{"id":"e9d2550a-b770-43b9-a9ed-4001e4b1b502","arxiv_id":"2504.20701","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The paper presents exact general-relativity metrics with static or asymptotically static horizons embedded in FLRW cosmologies, offered as counterexamples to no-go theorems.","lead":"This paper constructs black hole and white hole metrics with a horizon locked at a fixed radius while the surrounding universe expands. It offers these as counterexamples to recent claims that cosmological black hole horizons must grow with the universe.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The r=l1 surface is classified as a static event horizon from g^{rr}=0 alone; in a time-dependent cosmology this identifies at most an apparent horizon, and the paper's own dust analysis shows exact staticity is impossible generically.","rationale":"The stress-test pass confirms the reader's identification of the weakest assumption. For the abstract's central claim to hold, the constant-radius surface must be a genuine future event horizon, not merely a coordinate or trapping horizon. The authors' assumption (b) in Sec. 2.2 defines 'static horizon' as g^{rr}=0, and the coordinate transformation to (2.13) does not prove staticity because h(t,r) depends on cosmological time, so partial_tau is not shown to be a Killing vector. In Sec. 3.1.2 the authors themselves prove that an exactly static apparent horizon is impossible for dust (Eq. 3.35 and footnote 2), and the asymptotic constancy is tuned through the free function b(R). Thus the title and abstract overstate what is demonstrated: the paper provides explicit, internally consistent constructions with properties a)-f) and an honest discussion of energy-condition violations, but the global causal structure required to call the surfaces event horizons is absent. The proposed null-geodesic test would settle whether the r=l1 surface is a true event horizon in the black-hole sector, which is the decisive point for the claimed counterexample to the no-go theorems. This supports the original CONDITIONAL verdict without changing it.","tokens_in":12031,"tokens_out":16010,"duration_ms":164667,"concrete_test":"For the black-hole metric (2.33)-(2.39) with H(t)=2/(3t), lambda=1-3(l_s H^2)^{2/3}, and the sign of h chosen negative inside r0 and positive outside, numerically integrate the outgoing radial null geodesic equation derived from (2.33) for initial radii r0<l1, r0=l1-epsilon, and r0=l1+epsilon. Plot r(t) over many Hubble times and determine whether the boundary between geodesics that reach the asymptotic FLRW region (r ~ 1/H) and those that do not coincides with r=l1; if it does not, the surface is only an apparent horizon, not an event horizon.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the constructed metrics possess static event horizons rests on a local condition, not a global causal analysis. In Sec. 2.2, assumption (b) defines the 'static horizon' purely as g^{rr}|_{r=l1}=0, which is an apparent-horizon condition. The coordinate transformation to (2.13) removes g_{tr}, but because h(t,r) depends on t through a(t), the transformed metric retains tau-dependence via h(gamma(tau,r),r) and \\dot gamma; no Killing vector partial_tau is exhibited, so staticity is not established. In Sec. 3.1.2 the authors themselves prove that for dust an exactly static apparent horizon is impossible: Eq. (3.35) and the footnote after it show \\dot r_H=0 cannot hold. The asymptotic constancy obtained in (3.30)-(3.31) is an artifact of choosing b(R)=kappa l_s^4/R^3-d; a different b(R) gives a different late-time behavior. Thus the metrics demonstrate at most an asymptotically-static apparent horizon, not a genuine static event horizon, and the claimed falsification of the no-go theorems on cosmologically coupled event horizons is not supported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper constructs spherically symmetric metrics in Painlevé–Gullstrand form intended to describe black holes and white holes embedded in FLRW cosmology with a static horizon at r=l1. Section 2 derives a white-hole metric from assumptions of no radial energy flux, vanishing g^{rr} at r=l1, FLRW energy density, and asymptotic FLRW behavior. Later sections specialize to constant equations of state: dust white holes with and without cosmological constant, and black holes with sign-changing velocity function. The paper claims these metrics have static event horizons without curvature singularities, reproduce cosmological behavior at large distances, and have apparent horizons that asymptotically approach constant values at late times.","tokens_in":12318,"tokens_out":3967,"duration_ms":40286,"significance":"If the event-horizon claim were correct, it would contradict established no-go results and the recent claim that black hole event horizons are cosmologically coupled. The paper provides explicit exact solutions and a systematic, in places unique, derivation, and it honestly reports in Section 3.1.2 that a dust apparent horizon cannot be exactly static. However, the central claim rests on a local identification of the horizon, and the paper's own analysis shows the apparent horizon is generally dynamical. The significance is therefore conditional on a successful global causal analysis that is not provided in the manuscript.","major_comments":[{"comment":"The identification of r=l1 as a static event horizon is based solely on g^{rr}=0 (h=1) at fixed r, which is an apparent-horizon condition, not an event-horizon condition. After the coordinate transformation t=γ(τ,r), the metric (2.13) still has coefficients that depend on τ through h(γ(τ,r),r) and ˙γ(τ,r), so no Killing vector ∂_τ is exhibited. No global causal-structure analysis is given to prove that radial null geodesics cannot escape from r<l1 to future null infinity. The abstract's statement that these metrics 'retain static event horizons' is therefore not established by the evidence in the paper.","section":"Sec. 2.2, Eq. (2.13)"},{"comment":"The authors prove that for dust with ω=0 the apparent horizon cannot be exactly static: Eq. (3.35) shows ˙r_H=0 is impossible, and the footnote reinforces this point. The late-time constant behavior in Eqs. (3.30)–(3.31) is obtained only after the specific choice b(R)=κl_s^4/R^{3-d}, and a different b(R) would give a different late-time limit. Thus the claim of an 'asymptotically static horizon' is a property of selected free functions, not a generic feature of the solution, and in any case what is shown is an apparent horizon, not an event horizon.","section":"Sec. 3.1.2, Eq. (3.35)"},{"comment":"A static horizon is assumed as an input to the derivation via g^{rr}|_{r=l1}=0. The uniqueness result shows that the metric (2.8) is the unique solution under assumptions (a)–(d), but because the horizon is assumed, the construction does not by itself demonstrate that a static event horizon can exist in a cosmological setting. To support the paper's central claim, the authors would need to prove that the surface r=l1 is a global event horizon, or else explicitly reframe the result as a family of metrics with static apparent horizons and adjust the abstract and introduction accordingly.","section":"Sec. 2.2, assumption (b)"}],"minor_comments":[{"comment":"The notation ω(t,r) is introduced for h^2(t,r), but later in Section 3.1.2 the symbols β(R) and b(R) are introduced without a clear statement of their physical interpretation or the residual coordinate freedom; clarifying this would improve readability.","section":"Sec. 2.2"},{"comment":"The text states that curvature invariants are finite at the horizon, but the caption of Figure 1 does not label which curve corresponds to which invariant, and the dependence of the invariants on the scale factor and its derivatives (as in Eq. (2.14)) is not discussed for general t.","section":"Sec. 2.1, Fig. 1"},{"comment":"The statement that the white-hole horizon tends to its Schwarzschild–de Sitter counterpart relies on the approximation b(R) such that R_H becomes small at late times; this condition on the free function should be stated explicitly rather than implied.","section":"Sec. 3.1.3, Eq. (3.44)"},{"comment":"The word 'static' is used loosely throughout: in Section 3 the horizons are apparent horizons, and the paper should consistently distinguish apparent, isolated, and event horizons in the terminology.","section":"General presentation"},{"comment":"There is a typographical error 'the the metric is brought to the form' in the paragraph after Eq. (2.4).","section":"Sec. 2.1"}],"recommendation":"major_revision","confidential_remarks":"The paper contains explicit exact solutions and a systematic derivation, but the abstract and introduction overclaim the existence of static event horizons. The main technical gap is the identification of an apparent horizon as an event horizon without a global causal analysis. The authors could address this either by adding a rigorous proof of the event-horizon property (which may be difficult in time-dependent backgrounds) or by reframing the results as constructions of static or asymptotically static apparent horizons, which would still be a useful contribution. The latter path would require substantial rewriting of the claims but is within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nI read the Rasulian-Ashoorioon paper on static horizons in cosmology. The thing to know up front: the explicit metrics are a genuine bit of model-building, but the central claim — that they describe static event horizons in an expanding universe — is not established. On reading, the r=l1 surface is only shown to be an apparent horizon, and the paper's own equations in Sec 3.1.2 say an exactly static horizon is impossible for dust.\n\nWhat's new and useful: the systematic derivation in Sec 2.2, where they drop the isotropic-pressure assumption and impose g^{rr}=0 at r=l1, uniquely yields the metric (2.8). The exact white-hole dust solution and the dust+Lambda variants are explicit and reduce to known limits (Schwarzschild-de Sitter when H is constant, LTB dust at late times). The sign-changing velocity function for a black hole in an expanding dust cosmology is a nice construction, and the paper is honest about NEC violation inside the horizon and about the freedom in b(R).\n\nThe soft spot is load-bearing. Assumption (b) defines the 'static horizon' as g^{rr}|_{r=l1}=0. That's an apparent-horizon condition. The coordinate change to (2.13) removes g_tr, but h(t,r) still depends on t through \\dot a/a, so the metric in those coordinates is not static; no Killing vector is exhibited. The authors themselves prove in Sec 3.1.2, Eq (3.35) and the footnote, that \\dot r_H=0 cannot hold exactly for dust; the late-time constancy of r_H is obtained by choosing b(R)=...-d, so it's a tuned asymptotic limit. Thus these are exact metrics with apparent horizons that become asymptotically constant, not static event horizons. The claimed falsification of the no-go theorems on cosmologically coupled event horizons is not supported by the analysis.\n\nI also wish they had engaged the no-go arguments (Davidson-Rubin-Verbin; Faraoni-Rinaldi) in enough detail to say exactly which assumption they bypass. As it stands, the scope of the counterexample is unclear.\n\nWho is this for? Researchers working on McVittie-like metrics and LTB embeddings. It deserves referee time: the exact solutions and the new ansatz are worth having in the literature, and the flaws are fixable by either proving a global causal structure or revising the claims to apparent horizons. I would send it to peer review, but with the expectation of major revision.\n\nBest.","headline":"Clean exact solutions and a genuinely different ansatz, but the headline claim of static event horizons in cosmology is not established—these are apparent horizons with tuned late-time behavior.","tokens_in":12807,"tokens_out":4835,"would_cite":false,"duration_ms":48151,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83C57","83C15","83F05"],"pacs":["04.70.Bw","04.20.Jb","98.80.-k"],"model":"deepseek-v4-flash","headline":"The paper constructs black hole and white hole metrics with static event horizons embedded in expanding cosmologies, contradicting earlier no-go theorems.","keywords":["static event horizon","cosmological black hole","Painlevé-Gullstrand coordinates","white hole in expanding universe","Schwarzschild-de Sitter","apparent horizon","cosmological coupling","anisotropic pressure"],"falsifier":"Trace the paths of radial light rays in the metric (2.8) or in the dust white-hole solution and draw the conformal diagram; if any radial null geodesic from just inside $r=l_1$ reaches arbitrarily large radius, then the identified surface is only an apparent or isolated horizon, not a static event horizon.","tokens_in":11827,"feed_emoji":"🕳️","tokens_out":7833,"duration_ms":77250,"temperature":0.7,"pith_summary":"The paper aims to overturn a series of results that forbid static event horizons inside an expanding cosmological background. It presents explicit Painlevé–Gullstrand metrics in which the surface $r=l_1$ is a static horizon, curvature invariants stay finite there, and the spacetime reduces to the Schwarzschild–de Sitter solution when the Hubble parameter is constant. The key move is to drop the assumption that radial and tangential pressures are equal near the horizon, and instead to require only that the horizon be static and that the metric approach FLRW at large distances. For white holes in expanding universes this is straightforward; for black holes the velocity function must change sign, and a generalized ansatz is given to realize that transition. If the construction works, black holes embedded in cosmology do not have to be cosmologically coupled, and earlier no-go statements survive only under extra assumptions.","feed_headline":"Static event horizons can exist in an expanding cosmos","feed_subtitle":"Painlevé–Gullstrand metrics keep the horizon fixed while space expands far away, reducing to Schwarzschild–de Sitter when H is constant.","key_machinery":"The machinery is the Painlevé–Gullstrand metric ansatz $ds^2=-(1-h^2(t,r))\\,dt^2-2h(t,r)\\,dt\\,dr+dr^2+r^2\\,d\\Omega^2$, in which the horizon condition reduces to $h(t,l_1)=1$ and the sign of $h$ distinguishes white holes from black holes relative to the expanding background. A second form, $r=a(t,R)R$ with $h=R\\dot a$, turns the metric into a semi-homogeneous form that makes the dust and dust-plus-cosmological-constant solutions tractable. The same function $h$ carries the whole argument: it interpolates between Schwarzschild behavior near $r=l_1$ and FLRW behavior at large $r$, and in the black-hole case it is allowed to pass through zero so the spacetime can switch from an expanding cosmological phase to a contracting black-hole phase.","core_discovery":"On the paper's own terms, the central claim is that a static horizon can coexist with a cosmological background without a curvature singularity at the horizon, contrary to prior no-go theorems. The authors derive the metric from a minimal set of assumptions—no radial energy flux, a static horizon at $r=l_1$, cosmological energy density, and FLRW asymptotics—and show the resulting solution is unique in that class. For white holes in expanding universes, and black holes in contracting ones, the horizon is simply the surface where $h=1$; for black holes in expanding universes the velocity function $h$ must change sign, and the paper presents a generalized ansatz that allows this. The stress tensor, read through Einstein's equations, has anisotropic pressure, violates the null energy condition for the simplest family, and can be modified to respect that condition by relaxing the assumption that the energy density equals the FLRW value. In the constant-equation-of-state section, exact solutions with dust and with dust plus a cosmological constant show apparent horizons whose physical radius approaches a constant at late times, with the white-hole horizon in the latter case tending to its Schwarzschild–de Sitter value.","pith_inferences":["The paper verifies the horizon by the vanishing of the radial metric component and by finite curvature invariants; whether $r=l_1$ is a global event horizon in the strict causal sense requires a full conformal-diagram analysis, which the paper leaves implicit.","The same coordinate construction should extend to black holes with charge or rotation by generalizing the function $h$, a step not taken in this spherically symmetric treatment.","Because the escape route is the relaxation of pressure isotropy near the horizon, the construction suggests that the no-go results depend sensitively on that assumption and could be bypassed in modified gravity as well.","The sign-change criterion for $h$ offers a geometric way to identify the transition from cosmic expansion to local collapse, potentially useful for classifying apparent-horizon formation in inhomogeneous cosmologies."],"forward_implications":["If the central claim is correct, the statement that event horizons in cosmology must be cosmologically coupled is not a general theorem; it fails once the pressure near the horizon is allowed to be anisotropic.","The explicit metrics give a concrete starting point for studying accretion, shadows, or tidal effects of black holes embedded in an FLRW background, since they approach known cosmological and Schwarzschild–de Sitter limits.","In the constant-equation-of-state models, the physical apparent-horizon radius can become asymptotically constant at late times, so a cosmological white hole can appear static to a late-time observer.","The black-hole construction with sign-changing $h$ shows how a region of local gravitational collapse can smoothly emerge from an expanding cosmology, a behavior expected in structure formation but rarely realized in exact solutions."],"supporting_citations":[{"why":"supplies the classic cosmological black hole construction whose isotropic-pressure assumption the paper drops to achieve a static horizon","marker":"[1]"},{"why":"states the no-go result that an evolving universe cannot host a static event horizon, the claim being overturned","marker":"[4]"},{"why":"gives the recent theorem that black hole event horizons are cosmologically coupled, the central target of the paper","marker":"[5]"},{"why":"provides the original Painlevé–Gullstrand coordinates used to write the Schwarzschild metric","marker":"[13]"},{"why":"provides the complementary Gullstrand form of the same static coordinate system","marker":"[14]"},{"why":"supplies the FLRW and Schwarzschild–de Sitter metrics in Painlevé–Gullstrand coordinates from which the construction starts","marker":"[15]"},{"why":"supplies the Schwarzschild–de Sitter metric in Painlevé–Gullstrand form and the sign-choice ansatz used for the black-hole branch","marker":"[16]"}],"fun_headline_variants":["Static event horizons possible in expanding cosmos","White holes in expanding universes keep horizon static","Painlevé-Gullstrand metrics yield static horizons in cosmology","Black hole horizons can be static if velocity flips sign"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the surface $r=l_1$, where the radial metric component vanishes and the curvature invariants stay finite, is truly a global event horizon; the paper does not construct the full causal structure or prove that light rays starting just inside $r=l_1$ can never escape.","fun_headline_variants_meta":{"raw":{"variants":["Static event horizons possible in expanding cosmos","White holes in expanding universes keep horizon static","Painlevé-Gullstrand metrics yield static horizons in cosmology","Black hole horizons can be static if velocity flips sign"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000346,"raw_usage":{"total_tokens":1951,"prompt_tokens":1056,"completion_tokens":895,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":672,"completion_tokens_details":{"reasoning_tokens":832}},"tokens_in":672,"tokens_out":895,"duration_ms":9522,"temperature":1.0,"reasoning_tokens":832,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:23:32.501228+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Trace the paths of radial light rays in the metric (2.8) or in the dust white-hole solution and draw the conformal diagram; if any radial null geodesic from just inside $r=l_1$ reaches arbitrarily large radius, then the identified surface is only an apparent or isolated horizon, not a static event horizon.","supporting_citations":[{"cited_title":"The mass-particle in an expanding universe","cited_arxiv_id":null,"evidence_quote":"supplies the classic cosmological black hole construction whose isotropic-pressure assumption the paper drops to achieve a static horizon"},{"cited_title":"Can an evolving Universe host a static event horizon?","cited_arxiv_id":null,"evidence_quote":"states the no-go result that an evolving universe cannot host a static event horizon, the claim being overturned"},{"cited_title":"La m´ ecanique classique et la th´ eorie de la relativit´ e","cited_arxiv_id":null,"evidence_quote":"provides the original Painlevé–Gullstrand coordinates used to write the Schwarzschild metric"},{"cited_title":"Allgemeine L¨ osung des statischen Eink¨ orperproblems in der Einsteinschen Gravitationstheorie","cited_arxiv_id":null,"evidence_quote":"provides the complementary Gullstrand form of the same static coordinate system"},{"cited_title":"Cosmology in Painlev´ e-Gullstrand coordinates","cited_arxiv_id":null,"evidence_quote":"supplies the FLRW and Schwarzschild–de Sitter metrics in Painlevé–Gullstrand coordinates from which the construction starts"},{"cited_title":"Painlev´ e–Gullstrand coordinates for Schwarzschild–de Sitter spacetime","cited_arxiv_id":null,"evidence_quote":"supplies the Schwarzschild–de Sitter metric in Painlevé–Gullstrand form and the sign-choice ansatz used for the black-hole branch"}],"review_version":1}