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arxiv: 2607.01884 · v1 · pith:ZL2ZFW7Anew · submitted 2026-07-02 · 🌀 gr-qc · hep-th

Rotating Black Holes and the Kerr/CFT Correspondence in Einstein-Bumblebee Gravity

Yu-Qi Chen , Jin-Yang Shen , Hai-Shan Liu This is my paper

Pith reviewed 2026-07-03 08:43 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords rotating black holesEinstein-Bumblebee gravityKerr/CFT correspondencemicroscopic entropyWald entropyKomar integralfive-dimensional gravity
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The pith

Applying the Kerr/CFT correspondence to five-dimensional rotating black holes in Einstein-Bumblebee gravity yields microscopic entropy that matches the Komar-integral version rather than the Wald entropy.

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

The paper constructs rotating black holes with equal angular momentum in five-dimensional Einstein-Bumblebee gravity, both with and without a cosmological constant. Thermodynamic quantities including mass, angular momentum, and entropy are computed in two ways: the Wald formalism and the Komar integral. These two approaches produce results that differ by a constant prefactor fixed entirely by the Bumblebee coupling parameter. The authors then invoke the Kerr/CFT correspondence on the near-horizon geometry to obtain a microscopic entropy count and show that this count agrees exactly with the Komar result.

Core claim

We constructed rotating black holes with equal angular momentum in five dimensional Einstein-Bumblebee gravity with and without cosmological constant. Their thermodynamic properties are examined via two distinct methods: the Wald formalism and the Komar integral. Notably, the conserved charges, including mass, angular momentum, and entropy, computed from these two approaches differ by a constant prefactor that is solely determined by the Bumblebee coupling. Subsequently, we apply the Kerr/CFT correspondence to derive the microscopic entropy of these black holes and find that it precisely reproduces the entropy in Komar-integral version, rather than the Wald entropy.

What carries the argument

The Kerr/CFT correspondence applied to the near-horizon extremal geometry, which produces a microscopic entropy that selects the Komar-integral entropy over the Wald entropy when the Bumblebee coupling is nonzero.

If this is right

  • The Komar-integral entropy is the one that admits a microscopic holographic counting in this theory.
  • The Bumblebee coupling rescales the relation between Wald and Komar entropies but leaves the applicability of Kerr/CFT intact.
  • The same matching holds for both the asymptotically flat and anti-de Sitter cases in five dimensions.
  • Entropy definitions in modified gravity must be checked against holographic duals rather than assumed to coincide with Wald entropy.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar mismatches between Wald and Komar entropies may occur in other vector-tensor or Lorentz-violating theories, requiring case-by-case verification with Kerr/CFT.
  • The result suggests that the physical entropy in these models is the one compatible with a two-dimensional CFT dual rather than the one derived from the Noether charge alone.
  • Extending the construction to unequal angular momenta or higher dimensions could test whether the Komar-Kerr/CFT agreement persists.

Load-bearing premise

The Kerr/CFT correspondence applies without modification to the constructed five-dimensional rotating black holes in Einstein-Bumblebee gravity and directly yields the physical microscopic entropy.

What would settle it

An explicit computation of the central charge and left-moving temperature from the near-horizon CFT for a specific nonzero Bumblebee coupling value that produces an entropy different from the Komar integral would falsify the claim.

read the original abstract

We constructed rotating black holes with equal angular momentum in five dimensional Einstein-Bumblebee gravity with and without cosmological constant. Their thermodynamic properties are examined via two distinct methods: the Wald formalism and the Komar integral. Notably, the conserved charges, including mass, angular momentum, and entropy, computed from these two approaches differ by a constant prefactor that is solely determined by the Bumblebee coupling. Subsequently, we apply the Kerr/CFT correspondence to derive the microscopic entropy of these black holes and find that it precisely reproduces the entropy in Komar-integral version, rather than the Wald entropy.

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 / 2 minor

Summary. The manuscript constructs five-dimensional rotating black hole solutions with equal angular momenta in Einstein-Bumblebee gravity, both with and without a cosmological constant. Thermodynamic quantities (mass, angular momentum, entropy) are computed via the Wald formalism and the Komar integral; these differ by a constant prefactor fixed by the bumblebee coupling. The Kerr/CFT correspondence is then applied to the near-horizon extremal geometry, yielding a microscopic entropy that matches the Komar version rather than the Wald entropy.

Significance. If the central claim holds, the result indicates that the Kerr/CFT correspondence selects the Komar entropy over the Wald entropy in this Lorentz-violating theory. This would provide a concrete example in which a microscopic counting procedure distinguishes between two entropy definitions that differ by a theory-dependent factor, with potential implications for the physical entropy in modified gravity.

major comments (2)
  1. [Kerr/CFT correspondence section] The application of Kerr/CFT (near-horizon extremal geometry and asymptotic symmetry analysis) does not demonstrate that the Virasoro central charge extracted from the diffeomorphism generators receives no additional contribution from the bumblebee vector field. Because the bumblebee term modifies the gravitational action, the covariant phase-space Noether charge associated with the generators could acquire an extra term proportional to the bumblebee coupling; the manuscript must show explicitly that this term vanishes or cancels in the near-horizon limit, otherwise the claimed match to the Komar entropy is not justified.
  2. [Thermodynamic properties section] The statement that the two entropy expressions differ only by a constant prefactor determined solely by the bumblebee coupling must be verified against the explicit metric and the definitions of the Wald and Komar integrals; if the prefactor also depends on the horizon radius or other solution parameters, the subsequent claim that Kerr/CFT selects one entropy over the other would require re-examination.
minor comments (2)
  1. Notation for the bumblebee field and coupling constant should be introduced once and used consistently; the abstract refers to 'Bumblebee coupling' while the body appears to use a different symbol.
  2. The manuscript should include a brief comparison table of the Wald and Komar expressions for mass, angular momentum, and entropy evaluated on the same solution parameters.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major point below and indicate the revisions that will be made to the manuscript.

read point-by-point responses

  1. Referee: [Kerr/CFT correspondence section] The application of Kerr/CFT (near-horizon extremal geometry and asymptotic symmetry analysis) does not demonstrate that the Virasoro central charge extracted from the diffeomorphism generators receives no additional contribution from the bumblebee vector field. Because the bumblebee term modifies the gravitational action, the covariant phase-space Noether charge associated with the generators could acquire an extra term proportional to the bumblebee coupling; the manuscript must show explicitly that this term vanishes or cancels in the near-horizon limit, otherwise the claimed match to the Komar entropy is not justified.

    Authors: We agree that an explicit verification is required. In the near-horizon extremal limit the bumblebee vector field is covariantly constant along the relevant Killing directions, so its contribution to the Noether charge for the asymptotic symmetry generators vanishes identically. Nevertheless, to make this fully rigorous we will add a dedicated paragraph (or short appendix) in the revised manuscript that recomputes the central charge including the bumblebee term and demonstrates its cancellation. This will confirm that the Virasoro central charge remains the same as in the Einstein case and that the microscopic entropy continues to match the Komar expression. revision: yes

  2. Referee: [Thermodynamic properties section] The statement that the two entropy expressions differ only by a constant prefactor determined solely by the bumblebee coupling must be verified against the explicit metric and the definitions of the Wald and Komar integrals; if the prefactor also depends on the horizon radius or other solution parameters, the subsequent claim that Kerr/CFT selects one entropy over the other would require re-examination.

    Authors: We have performed this verification using the explicit five-dimensional metric (both with and without cosmological constant) and the standard definitions of the Wald and Komar integrals. After substituting the metric components, all dependence on the horizon radius, angular momenta, and cosmological constant cancels, leaving a prefactor that depends only on the bumblebee coupling constant. This is already visible in the ratio of the two entropy expressions given in the thermodynamic-properties section; the subsequent Kerr/CFT analysis is therefore unaffected. revision: no

Circularity Check

0 steps flagged

No significant circularity; Kerr/CFT match is non-trivial result

full rationale

The paper constructs explicit rotating black-hole solutions in 5D Einstein-Bumblebee gravity, evaluates conserved charges and entropy via two independent thermodynamic prescriptions (Wald vs. Komar), and then applies the pre-existing Kerr/CFT dictionary to the near-horizon extremal geometry. The reported agreement with the Komar entropy is an output of that external correspondence rather than an identity enforced by the paper's own definitions or by any self-citation chain. No equation is shown to reduce to its input by construction, and the central charge extraction is not demonstrated to be defined in terms of the Komar charges.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the constructed solutions, the standard thermodynamic formulas, and the direct applicability of the Kerr/CFT correspondence in the presence of the bumblebee field; the bumblebee coupling enters only as a theory parameter, not a fitted constant.

free parameters (1)
  • Bumblebee coupling constant
    The constant prefactor between Wald and Komar quantities is fixed by this parameter of the Einstein-Bumblebee theory.
axioms (2)
  • domain assumption The Kerr/CFT correspondence applies directly to the constructed black holes
    Invoked without modification to obtain the microscopic entropy.
  • domain assumption The Wald and Komar formulas remain the appropriate thermodynamic definitions in this modified theory
    Used to compute the macroscopic charges that are then compared.

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