{"id":"904adb36-9388-4aad-b6f9-ccaea627e8da","arxiv_id":"2412.15395","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Static spherically symmetric vacuum solutions of AeST include two classes of stealth Reissner-Nordstrom black holes with nontrivial secondary scalar and vector hair.","lead":"This paper finds exact black hole solutions in Aether Scalar Tensor theory, a modified gravity framework designed to explain galactic rotation without dark matter. The black holes have the same Reissner-Nordstrom geometry as in general relativity but carry extra scalar and vector hair, giving future strong-field experiments concrete targets to test.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'most general' classification rests on an unproven restriction of the static scalar ansatz to q in {0,1}; a q=-1 or arbitrary-q branch would add missing solution families.","rationale":"The reader's weakest_assumption identifies the same gap: the classification is only as general as the scalar ansatz restriction q in {0,1}. I agree that this is the most load-bearing concern because the abstract's headline claim is 'we solve the most general static spherically symmetric vacuum equations' and the paper's enumeration of solution classes rests on the two cases q=1 and q=0. The paper itself flags q=-1 as a possibility but never analyzes it, which is an explicit missing analysis that should count against the completeness claim. I do not see an internal inconsistency in the q=1 or q=0 derivations themselves; the explicit checks of horizon regularity and the RN geometry support the existence half of the paper. Thus the correct response is not rejection but a conditional acceptance pending a proof that q outside {0,1} is excluded or gauge-equivalent. Secondary issues, such as the cosmological-joining claim being only conjectural and stability being unstudied, are acknowledged by the authors and are less decisive for the formal classification claim. For those reasons I would keep the reader's CONDITIONAL verdict unchanged.","tokens_in":26455,"tokens_out":13688,"duration_ms":129220,"concrete_test":"Treat q as a free real parameter in the mu=0 static spherically symmetric system: substitute phi = Q0(q t + R) into Eqs. (2.14)-(2.23), impose Psi = -Phi, and solve for q=-1 and q=2 with phi0=0, using the same asymptotic-frame normalization as in Section 3. If a new family with the RN metric and nontrivial hair exists for either value, the classification is incomplete. As a second check, re-derive the Phi-only equation analogous to (3.4) without fixing q; if any q-dependent term survives, the blanket 'RN is the unique solution' step fails and the missing proof must be supplied.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2.2, Eq. (2.12) asserts that q is a constant integer taking only q=0 or q=1, with q=-1 'discussed briefly below'; the promised discussion never appears. The completeness of the entire classification—the abstract's 'most general static spherically symmetric vacuum equations' and the enumeration in Table 1—depends entirely on this restriction. Nothing in the staticity argument forces q to be integer or to lie in {0,1}: staticity only forces the coefficient of t in the scalar field to be constant (or forbids time-dependent Q when A is nonzero), and q enters the field equations through the combination e^{-Phi} chi q + e^{-2Psi} A R' (Eq. (2.15)). The constraint (2.20) shows q=1 is structurally different from q != 1 because it kills the shift charge phi0, but it does not exclude intermediate or negative q values. If q=-1, q=2, or a fractional q admits a solution branch, then the claimed 'two classes' are not the most general ones and the solution tables in Sections 3 and 4 are incomplete. The onus is on the authors to show that every q outside {0,1} either fails the field equations or is gauge-equivalent to one of the two treated cases; the paper contains no such proof. This is a load-bearing gap because it directly undermines the abstract's 'most general' claim, even though the existence of the q=1 branches themselves is not threatened.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper analyzes static spherically symmetric vacuum solutions in the Aether Scalar Tensor (AeST) theory in the strong-field regime, where the free function F is taken in the quadratic form (2.2) and MOND corrections are neglected. Using the ansatz phi = Q0(q t + R) with q restricted to 0 or 1 and a radial vector component A(r), the authors reduce the field equations (2.14), (2.16), (2.20), (2.21), (2.22), (2.23) to a tractable system and solve it. They find two families of stealth black holes with Reissner-Nordström metrics and nontrivial secondary hair (q = 1 and q = 0), plus algebraically special solutions with A = 0 that include a Schwarzschild-type solution and wormhole-like branches. The paper claims these are the most general static spherically symmetric vacuum solutions in this regime and that the q = 1 branch can be continuously joined to the cosmological AeST solution.","tokens_in":26765,"tokens_out":7385,"duration_ms":63810,"significance":"If the classification is complete, the paper makes a strong contribution by providing explicit, exact stealth black hole solutions in a modified-gravity theory designed to reproduce MOND phenomenology and cosmological observations. The derivations are algebraic rather than numerical, with useful internal consistency checks: regularity of Q and of the Noether current at the horizon, coordinate regularizations in Eddington-Finkelstein and Lemaitre-Novikov forms, and explicit constraints on parameters for avoiding pathologies. The solutions are in principle falsifiable through strong-field tests. However, the significance is moderated by the unproven restriction on the scalar ansatz parameter q, on which the 'most general' claim rests, and by the conjectural status of the cosmological matching advertised in the abstract.","major_comments":[{"comment":"The claim that the solutions are the 'most general' static spherically symmetric vacuum solutions rests on the assertion in Sec. 2.2 that the constant q in the ansatz phi = Q0(q t + R) takes only the values q = 0 or q = 1. No derivation of this restriction is given. The text promises a discussion of q = -1, but no such discussion appears anywhere in the paper. The field equations (2.16)-(2.20) do not force q to be an integer or to lie in {0,1}; in particular, the constraint (2.20) only forces phi0 = 0 for any q != 0. Unless the authors prove that all other real q either make the field equations inconsistent or are gauge-equivalent to the q = 0 or q = 1 cases, the abstract's 'most general' claim and the enumeration in Table 1 are not established. This is a load-bearing gap because additional allowed q values would correspond to additional solution branches not covered by the paper.","section":"2.2, Eq. (2.12)"},{"comment":"The abstract states that one of the solution classes 'can be continuously joined to the cosmological solution of AeST.' The body of the paper does not demonstrate such a join. Section 5 notes that the solutions are asymptotically flat and that 'more checking is necessary' for a continuous extension to cosmology, and the authors only 'conjecture' that this poses no problem. Section 6 repeats that the connection can be made 'in principle.' As written, the abstract overstates what has been shown. Either the matching to an FLRW or asymptotically de Sitter solution should be performed (or at least explicitly constructed at the level of the asymptotic matching), or the abstract should be softened to say the solution 'has properties expected to allow' such a join.","section":"Abstract; Sec. 5 and 6"}],"minor_comments":[{"comment":"The sentence 'We briefly discuss the possibility q = -1 below' is never followed up; either provide the discussion or remove the promise.","section":"2.2, after Eq. (2.12)"},{"comment":"There is a typo: 'withF having the expansion' should read 'with F having the expansion'.","section":"2.1, Eq. (2.2)"},{"comment":"'the fullJ (Y)' should be 'the full J(Y)'.","section":"5, first paragraph"},{"comment":"The author name 'Z/suppress lo´ snik' contains a LaTeX artifact and should be corrected to 'Zlosnik'.","section":"References [33] and [37]"},{"comment":"The entry for R' contains qA in the numerator of the first term, while Eq. (3.12) has |qA|; please clarify the notation or correct the table if these differ.","section":"Table 1, q=1 row"}],"recommendation":"major_revision","confidential_remarks":"The main gap (the q restriction) is in principle fixable by adding a proof of exclusion for q outside {0,1} or by explicitly relabeling the claim as a classification within that ansatz. The cosmological-matching claim is more easily addressed by rewording. The rest of the technical content appears sound and the paper is likely publishable after these revisions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know this paper is the real thing on the existence side and shaky on the completeness side. Skordis and Vokrouhlicky solve the strong-field AeST vacuum equations under a static spherically symmetric ansatz and produce two explicit stealth Reissner-Nordstrom families with nontrivial secondary hair: q=1 with zero shift charge, q=0 with non-zero shift charge. That is genuinely new. The earlier AeST black hole work [70] only found specific hairy Schwarzschild solutions outside the stable parameter range, and the TeVeS stealth solutions live in a different theory. The q=1 family has a timelike scalar gradient, which makes the claim of possible smooth joining to the cosmological AeST background plausible, and they show the right asymptotic frame behavior.\n\nThe technical work is careful. They do not just write down metrics; they check the Noether current, the scalar Q, and the kinetic term Y are regular at the horizons, and they remove the apparent divergences in the vector and scalar fields via Eddington-Finkelstein coordinates. They also identify the A=0 branch as the Eling-Jacobson wormhole from Einstein-Aether theory, which is honest attribution.\n\nThe soft spot is the classification claim. The abstract says 'most general static spherically symmetric vacuum equations,' but the scalar ansatz (2.12) restricts q to {0,1} with no proof that other real values are impossible. The text promises a discussion of q=-1 that never arrives. Staticity alone does not force q to be integer or to lie in that set; q enters the equations through combinations that do not obviously exclude intermediate, negative, or fractional values. So the 'most general' statement is load-bearing and unproven. The existence of the q=1 and q=0 branches stands, but the paper should either prove the restriction or soften the completeness claim.\n\nTwo more minor points. The cosmological joining is stated in the abstract as if established, but Section 5 says it is a conjecture that needs more checking; that mismatch should be fixed. And stability is left open, which is fine, but it means the physical selection between branches is unresolved.\n\nBottom line: the core existence result is solid and worth a serious referee. The paper deserves review, not desk rejection, and the referee should push for a proof or a weakened claim on the q-restriction. I would cite this if I were working on AeST or stealth black holes.","headline":"New stealth Reissner-Nordstrom black holes in AeST are genuinely derived and worth publishing, but the 'most general' classification rests on an unproven restriction of the scalar ansatz to q=0,1.","tokens_in":27262,"tokens_out":2458,"would_cite":true,"duration_ms":21301,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83C57","83D05","83C15"],"pacs":["04.70.-s","04.50.Kd"],"model":"deepseek-v4-flash","headline":"Solving AeST's most general static, spherically symmetric vacuum equations, this paper finds two classes of stealth black holes with exact Reissner-Nordstrom geometry and secondary hair, one joinable to cosmology.","keywords":["Aether Scalar Tensor theory","stealth black holes","secondary hair","Reissner-Nordstrom metric","static spherically symmetric solutions","modified Newtonian dynamics","shift symmetry","wormhole solutions"],"falsifier":"Take the field equations (2.14)-(2.23) with $\\varphi=Q_0(qt+R)$ and $A\\neq0$ for $q=-1$ (or any other real $q$ outside $\\{0,1\\}$) and look for a regular static, spherically symmetric vacuum solution; one such branch would break the claimed two-class completeness, while a proof that all such $q$ are inconsistent would confirm it.","tokens_in":26265,"feed_emoji":"🕳️","tokens_out":19865,"duration_ms":152225,"temperature":0.7,"pith_summary":"This paper aims to close a gap in the Aether Scalar Tensor (AeST) theory: before the theory can stand as a dark-matter-free explanation of galaxy and cosmological observations, it needs consistent strong-field objects that look like the black holes we observe. The authors solve the most general static, spherically symmetric vacuum equations of AeST in its strong-field regime and find two classes of stealth black holes, both with exact Reissner-Nordstrom geometry and with non-trivial secondary hair. The $q=1$ class has a timelike scalar gradient and can in principle be smoothly joined to the cosmological solution, making it a concrete black-hole candidate for the theory. The $q=0$ class carries non-zero shift charge and a spacelike gradient, so it is not a cosmological-join candidate but completes the classification. A separate $A=0$ branch gives non-black-hole wormhole-type solutions with no horizon.","feed_headline":"AeST theory admits black holes with GR geometry and hair","feed_subtitle":"Two families yield stealth Reissner-Nordstrom black holes, one joinable to AeST cosmology, enabling strong-field tests.","key_machinery":"The load-bearing ansatz is the static shift-symmetric scalar $\\varphi=Q_0(qt+R(r))$ with $q$ restricted to 0 or 1, together with the unit-timelike vector field written in terms of one function $A(r)$ and $\\chi=\\pm\\sqrt{1+A^2e^{-2\\Psi}}$. Integrating the shift-symmetry Noether current yields a conserved charge $\\varphi_0$, and the constraint $q\\varphi_0=0$ splits the analysis into the two families. The central reduction is the combination of the gravitational field equations that, when the $\\mu^2$ term is negligible, enforces $\\Psi=-\\Phi$ and leaves a single ODE for $\\Phi$ whose unique solution is $e^{2\\Phi}=1-2G_N M/r+q_{\\rm BH}^2/r^2$. Once the metric is fixed, the remaining equations determine $E=\\chi'+\\chi\\Phi'$ and the hair fields algebraically, and the asymptotic frame freedom fixes the integration constants. The discrete symmetry $A_\\mu\\to-A_\\mu$ then organizes the two sign branches that appear in the solutions.","core_discovery":"Within AeST's strong-field regime, meaning scales well below the MOND radius where the free function takes the form $F=(2-K_B)\\lambda_s Y-2K_2(Q-Q_0)^2$, the paper shows that every static, spherically symmetric vacuum solution in the $q=1$ or $q=0$ branch has the Reissner-Nordstrom metric $e^{2\\Phi}=1-2G_N M/r+q_{\\rm BH}^2/r^2$. The hair is secondary: the vector charge $q_A$ and scalar charge $\\varphi_0$ obey fixed relations to $M$ and $q_{\\rm BH}$, for example $q_A^2=\\tilde{m}^2\\varphi_0^2/Q_0^2+q_{\\rm BH}^2/\\tilde{n}$ in the $q=0$ branch, so they do not add independent charges. The $q=1$ branch has a timelike scalar gradient and zero shift charge, and in the Schwarzschild limit $Q=Q_0$ exactly, which is why it can in principle connect to the AeST cosmological scalar; the $q=0$ branch has a spacelike gradient and non-zero shift charge, so it is not a cosmology-join candidate. The algebraically special $A=0$ family yields horizonless wormhole-type solutions with a minimum radius $r_0$; some branches are regular and others contain naked singularities. The hair fields are regular at the black-hole horizons once the coordinates are changed to regular null coordinates.","pith_inferences":["If the $q=-1$ case, or any real $q$ outside $\\{0,1\\}$, turned out to admit a regular solution, the claimed two-class completeness would fail; checking that case is the most direct test of the classification.","Because the hair is secondary and tied algebraically to $M$ and $q_{\\rm BH}$, the $q=1$ family may predict parameter-free relations between gravitational-wave ringdown frequencies and the hair charge; computing the perturbation equations would make such predictions testable.","Embedding the $q=1$ black hole into the actual FLRW AeST background, rather than an asymptotically flat patch, could reveal whether the scalar gradient can pass through both the black-hole and cosmological horizons without acausal features; the paper conjectures this works, but the calculation remains open."],"forward_implications":["The $q=1$ branch gives AeST black holes that are geometrically indistinguishable from general relativity's Reissner-Nordstrom solutions, so any observational discrimination must come from the hair's imprint on perturbations, quasinormal modes, or thermodynamics.","The $q=1$ Schwarzschild subclass has $Q=Q_0$ exactly and can in principle be the strong-field endpoint of the same scalar gradient that drives AeST cosmology; the authors conjecture that a full cosmological embedding is regular but leave the explicit check to future work.","For one $q=1$ sign branch ($\\epsilon_A=-1$) the requirement that the scalar $Q$ not vanish outside the horizon imposes a lower bound on the black hole mass, equation (3.14), suggesting that such objects may only form above a minimum mass.","The $q=0$ branch carries non-zero shift charge and a spacelike scalar gradient, so it is unlikely to join onto the cosmological solution; it nevertheless provides a complete second family that stability analysis must treat separately.","The $A=0$ algebraically special family yields horizonless compact objects with a minimum radius $r_0$; some branches reproduce the spherical wormhole solutions of the preceding vector-tensor theory, while other branches contain naked singularities."],"supporting_citations":[{"why":"Supplies the AeST action and the strong-field form of the free function whose field equations are solved.","marker":"[64]"},{"why":"Fixes the linear-stability conditions and parameter ranges that the paper assumes throughout.","marker":"[65]"},{"why":"Presents the earlier AeST black-hole constructions that this paper generalizes by solving the full field equations.","marker":"[70]"},{"why":"Provides the shift-symmetric static scalar ansatz underlying the q=0 and q=1 classification.","marker":"[98]"},{"why":"Provides the spherical wormhole-type vacuum solutions that the paper's A=0 branch reproduces.","marker":"[101]"},{"why":"Gives the follow-up treatment of those spherical vacuum solutions used to confirm the branch identification.","marker":"[102]"}],"fun_headline_variants":["Stealth black holes with GR geometry emerge in AeST theory","AeST theory admits stealth black holes with GR metric and hair","Stealth black holes in AeST: GR spacetime, extra hair locked in","Two stealth black hole families found in Aether Scalar Tensor theory","AeST stealth black holes mirror GR but carry hidden charges"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The classification's claim to completeness rests on restricting the scalar ansatz to $q\\in\\{0,1\\}$; the paper mentions $q=-1$ but never analyzes it and gives no proof that other real values of $q$ are excluded by staticity, shift symmetry, or boundary conditions.","fun_headline_variants_meta":{"raw":{"variants":["Stealth black holes with GR geometry emerge in AeST theory","AeST theory admits stealth black holes with GR metric and hair","Stealth black holes in AeST: GR spacetime, extra hair locked in","Two stealth black hole families found in Aether Scalar Tensor theory","AeST stealth black holes mirror GR but carry hidden charges"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00019,"raw_usage":{"total_tokens":1361,"prompt_tokens":990,"completion_tokens":371,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":606,"completion_tokens_details":{"reasoning_tokens":280}},"tokens_in":606,"tokens_out":371,"duration_ms":3593,"temperature":1.0,"reasoning_tokens":280,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T11:28:40.861021+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the field equations (2.14)-(2.23) with $\\varphi=Q_0(qt+R)$ and $A\\neq0$ for $q=-1$ (or any other real $q$ outside $\\{0,1\\}$) and look for a regular static, spherically symmetric vacuum solution; one such branch would break the claimed two-class completeness, while a proof that all such $q$ are inconsistent would confirm it.","supporting_citations":[{"cited_title":"Aether scalar tensor theory: Linear stability on Minkowski space","cited_arxiv_id":"2109.13287","evidence_quote":"Fixes the linear-stability conditions and parameter ranges that the paper assumes throughout."},{"cited_title":"Dressed black holes in the new tensor-vector-scalar theory","cited_arxiv_id":"2202.08460","evidence_quote":"Presents the earlier AeST black-hole constructions that this paper generalizes by solving the full field equations."},{"cited_title":"Babichev and C","cited_arxiv_id":null,"evidence_quote":"Provides the shift-symmetric static scalar ansatz underlying the q=0 and q=1 classification."}],"review_version":1}