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arxiv: 2512.07825 · v3 · submitted 2025-12-08 · 🌀 gr-qc · hep-th

Recognition: 2 theorem links

· Lean Theorem

Novel thermodynamic inequality for rotating AdS black holes

Hamid R. Bakhtiarizadeh
Authors on Pith no claims yet

Pith reviewed 2026-05-17 00:23 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords thermodynamic inequalityrotating AdS black holescosmic censorshipKerr-AdSblack stringsreverse isoperimetric inequalitynaked singularities
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The pith

Rotating AdS black holes obey 4πJ²/(3MV) < 1 to keep singularities hidden behind horizons.

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

The paper proposes a new thermodynamic inequality 4πJ²/(3MV) < 1 for stationary asymptotically Anti-de Sitter rotating black holes. It arises from requiring that an identity linking thermodynamic variables has real roots that correspond to solutions with event horizons. A sympathetic reader would care because this condition would rule out naked singularities and thereby support the cosmic censorship conjecture. The authors verify the inequality for the Kerr-AdS black hole and for uncharged rotating AdS black strings across different horizon topologies. They further show that the reverse isoperimetric inequality continues to hold when rotation is present and conjecture a higher-dimensional version.

Core claim

We propose a new thermodynamic inequality for stationary and asymptotically Anti-de Sitter rotating black holes, 4πJ²/(3MV)<1. This inequality is derived by analyzing the roots of the identity relating the thermodynamic variables, ensuring the avoidance of naked singularities, and consequently preventing violations of the cosmic censorship conjecture. We examine the Kerr-AdS black hole as well as uncharged rotating AdS black strings, and find strong supporting evidence for the inequality across different horizon topologies. Using this inequality, we further demonstrate that the reverse isoperimetric inequality remains unchanged in the presence of rotation.

What carries the argument

Analysis of the roots of the thermodynamic identity that relates mass M, angular momentum J, and thermodynamic volume V, requiring real roots to ensure an event horizon exists.

Load-bearing premise

Requiring real roots of the thermodynamic identity is both necessary and sufficient to guarantee an event horizon and thereby enforce cosmic censorship.

What would settle it

A rotating asymptotically AdS black hole solution in which 4πJ²/(3MV) is greater than or equal to 1 yet the geometry still possesses an event horizon and no naked singularity.

read the original abstract

We propose a new thermodynamic inequality for stationary and asymptotically Anti-de Sitter rotating black holes, $ 4\pi J^2/(3MV)<1 $. This inequality is derived by analyzing the roots of the identity relating the thermodynamic variables, ensuring the avoidance of naked singularities, and consequently preventing violations of the cosmic censorship conjecture. We examine the Kerr-AdS black hole as well as uncharged rotating AdS black strings, and find strong supporting evidence for the inequality across different horizon topologies. Using this inequality, we further demonstrate that the reverse isoperimetric inequality ($ {\cal R}\geq 1 $), remains unchanged, in the presence of rotation. Our investigations of a broad class of black hole solutions provide additional confirmation of the proposed inequality. Assuming that the reverse isoperimetric inequality in the presence of rotation continues to hold in higher dimensions, we conjecture the corresponding higher-dimensional generalization of the inequality.

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 proposes a new thermodynamic inequality 4πJ²/(3MV)<1 for stationary asymptotically Anti-de Sitter rotating black holes. It is derived by analyzing the roots of a thermodynamic identity relating M, J and V, with the existence of real roots taken to guarantee an event horizon and thereby uphold cosmic censorship. The authors verify the inequality explicitly for the Kerr-AdS black hole and for uncharged rotating AdS black strings (different horizon topologies), show that the reverse isoperimetric inequality remains valid under rotation, and report supporting evidence from a broader class of solutions. They conjecture a higher-dimensional generalization assuming the reverse isoperimetric inequality continues to hold.

Significance. If the central claim is established, the inequality supplies a new, parameter-free thermodynamic constraint on rotating AdS black holes that directly ties thermodynamic variables to the absence of naked singularities. The explicit verification on Kerr-AdS and rotating AdS black strings, together with the demonstration that the reverse isoperimetric inequality is preserved in the presence of rotation, constitute concrete supporting evidence. The conjecture for higher dimensions, if confirmed, would extend the result beyond four-dimensional stationary solutions.

major comments (2)
  1. [Section 2] The derivation (Section 2 and the paragraph following Eq. (3)) treats the existence of real roots of the thermodynamic identity as both necessary and sufficient for the presence of an event horizon. While this is checked for Kerr-AdS and rotating AdS black strings, the manuscript does not supply a general argument establishing that the root condition maps one-to-one onto horizon existence when horizon topology changes or when additional matter fields are present; this step is load-bearing for the claimed link to cosmic censorship.
  2. [Concluding remarks] The higher-dimensional conjecture (final paragraph) assumes that the reverse isoperimetric inequality continues to hold with rotation in D>4, yet no supporting calculation or reference is provided for even a single higher-dimensional rotating AdS solution; this assumption is central to the proposed generalization.
minor comments (2)
  1. [Introduction] The thermodynamic volume V is introduced without an explicit definition in the opening paragraphs; a brief reminder of its standard definition (e.g., via the first law) would improve readability.
  2. [Section 3] Figure 1 (or the corresponding plot of the inequality boundary) lacks axis labels indicating the range of the rotation parameter a/L; adding these would make the supporting evidence easier to assess.

Simulated Author's Rebuttal

2 responses · 0 unresolved

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

read point-by-point responses

  1. Referee: [Section 2] The derivation (Section 2 and the paragraph following Eq. (3)) treats the existence of real roots of the thermodynamic identity as both necessary and sufficient for the presence of an event horizon. While this is checked for Kerr-AdS and rotating AdS black strings, the manuscript does not supply a general argument establishing that the root condition maps one-to-one onto horizon existence when horizon topology changes or when additional matter fields are present; this step is load-bearing for the claimed link to cosmic censorship.

    Authors: We acknowledge that the manuscript verifies the correspondence between real roots and horizon existence explicitly only for the Kerr-AdS black hole and rotating AdS black strings (including different horizon topologies), together with supporting checks on a broader class of solutions. No general proof is supplied that the root condition is necessary and sufficient for arbitrary horizon topologies or when additional matter fields are present. We will revise Section 2 and the relevant discussion to state the scope of the verification more precisely and to clarify that the proposed link to cosmic censorship is supported by the thermodynamic identity and the explicit cases examined, while noting that a fully general demonstration lies beyond the present work. revision: partial

  2. Referee: [Concluding remarks] The higher-dimensional conjecture (final paragraph) assumes that the reverse isoperimetric inequality continues to hold with rotation in D>4, yet no supporting calculation or reference is provided for even a single higher-dimensional rotating AdS solution; this assumption is central to the proposed generalization.

    Authors: The conjecture is already framed conditionally on the assumption that the reverse isoperimetric inequality continues to hold under rotation in higher dimensions. The manuscript contains no explicit calculation or reference for any D>4 rotating AdS solution. We will revise the final paragraph to emphasize the conditional character of the conjecture and to identify the verification of the reverse isoperimetric inequality in higher dimensions as an open question for future investigation. revision: yes

Circularity Check

0 steps flagged

Derivation from root analysis of thermodynamic identity is self-contained

full rationale

The paper obtains the inequality 4πJ²/(3MV)<1 by requiring real roots of the standard thermodynamic identity in the variables M, J, V for stationary asymptotically AdS rotating black holes; this algebraic condition is presented as necessary to ensure an event horizon and thereby support cosmic censorship. The derivation proceeds from the identity itself rather than by fitting parameters to data, redefining quantities in terms of the target result, or relying on load-bearing self-citations. Explicit checks for Kerr-AdS and rotating AdS black strings supply independent verification across topologies, and the demonstration that the reverse isoperimetric inequality remains unchanged follows directly from the same root condition without circular reduction. The central claim therefore remains non-circular and self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the existence of a thermodynamic identity whose roots determine horizon formation, on the cosmic censorship conjecture as a selection principle, and on the validity of the reverse isoperimetric inequality when rotation is included.

axioms (2)
  • domain assumption Standard thermodynamic relations for asymptotically AdS black holes hold and connect mass, angular momentum, and thermodynamic volume.
    Invoked when the authors analyze the roots of the identity relating thermodynamic variables.
  • domain assumption Naked singularities are forbidden by the cosmic censorship conjecture.
    Used to interpret the absence of real roots as a physical requirement.

pith-pipeline@v0.9.0 · 5444 in / 1392 out tokens · 43206 ms · 2026-05-17T00:23:26.397345+00:00 · methodology

discussion (0)

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Reference graph

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