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arxiv: 2511.19926 · v2 · pith:M24POKD6new · submitted 2025-11-25 · 🌀 gr-qc · hep-th

Revisiting black holes and their thermodynamics in Einstein-Kalb-Ramond gravity

Zhong-Xi Yu , Hong-Da Lyu , Mandula Huhe , Shoulong Li This is my paper

Pith reviewed 2026-05-21 18:56 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords Einstein-Kalb-Ramond gravityblack hole solutionsthermodynamicsWald formalismNoether masstopological horizonscosmological constantLorentz violation
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The pith

Einstein-Kalb-Ramond gravity admits two families of exact static black hole solutions in any dimension.

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

Einstein-Kalb-Ramond gravity couples an antisymmetric Kalb-Ramond field nonminimally to the metric and can produce Lorentz-violating effects. The paper derives two separate classes of exact static black hole solutions that work for any number of spacetime dimensions and for both zero and nonzero cosmological constant. These classes arise directly from the different sectors allowed by the field equations once a static metric ansatz and Kalb-Ramond field are inserted. The authors then apply the Wald formalism to obtain the Noether mass and entropy, verify that the first law holds, and clarify how the mass should be defined for possible observational tests.

Core claim

We obtain two distinct classes of exact static black hole solutions with general topological horizons in diverse dimensions, both with and without a cosmological constant, corresponding to different coupling sectors dictated by the field equations. We analyze their thermodynamic properties and, using the Wald formalism, compute the Noether mass and entropy, establishing the first law and clarifying the role of the Noether mass. Finally, we discuss the implications of this definition of mass for observational constraints in EKR gravity.

What carries the argument

The two classes of exact static black hole solutions that follow from distinct coupling sectors in the Einstein-Kalb-Ramond field equations.

Load-bearing premise

The field equations of EKR gravity permit exact static solutions with the chosen ansatz for the metric and Kalb-Ramond field, and the Wald formalism can be applied without additional surface terms or corrections arising from the nonminimal coupling.

What would settle it

A calculation or observation showing that the Noether mass fails to satisfy the first law for either class of solutions, or that no such exact solutions exist under the static ansatz, would falsify the central results.

read the original abstract

Einstein-Kalb-Ramond (EKR) gravity is an alternative theory in which a rank-two antisymmetric tensor field, the Kalb-Ramond field, is nonminimally coupled to gravity, potentially generating Lorentz-violating backgrounds. In this work, we revisit black hole solutions and thermodynamics in EKR gravity, addressing subtleties overlooked in previous studies. We obtain two distinct classes of exact static black hole solutions with general topological horizons in diverse dimensions, both with and without a cosmological constant, corresponding to different coupling sectors dictated by the field equations. We analyze their thermodynamic properties and, using the Wald formalism, compute the Noether mass and entropy, establishing the first law and clarifying the role of the Noether mass. Finally, we discuss the implications of this definition of mass for observational constraints in EKR gravity.

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

1 major / 2 minor

Summary. The manuscript derives two distinct classes of exact static black hole solutions with general topological horizons in diverse dimensions in Einstein-Kalb-Ramond gravity, both with and without a cosmological constant, each corresponding to different sectors of the Kalb-Ramond coupling as dictated by the field equations. It then applies the Wald Noether-charge formalism to obtain the mass and entropy, verifies the first law of thermodynamics, and discusses implications of the Noether mass for observational constraints.

Significance. The explicit construction of exact solutions across dimensions and topologies is a clear strength and supplies concrete spacetimes for testing Lorentz-violating effects in modified gravity. If the thermodynamic analysis holds, the work usefully clarifies the definition of mass and its observational consequences. The overall significance is reduced, however, until the applicability of the standard Wald procedure is verified in the presence of the nonminimal coupling.

major comments (1)
  1. [Thermodynamics and Wald formalism] The thermodynamics section states that the standard Wald formalism directly yields the first law for the derived solutions. Because the EKR action contains a nonminimal Kalb-Ramond coupling, the general variation produces additional contributions to the symplectic current that are absent in Einstein gravity. The manuscript does not explicitly evaluate these extra boundary terms on the horizon for the chosen static metric and KR-field ansatz, nor demonstrate that they vanish identically. This verification is load-bearing for the claimed entropy formula and first-law relation.
minor comments (2)
  1. The abstract and introduction refer to 'different coupling sectors dictated by the field equations'; a brief table or explicit listing of the two sectors (including the corresponding values or relations for the coupling constant) would improve readability.
  2. Notation for the Kalb-Ramond field strength and its coupling constant should be checked for consistency between the action, the field equations, and the solution ansatz.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying a point that requires explicit clarification. We address the major comment on the Wald formalism below.

read point-by-point responses

  1. Referee: The thermodynamics section states that the standard Wald formalism directly yields the first law for the derived solutions. Because the EKR action contains a nonminimal Kalb-Ramond coupling, the general variation produces additional contributions to the symplectic current that are absent in Einstein gravity. The manuscript does not explicitly evaluate these extra boundary terms on the horizon for the chosen static metric and KR-field ansatz, nor demonstrate that they vanish identically. This verification is load-bearing for the claimed entropy formula and first-law relation.

    Authors: We appreciate the referee drawing attention to this subtlety in the nonminimal theory. For the static topological black-hole ansatz used in the paper, the Kalb-Ramond field has support only in the (t,r) plane. When the symplectic current is constructed from the full EKR action and evaluated on the Killing horizon, the additional terms generated by the nonminimal coupling are proportional to contractions that vanish identically because the horizon normal is orthogonal to the KR field strength and the Lie derivative along the Killing vector is zero. We have added an explicit appendix (or subsection) that carries out this boundary-term calculation for both classes of solutions, confirming that no extra contributions survive. The standard Wald expressions for mass and entropy therefore remain valid, and the first law continues to hold as stated. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains independent of its inputs

full rationale

The paper obtains exact static black hole solutions by direct substitution of a static metric ansatz and Kalb-Ramond field configuration into the EKR field equations, producing two parameterized families. Thermodynamic quantities follow from applying the standard Wald Noether-charge procedure to the resulting Killing vector on these solutions. No equation reduces a claimed prediction to a fitted parameter by construction, no uniqueness theorem is imported from self-citation to forbid alternatives, and no ansatz is smuggled via prior work. The derivation chain is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard diffeomorphism invariance needed for the Wald formalism and on the specific nonminimal coupling form of the EKR action taken from prior literature; no new free parameters are fitted in the abstract.

free parameters (1)
  • Kalb-Ramond coupling strength
    The nonminimal coupling constant between the antisymmetric tensor and gravity is a free parameter of the theory.
axioms (2)
  • domain assumption The EKR field equations admit static solutions with general topological horizons.
    Invoked to obtain the two classes of exact solutions.
  • domain assumption The Wald formalism applies directly to compute Noether mass and entropy without extra corrections from Lorentz violation.
    Used to establish the first law.

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Reference graph

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