{"id":"cfb57592-55a7-4b25-96ec-7ba5d63c57a2","arxiv_id":"2508.12912","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"In f(Q) gravity, static spherical vacuum black holes satisfying g_tt g_rr = const are impossible except as trivial general relativity copies, because the non-metricity scalar is forced to zero.","lead":"A comment paper argues that a class of black hole solutions previously published in f(Q) gravity do not actually exist, because the special condition they satisfy forces the theory back to general relativity. If correct, this removes a set of claimed solutions and redirects searches for black holes in this modified gravity.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No-go proof is conditional on a single connection branch/parameter slice; unhandled branches may admit Q≠0 solutions.","rationale":"The reader's review was abstract-only and returned UNVERDICTED. My stress test does not change that epistemic status, but it sharpens the reason: the paper's no-go result depends on an exhaustive enumeration of connection branches and parameter choices, and the abstract explicitly admits the main derivation is for one slice (Set 2, c=k=0) with only brief discussion of Option 1. That is a genuine potential gap, not an artifact of disagreement with the consensus. The proposed concrete test would settle it by independently scanning the remaining branches/parameters for Q≠0 solutions with the stated metric condition. Because the full text is unavailable, I cannot determine whether the authors already close this gap; hence the reader's UNVERDICTED verdict should stand.","tokens_in":785,"tokens_out":4183,"duration_ms":46448,"concrete_test":"Reconstruct the D'Ambrosio et al. f(Q) field equations for all spherically symmetric connection branches (including Set 1 and any alternative 'Set 2' subcases) with general parameters c,k. Impose the ansatz ds² = -A(r)dt² + B(r)dr² + r²dΩ² and the condition A(r)B(r) = const, then solve the full f(Q) equations (or their trace/torsion constraints) for Q(r) without setting c,k to zero. For each branch, test whether a solution with Q not identically zero, finite horizon, and physically acceptable falloff exists. If any such solution appears, the universal no-go claim is refuted; if none does, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is a universal no-go: no nontrivial vacuum f(Q) black hole satisfies g_tt g_rr = const, independent of f(Q). But the proof strategy described in the abstract is narrower than the claim. The derivation is carried out for the 'Set 2' connection with the parameters set to c = k = 0 (Option 2), and Option 1 is only 'briefly discussed'. This means the argument has not been shown to cover all connection branches and parameter choices that D'Ambrosio et al. identified as capable of producing non-GR solutions. If, in any unanalyzed branch or with nonzero c or k, the field equations admit a static spherically symmetric vacuum solution with Q ≠ 0 and g_tt g_rr = const, the no-go statement is false. The asserted f(Q)-independence makes this gap particularly load-bearing, because it claims to rule out every f(Q) without needing to examine each one; that universality is only as strong as the exhaustive enumeration of connection sectors and parameter values. The abstract's own limitation statement ('briefly discuss Option 1') indicates a potentially unhandled case, which is exactly where a counterexample could hide.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":1065,"tokens_out":3319,"duration_ms":37129,"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":[{"comment":"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.","section":"Abstract"},{"comment":"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.","section":"Abstract"},{"comment":"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.","section":"Abstract"},{"comment":"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.","section":"Abstract"}],"minor_comments":[{"comment":"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.","section":"Abstract"},{"comment":"'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.","section":"Abstract"},{"comment":"'Trivializes the field equations' is ambiguous: does it mean 'reduces to GR', 'becomes identically satisfied', or 'becomes inconsistent'? More precise language is needed.","section":"Abstract"},{"comment":"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.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":"This is an abstract-only submission, so I could not inspect the derivation itself. My recommendation is driven by the abstract's internal scope limitation: a universal no-go is asserted on the basis of a single connection branch and parameter slice. If the full text actually contains a complete treatment of all connection branches and parameter choices, the abstract should be revised to state that; if not, the no-go claim should be weakened accordingly. A full review of the complete manuscript is advisable before a final decision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"What you should know: this is a Comment on a published PRD paper. The authors claim that under the 'Set 2' connection with c=k=0, any attempt to get a non-GR vacuum black hole satisfying g_tt g_rr = const forces Q=0, which trivializes the field equations. That is a concrete, checkable mathematical claim. If it holds, it invalidates a set of published solutions, and that matters within the f(Q) subfield.\n\nCredit where it's due: the argument is direct field-equation manipulation, with no fitting parameters and no target-defined predictions. So no circularity. The claim that this specific parameter slice fails independent of the form of f(Q) is useful, and the authors also flag that D'Ambrosio et al. never addressed Option 1. That service alone is worth something.\n\nNow the soft spot, and it's the central one. The abstract's headline claim is universal: no nontrivial vacuum black holes satisfy g_tt g_rr = const in f(Q) gravity. The proof sketch only covers Set 2 with c=k=0 (Option 2). Option 1 is \"briefly discussed,\" which is not the same as exhaustively analyzed. Unless the full text rules out every other connection branch and every other parameter choice, the no-go statement is not established. A counterexample could hide in an unhandled branch, and the paper's own language suggests the authors know the enumeration is incomplete. The f(Q)-independence makes this gap load-bearing: it claims universality while demonstrating only a slice.\n\nI can't check the algebra from the abstract, so the actual derivation might be fine. But as presented, the conclusion is wider than the proof. That's a proportionate concern, not necessarily a fatal one.\n\nWho should read this? People working on f(Q) gravity and black hole no-go results. The paper deserves a serious referee because it directly challenges published results and the core is formal verification of field equations. My recommendation: send it to peer review, but the referee should demand a precise statement of which connection sectors are covered. If the full derivation covers all branches, publish as a Comment. If not, the authors need to narrow the claim or extend the proof.","headline":"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.","tokens_in":1471,"tokens_out":1872,"would_cite":true,"duration_ms":22890,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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","keywords":["f(Q) gravity","non-metricity","black hole no-go","spherically symmetric vacuum","g_tt g_rr constant","modified gravity","teleparallel gravity","connection branches"],"falsifier":"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.","tokens_in":739,"feed_emoji":"🕳️","tokens_out":4042,"duration_ms":44134,"temperature":0.7,"pith_summary":"The paper targets a common shortcut in modified-gravity black hole searches: assuming the metric product g_tt g_rr is constant, as in Schwarzschild. It claims that in f(Q) gravity this condition is too restrictive to allow any genuinely new static, spherically symmetric vacuum black hole. Re-examining the field equations under the connection branch that can yield non-GR solutions, the authors find that any solution beyond general relativity forces the non-metricity scalar Q to vanish, which leaves no valid black hole at all. The conclusion is stated to hold for any smooth function f(Q). If correct, this eliminates a whole class of candidate solutions from the literature.","feed_headline":"No new black holes in f(Q) gravity when g_tt g_rr is constant","feed_subtitle":"Going beyond general relativity forces the non-metricity scalar to zero, trivializing the field equations.","key_machinery":"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.","core_discovery":"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","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[],"fun_headline_variants":["Constant g_tt g_rr kills f(Q) black hole alternatives","No new black holes in f(Q) gravity under constant product","f(Q) gravity forces Q=0 for constant g_tt g_rr black holes","No-go: f(Q) black holes beyond GR don't exist with this condition","Trivializing: constant g_tt g_rr blocks f(Q) black hole novelty"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Constant g_tt g_rr kills f(Q) black hole alternatives","No new black holes in f(Q) gravity under constant product","f(Q) gravity forces Q=0 for constant g_tt g_rr black holes","No-go: f(Q) black holes beyond GR don't exist with this condition","Trivializing: constant g_tt g_rr blocks f(Q) black hole novelty"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000231,"raw_usage":{"total_tokens":1372,"prompt_tokens":843,"completion_tokens":529,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":587,"completion_tokens_details":{"reasoning_tokens":425}},"tokens_in":587,"tokens_out":529,"duration_ms":5834,"temperature":1.0,"reasoning_tokens":425,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T19:11:43.471741+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}