REVIEW 4 major objections 4 minor 1 cited by
Comment on "Black holes in $f(\mathbb{Q})$ gravity"
T0 review · 4 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash
Pith's one-line read This paper argues that no nontrivial vacuum black hole solutions in f(Q) gravity satisfy the condition g_tt g_rr = constant, because any attempt to go beyond general relativity forces the non-metricity scalar Q to zero, trivializing the fie
desk verdict The Comment makes a plausible case that one branch of f(Q) black holes collapses to Q=0, but the abstract overreaches when it generalizes that to all nontrivial vacuum solutions. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The central object is the f(Q) gravity field equation combined with the constant-product metric condition g_tt g_rr = const and the 'Set 2' connection, the branch required to obtain solutions distinct from general relativity. The equation system forces the non-metricity scalar Q to vanish once the constant-product condition is imposed together with the parameter choice c = k = 0, trivializing the dynamics and leaving only the general-relativistic sector.
What would settle it
Construct a static, spherically symmetric, vacuum solution of f(Q) gravity with g_tt g_rr = const and Q ≠ 0, for any smooth f(Q), using any connection branch. For instance, choose f(Q) = Q + α $Q^{2}$ and solve the field equations with the Set-2 connection and c = k = 0; a non-Schwarzschild metric with Q ≠ 0 would overturn the claim.
Extended reading notes
Core claim
The central claim is a no-go result: in f(Q) gravity, static and spherically symmetric vacuum black hole metrics with g_tt g_rr = const cannot be distinct from general relativity. Working with the connection branch labeled 'Set 2' in the paper under comment and setting the free parameters c and k to zero (Option 2), the authors show that the field equations force the non-metricity scalar to vanish, Q = 0. With Q = 0, the f(Q) equations reduce to those of general relativity with a trivial modification, so no new black hole emerges. The argument is independent of the explicit form of f(Q). The paper also briefly considers the remaining parameter branch (Option 1) and derives constraints on the
Load-bearing premise
The no-go proof assumes that the connection branch 'Set 2' with the parameter choice c = k = 0 covers every way of going beyond general relativity for static spherical vacuum f(Q) black holes; if another connection branch or parameter choice yields a non-GR solution, the conclusion would not apply.
Editorial extensions
If this is right
- The common ansatz g_tt g_rr = const cannot serve as a starting point for finding new static vacuum black holes in f(Q) gravity; searches must relax this condition.
- Candidate black hole solutions in the literature that satisfy g_tt g_rr = const are either general-relativistic solutions dressed by a trivial f(Q) or are not valid solutions of the full field equations.
- The no-go conclusion applies for every smooth form of f(Q), so it cannot be evaded by choosing a more complicated function.
- The parameter branch c = k = 0 is the only branch analyzed in full; the accompanying discussion of Option 1 suggests that the remaining parameter space can be constrained similarly.
Reading between the lines
- If this no-go result holds, analogous constant-product conditions in other metric-affine or symmetric-teleparallel gravity theories may also fail to produce new black holes, since the same Q-trivialization mechanism could appear.
- A natural extension is to test whether relaxing g_tt g_rr = const to a more general relation while keeping Q ≠ 0 restores a space of nontrivial solutions; the present argument does not rule that out.
- The parameter constraints derived for Option 1 could be studied numerically to see whether any non-Schwarzschild solutions with Q ≠ 0 survive in that connection branch.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. This manuscript is a Comment on D'Ambrosio et al.'s black hole solutions in f(Q) gravity. It argues that no nontrivial static, spherically symmetric vacuum black hole in f(Q) gravity satisfies the condition g_tt g_rr = const. The argument is based on a reexamination of the field equations under the 'Set 2' connection with the free parameters set to c = k = 0 (Option 2). The authors claim that any attempt to find a solution beyond general relativity forces Q = 0, which trivializes the field equations and rules out a valid black hole solution. The conclusion is stated to be independent of the specific form of f(Q). Option 1 is said to be briefly discussed.
Significance. If correct, the paper would invalidate a class of non-GR black hole solutions in symmetric teleparallel gravity and would sharpen the conditions under which f(Q) gravity can deviate from general relativity. The claimed f(Q)-independence is a strong and potentially useful statement. However, the abstract does not permit verification of the derivation or of the exhaustive treatment of connection branches, so the significance is conditional on the full analysis being as complete as claimed.
major comments (4)
- [Abstract] The universal no-go claim ('no nontrivial vacuum black hole solutions satisfy this condition... conclusion does not depend on the specific form of f(Q)') is supported only by the Set 2 connection with c = k = 0 (Option 2). Option 1 is only 'briefly discussed.' The proof is therefore not shown to cover all connection branches and parameter choices identified by D'Ambrosio et al. If any unexamined branch or nonzero c/k allows Q ≠ 0 with g_tt g_rr = const, the central claim fails. The paper should either extend the derivation to all sectors or restrict the concluding claim accordingly.
- [Abstract] The statement that Q = 0 'trivializes the field equations and does not describe a valid black hole solution' needs a precise derivation. It must be shown whether Q = 0 forces the GR field equations (which would allow Schwarzschild or de Sitter solutions and satisfy g_tt g_rr = const) or leads to an inconsistency. Without this, the inference from Q = 0 to 'no valid black hole solution' is unsupported.
- [Abstract] A Comment targeting a published paper should identify the specific error in D'Ambrosio et al.'s solutions. The abstract does not state which of their displayed solutions violate the field equations or where the algebraic or conceptual error lies. Showing that one parameter slice yields Q = 0 is not by itself a refutation of explicit solutions; the paper must pinpoint the inconsistency in the target results.
- [Abstract] The f(Q)-independence claim requires handling special forms such as f(Q) = Q + const, f(Q) = Q^n, or cases where f'(0) = 0. The abstract gives no indication that the Set 2/Option 2 calculation covers these cases. Since the no-go is claimed for every f(Q), degenerate limits of the f-dependence must be addressed explicitly.
minor comments (4)
- [Abstract] The terms 'Set 2 connection' and 'Option 2' are used without definitions; a reader needs a pointer to the target paper's numbering or equations.
- [Abstract] 'Briefly discuss Option 1' is vague. If Option 1 is excluded from the no-go, the abstract should say so explicitly; if it is included, the discussion must be complete.
- [Abstract] 'Trivializes the field equations' is ambiguous: does it mean 'reduces to GR', 'becomes identically satisfied', or 'becomes inconsistent'? More precise language is needed.
- [Abstract] The condition g_tt g_rr = const does not specify whether the constant is nonzero. This matters because the constant can affect the coordinate interpretation and horizon structure.
Circularity Check
No circularity found in abstract-level argument; unhandled Option 1 is a scope concern, not circularity.
full rationale
This is an abstract-only review. The paper's argument is a direct field-equation analysis: it reexamines the f(Q) field equations under the 'Set 2' connection with c = k = 0 and shows that a solution beyond GR forces Q = 0, trivializing the equations. There are no fitted parameters, no quantities defined in terms of the target conclusion, and no load-bearing self-citations. The claim that the conclusion is independent of the form of f(Q) is a generalization from the field equations, not a circular reduction. The acknowledged limitation that Option 1 is only 'briefly discussed' is an incompleteness or scope issue: the no-go theorem may not cover all connection branches or parameter choices, so a counterexample could hide there. But that is a correctness/completeness concern, not circularity. No equation or self-citation is exhibited that would reduce the conclusion to its own inputs. Therefore the appropriate finding is no significant circularity (score 0).
Assumptions & free parameters
assumptions (2)
- domain assumption The field equations of f(Q) gravity as formulated in D'Ambrosio et al., including the 'Set 2' connection choice.
- domain assumption The static, spherically symmetric vacuum metric ansatz with the condition g_tt g_rr = const.
Cite this review
Pith. "Pith review of Comment on "Black holes in $f(\mathbb{Q})$ gravity"." pith.science (2026). https://pith.science/paper/CFZGB74I
@misc{pith2026250812912,
author = {Pith},
title = {Pith review of: Comment on "Black holes in $f(\mathbbQ)$ gravity"},
year = {2026},
howpublished = {\url{https://pith.science/paper/CFZGB74I}},
note = {Machine review of arXiv:2508.12912}
}
abstract
In the work [Phys.Rev.D 105 (2022) 2, 024042], D'Ambrosio et al. investigated spherically symmetric black hole solutions in $f(\mathbb{Q})$ gravity, where several solutions satisfy the condition: $g_{tt}g_{rr} = \mathrm{const}$. This condition is characteristic of many black holes, including the Schwarzschild spacetime. In this Comment, we argue that no nontrivial vacuum black hole solutions satisfy this condition in $f(\mathbb{Q})$ gravity. We demonstrate our claim by reexamining the field equations under the "Set 2" connection called by D'Ambrosio et al., which is necessary for obtaining solutions distinct from those of general relativity (GR). For the case where the free parameters $c$ and $k$ are zero, i.e., Option 2 in their work, we show that any attempt to find a solution beyond GR forces the non-metricity scalar to vanish ($\mathbb{Q}=0$), which trivializes the field equations and does not describe a valid black hole solution. Our findings indicate that the condition, $g_{tt}g_{rr} = \mathrm{const.}$, is overly restrictive for finding new, static and spherically symmetric vacuum black holes in $f(\mathbb{Q})$ gravity. This conclusion does not depend on the specific form of $f(\mathbb{Q})$. We also briefly discuss Option 1 that was not addressed in D'Ambrosio et al.'s work, and give new constraints for the selection of parameters $c$ and $k$.
Forward citations
Cited by 1 Pith paper
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Neutron stars in $f(\mathbb{Q})$ gravity
For f(Q)=Q+αQ² and f(Q)=Q^β, neutron-star solutions that admit power-series expansions at the center or at infinity collapse to General Relativity; genuine beyond-GR effects must be non-analytic.
Reviewed August 5, 2026 · model on record in the stance chip above.
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