime that includes a cosmological horizon without a cosmological constant.

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