{"id":"bb44f837-3833-417f-bd64-befe0c929925","arxiv_id":"2501.10298","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Given identical boundary data near infinity, two solutions of the AdS-Einstein-Maxwell equations must agree near that boundary, provided the boundary region satisfies a null-convexity condition.","lead":"This mathematics paper proves a new rigidity theorem for spacetimes with a negative cosmological constant coupled to an electromagnetic field: boundary data seen at infinity uniquely determine the spacetime near the boundary. It is the first treatment of this uniqueness problem for a matter field, extending the vacuum results of Holzegel and Shao, and matters because it makes rigorous progress on the mathematical side of the AdS/CFT correspondence.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Proposition 4.29's rho-weight hierarchy for renormalised difference wave equations is asserted after 'careful analysis'; if any displayed decay is off by one, the Carleman closing step in Prop 4.45 fails, so the central claim rests on an unverified algebraic estimate.","rationale":"The paper's central theorem is structural: under the GNCC, identical or gauge-equivalent holographic data force the nonlinear Einstein-Maxwell system to coincide near the boundary. I read the near-boundary asymptotics chapter (Theorem 3.5, Corollary 3.7, Proposition 3.8) as a substantial and mostly self-contained ODE/transport analysis, and the fixed-gauge uniqueness argument (Proposition 4.45) follows a standard architecture with plausible boundary-term vanishing (Proposition 4.34, Corollary 4.35). The place where the argument is least secure is Proposition 4.29, where the asymptotic weights of the renormalised difference wave equations are not actually derived. These weights control exactly the terms that must be absorbed by the Carleman estimate; a single rho-power error would break the closure. This is a concrete algebraic gap, not a disagreement with consensus. It is also independent of the gauge-transformation issue: even the fixed-gauge result needs (4.51)-(4.52). The transformation of g(n) under a FG radius change (Proposition 4.48) is indeed asserted rather than proved, but it affects only the gauge-invariant packaging; if that formula were incomplete, the core fixed-gauge theorem could still hold. Thus I keep the reader's CONDITIONAL verdict: the concern is serious but plausibly fixable by a direct computation, so no verdict change is needed.","tokens_in":91074,"tokens_out":10809,"duration_ms":113032,"concrete_test":"Independently derive (4.52) for G_{h2} by taking the difference of the wave equations (square + 2(n-2)) h2 = RW,h2 and their checked counterparts, applying the renormalisation (4.35), and using (2.12), Proposition 2.24, Proposition 4.27 and Proposition 4.28 to track every term in (4.28). Specifically verify that all D^2 delta g terms cancel and that the resulting D Delta h coefficient is O_{M-2}(rho^3; D Delta h), with no residual O_{M-2}(rho^2; D Delta h) or O_{M-3}(rho; D Delta h) term. A symbolic computation of the I_{2,h}+I_{3,h} sum in the proof of Proposition 4.29 with a generic (0,2)-tensor Q satisfying (4.33) would settle the question.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Proposition 4.29 (equations (4.51)-(4.52)) is the hinge of the Carleman closing argument. The displayed rho-decay of the error terms for the renormalised Maxwell-curvature fields Delta h_0 and Delta h_2 must be exactly as stated: for example, the coefficient of D Delta h is O_{M-2}(rho^3), not O_{M-2}(rho^2), because the Carleman estimate (4.93) controls rho^4 |DA|^2. The proof expands many delta S terms but then says 'after a careful analysis' to assemble I_{1,h}+I_{2,h}+I_{3,h} into (4.52). The critical cancellation of the uncontrolled D^2 delta g terms (in I_2 and I_3) is not displayed; it relies on the precise symmetrisation in the definitions of Q (4.33) and B (4.34). If any rho-power in (4.51)-(4.52) is off by one, the absorption step in Proposition 4.45 (just after inequality (4.97)) no longer closes. This is a concrete algebraic gap, not a matter of convention, and it is the one place where the new Maxwell degrees of freedom could destabilise the vacuum Holzegel-Shao mechanism.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper extends the near-boundary Fefferman-Graham expansion of Shao and the local unique-continuation theorem of Holzegel–Shao from the vacuum AdS Einstein equations to the coupled Einstein–Maxwell system with negative cosmological constant. In the first part, the author derives, under finite regularity assumptions, a partial near-boundary expansion of the metric and of the Maxwell field, identifies the free holographic data (g(0), g(n), f0,((n−4)+), f1,(0)), and derives constraints on these data. In the second part, using a vertical wave–transport formalism, renormalised difference fields Q, B and ΔA, and Carleman estimates imported from [6], the author proves that two Maxwell-FG-aAdS segments with gauge-equivalent holographic data on a domain D satisfying the generalised null convexity criterion (GNCC) are isometric near D, with the Maxwell fields equal up to a boundary-preserving diffeomorphism. The proof is presented in a fixed Fefferman-Graham gauge first and then extended to the gauge-invariant statement via conformal transformations of the boundary data.","tokens_in":91204,"tokens_out":3134,"duration_ms":36197,"significance":"If the proof is correct, this is a substantive extension of the existing vacuum results to the first nontrivial matter model, and it confirms that the electromagnetic field does not alter the geometric null-convexity condition for unique continuation, since g(2) is still the Schouten tensor of g(0) for n ≥ 3. The paper is largely self-contained in its analytic framework: the transport equations (3.33)–(3.36) and the ODE proposition (Proposition 3.22) are standard and internally consistent, the free coefficients are genuinely boundary data delivered by Frobenius analysis rather than fitted parameters, and the F=0 limit reduces the results to the vacuum theorems. The main result, Theorem 4.51, is conditional on the Carleman estimate of [6] and on the weight hierarchy in Proposition 4.29, both of which are clearly stated hypotheses. The paper is written in a detailed, if long, style and gives many of the intermediate computations in appendices.","major_comments":[{"comment":"The central claim rests on Proposition 4.29, but its proof is not complete: the passage from the displayed individual estimates in the proof of Proposition 4.29 to the final formulas (4.51)–(4.52) is asserted with the phrase “after a careful analysis”. In particular, the cancellation of the uncontrollable D^2δg terms in I_{2,h}+I_{3,h} and I_{2,w}+I_{3,w} is not demonstrated; the reader is asked to trust that the terms in (4.60)–(4.61) and (4.66)–(4.67) exactly cancel. Since the Carleman estimate (4.93) controls only ρ^4|DA|^2 and not D^2δg, any residual D^2(δg+Q) term, or an error term whose ρ-power is one less than stated, would break the absorption step in Proposition 4.45. This is a load-bearing algebraic gap and needs a step-by-step verification.","section":"§4.6, Theorem 4.51 (and §4.5, Proposition 4.45)"},{"comment":"The ρ-weight hierarchy in Proposition 4.29 is exactly what allows the Carleman closing argument to work, and it is not robust to off-by-one errors. The proof of Proposition 4.29 lists many estimates for terms such as ρ^2δS(g; Dw, f) and ρ^2δS(g; Dh, f), but it does not show how the final sums I_{1,h}+I_{2,h}+I_{3,h} and I_{1,w}+I_{2,w}+I_{3,w} are assembled into the displayed forms (4.52) and (4.51), respectively. The extra Maxwell fields h0 and h2 introduce many new error terms, and the boundary of the claim is precisely that these do not destabilise the vacuum mechanism. The author should either display the relevant summation or give a precise combinatorial lemma covering all terms in the wave equations (4.26)–(4.29) and their differences.","section":"§4.2, Proposition 4.29, equations (4.51)–(4.52)"},{"comment":"The iteration that improves the order of vanishing of the difference fields is only sketched: the hierarchy (4.80), the assertion that each integration gains “two powers of ρ”, and the claimed regularity losses are stated without a formal proof. In particular, the repeated integrations of the transport equations (4.70)–(4.77) require tracking the regularity index M0 in each step, and the final statement in (4.86) depends on a specific choice of M0−n even. The current proof is plausible and the displayed formulas are consistent, but the induction is not written out. Since Proposition 4.34 is used to eliminate the boundary terms in the Carleman estimate, a concise but complete induction should be included.","section":"§4.3, Proposition 4.34 and Corollary 4.35"}],"minor_comments":[{"comment":"The sentence “the coefficient g(0), as well as the divergence– and trace–free parts of g(n) are not constrained by the equations of motion” is accurate, but the parenthetical in footnote 1 says the trace and divergence are constrained; the text should explicitly distinguish the free parts from the constrained trace/divergence to avoid confusion.","section":"§1.1, after Eq. (1.8)"},{"comment":"In the proof of Lemma 3.28, the phrase “Let first n ≥ 4; the case n = 3 follows an identical reasoning” appears after formulas that are only written for n ≥ 4; the n=3 case is then not actually demonstrated. The reader would benefit from a short sentence explaining the n=3 modifications, especially in the treatment of the stress-energy tensor terms.","section":"§3.2, Lemma 3.28"},{"comment":"The GNCC is defined for a strongly FG-aAdS segment, but Theorem 4.51 assumes only Maxwell-FG-aAdS segments; the proof of Proposition 3.8 shows that such segments are strongly FG-aAdS, but this implication should be stated explicitly at the point where the GNCC is invoked.","section":"§4.4, Definition 4.38"},{"comment":"The constants “M0 big enough” and “f⋆ small enough” are not quantified. This is common in unique-continuation arguments, but the author should at least state an explicit lower bound on M0 (e.g., M0 ≥ n + 6 or whatever the proof requires) so the statement can be verified.","section":"§4.5, Proposition 4.45"},{"comment":"There are several typographical issues, including “Ho lzegel” in the abstract, “satsifies” in Assumption 1, and missing closing parentheses in some displayed formulas (e.g., Eq. (3.20) and the line after (4.91)). A careful proofreading pass is needed.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The paper is a detailed and valuable contribution, but the proof of the central unique-continuation result contains an explicitly identified gap in Proposition 4.29 that must be addressed. The gap is local and algebraic in nature and likely fixable, but it is load-bearing, so I recommend major revision rather than rejection or acceptance. The author should also be encouraged to provide a fuller proof of the higher-order vanishing iteration in Proposition 4.34. The paper fits the scope of the journal and, if repaired, would be a strong addition to the literature."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First the headline: this is the first generalization of the Holzegel–Shao uniqueness program to a nontrivial matter model, and the near-boundary expansion for Einstein–Maxwell is a real step forward. The fixed-gauge unique continuation looks structurally sound, but the hinge of the Carleman argument — the rho-weight hierarchy in Proposition 4.29 — is asserted after \"a careful analysis\" rather than shown, and that is the one place where the Maxwell degrees of freedom could break the vacuum mechanism.\n\nWhat the paper does well: the ODE/transport analysis in Section 3 is substantial and mostly present. The dimension-dependent free data for F, the constraints on g(n), f0, and f1, and the observation that g(2) remains the Schouten tensor of g(0) (so the GNCC is unchanged by the Maxwell field) all check out at the level of the displayed equations. The renormalised difference fields Q, B, and ΔA follow the Holzegel–Shao architecture, and the F=0 limit reduces cleanly to the vacuum theorems. There are no fitted parameters or circular benchmarks.\n\nThe soft spots are real but proportionate. First, Proposition 4.29 is the load-bearing step. The proof expands many δS terms and then says \"after a careful analysis\" to assemble the rho-decay rates (4.51)–(4.52). The critical cancellation of the uncontrolled D^2δg terms is summarised, not derived, and the absorption step in Proposition 4.45 depends on exactly those weights. This is a concrete algebraic gap, not a matter of convention. Second, the gauge transformation of g(n) in Proposition 4.48 is asserted via universal functions rather than derived; since the gauge-invariant theorem relies on it, that needs a real proof, not a pointer to the physics literature. Third, the abstract claims unique continuation without the n>2 restriction that appears in Theorem 4.51; minor, but worth fixing.\n\nI did not find an internal contradiction in the fixed-gauge result, and the higher-order vanishing argument is persuasive in outline. For mathematical GR readers working on bulk-boundary correspondence or unique continuation, this is worth engaging with seriously.\n\nRecommendation: send to peer review. Ask the author to write out the full computation behind Proposition 4.29 and to give a derivation of the g(n) gauge transformation. The paper deserves referee time; it is not ready to pass without those details.","headline":"First extension of Holzegel–Shao unique continuation to a nontrivial matter model, with a genuinely new Fefferman–Graham expansion, but the Carleman closing argument hides a key algebraic estimate that needs referee scrutiny.","tokens_in":91928,"tokens_out":3604,"would_cite":true,"duration_ms":32387,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83C05","35B60","35L05","58J45"],"pacs":[],"model":"deepseek-v4-flash","headline":"Boundary data uniquely determine the metric and Maxwell field near the conformal boundary in AdS–Einstein–Maxwell theory, under the same geometric condition as the vacuum case.","keywords":["asymptotically anti-de Sitter spacetimes","Einstein–Maxwell system","Fefferman–Graham expansion","unique continuation","Carleman estimates","holographic data","generalised null convexity criterion","conformal boundary"],"falsifier":"A concrete observation that would refute the central claim is a pair of smooth Maxwell-FG-aAdS solutions whose holographic data are gauge-equivalent on a domain $D$ satisfying the GNCC but whose metrics are not isometric in any neighbourhood of $\\{0\\}\\times D$; Theorem 4.51 asserts no such pair exists, so one explicit counterexample would settle the question negatively. A more computational check is to verify the claimed cancellation of the $\\mathrm{D}^2\\delta g$ terms in Proposition 4.29: locating a missed term with the same weight as the left-hand side of (4.49) would break the Carleman closing argument.","tokens_in":90688,"feed_emoji":"🌌","tokens_out":10069,"duration_ms":90392,"temperature":0.7,"pith_summary":"This paper proves that the coupled Einstein–Maxwell system in asymptotically anti-de Sitter (AdS) spacetimes has the same near-boundary uniqueness behaviour as the vacuum Einstein equations. The main claim is that on a boundary domain satisfying the generalised null convexity criterion (GNCC)—a geometric condition that prevents near-boundary null geodesics from hovering over the domain—the holographic data, namely the metric coefficients $(\\mathfrak{g}^{(0)},\\mathfrak{g}^{(n)})$ together with the Maxwell coefficients $(\\mathfrak{f}^{(0)},\\mathfrak{f}^{(1)})$, determine the bulk metric and electromagnetic field uniquely in a neighbourhood of the boundary domain, up to gauge. To support this, the paper first derives a Fefferman–Graham-type expansion for the metric and Maxwell field in finite regularity, identifies which expansion coefficients are free and which are constrained, and characterises when two sets of boundary data are gauge-equivalent. If correct, this is the first nonlinear unique-continuation result for a nontrivial matter-coupled Einstein system from the conformal boundary, and it shows the geometric hypothesis does not need to be strengthened when matter is added.","feed_headline":"Boundary data pin down the bulk in AdS gravity with Maxwell fields","feed_subtitle":"Two solutions sharing holographic data on a convex boundary patch must be isometric nearby.","key_machinery":"The load-bearing object is the renormalised difference field $\\Delta A := \\delta A - \\tfrac12 g^{bc}\\sum_{j} A_{\\cdots b \\cdots}(\\delta g+Q)_{\\cdots c \\cdots}$ (with $Q$ an auxiliary antisymmetric tensor solving a transport equation and $B\\sim D\\delta g$ its curl companion), because it makes the uncontrollable second derivatives of $\\delta g$ cancel in the difference wave equations. Around this, the paper builds a vertical wave-transport system for the Weyl-tensor components $w_\\star,w_1,w_2$ and the Maxwell-derived fields $h_0,h_2$, closes it with the Carleman estimate of Theorem 4.43 whose weight is constructed from the GNCC-defining function $\\eta$, and kills the boundary terms using the improved vanishing of the difference fields obtained by iterating the transport equations. For the expansion part, the key mechanism is an ODE/Frobenius analysis of transport equations of the form $\\rho f'(\\rho)-c f(\\rho)=h(\\rho)$, which yields the power-of-$\\rho$ and logarithmic terms in the Fefferman–Graham expansion and identifies the free coefficients.","core_discovery":"The central result, Theorem 4.51, states that two Maxwell-FG-aAdS segments (spacetimes of the form $\\rho^{-2}(d\\rho^2 + g(\\rho))$ solving the Einstein–Maxwell equations with the stated boundary limits) whose holographic data $(\\mathfrak{g}^{(0)}, \\mathfrak{g}^{(n)}, \\mathfrak{f}_{0,((n-4)+)}, \\mathfrak{f}_{1,(0)})$ are gauge-equivalent on a domain $D \\subset \\mathcal{I}$ satisfying the GNCC must be isometric in a neighbourhood of $\\{0\\}\\times D$, with the Maxwell fields mapped to each other by the same boundary-preserving diffeomorphism. In the fixed Fefferman–Graham gauge, Proposition 4.45 sharpens this: identical data on $D$ force $(g,F)=(\\check g,\\check F)$ near the boundary. The proof route is: first derive the near-boundary expansion (Theorem 3.5) showing which data are free; then write the difference of two solutions as a coupled wave-transport system for renormalised fields; then apply Carleman estimates whose boundary terms vanish because of the improved vanishing order from Corollary 4.35. The paper also proves that the coefficient $g_{(2)}$ in the expansion is the same combination of the boundary Ricci tensor as in vacuum, so the GNCC is not affected by the Maxwell field.","pith_inferences":["One testable extension is to verify the transformation laws (4.101)–(4.102) against an explicit exact family, such as the AdS–Reissner–Nordström solutions, where the holographic data can be computed explicitly in two different Fefferman–Graham gauges.","The paper's machinery suggests that for Klein–Gordon matter the same unique continuation may hold in the well-posed mass range, but the scalar mass would mix powers in the ODE analysis, making the existence of a clean free-coefficient hierarchy the main open technical question.","Because the boundary coefficient $g_{(2)}$ is shown to be independent of the Maxwell data, the GNCC remains a property of the boundary geometry alone; one could therefore search for a purely geometric characterisation of the largest domains on which the unique continuation holds, without solving the coupled system."],"forward_implications":["Any two Maxwell-FG-aAdS solutions with gauge-equivalent holographic data on a GNCC domain are isometric near that domain, so the map from boundary data to near-boundary bulk solutions is injective.","The Maxwell field does not change the unique-continuation condition: the GNCC for the coupled system is exactly the vacuum GNCC, since $g_{(2)}$ is the same Schouten-type combination of the boundary Ricci tensor.","The free holographic data are precisely $(\\mathfrak{g}^{(0)}, \\mathfrak{g}^{(n)}, \\mathfrak{f}_{0,((n-4)+)},\\mathfrak{f}_{1,(0)})$, and the remaining lower-order coefficients in the Fefferman–Graham expansion are determined from these data, with the constraints on the free data written down explicitly.","The local isometry extends the symmetries of the boundary data, so any Killing field of the boundary data on $D$ extends to a bulk symmetry near $\\{0\\}\\times D$ in the gauge-invariant sense of Theorem 4.51.","The known linear counterexamples on domains violating the GNCC mean the condition cannot simply be dropped, so the nonlinear theorem is at the expected sharp boundary."],"supporting_citations":[{"why":"Supplies the vacuum near-boundary Fefferman–Graham expansion in finite regularity that Section 3 extends to the coupled Maxwell system.","marker":"[41]"},{"why":"Gives the vacuum bulk-boundary correspondence and the renormalised-difference method that Section 4 adapts to the Einstein–Maxwell differences.","marker":"[18]"},{"why":"Proves the gauge-invariant wave Carleman estimate (Theorem 4.43) used for the difference fields.","marker":"[6]"},{"why":"Provides linear counterexamples to unique continuation when the GNCC fails, marking the condition as the sharp threshold.","marker":"[15]"},{"why":"Establishes unique continuation from infinity for tensorial wave equations in asymptotically AdS spacetimes, the linear foundation.","marker":"[19]"},{"why":"Extends the linear unique continuation to non-static boundary geometries, informing the boundary-geometry hypotheses.","marker":"[20]"},{"why":"Relates null-pseudoconvexity to the absence of near-boundary null geodesics and gives the geometric content of the GNCC.","marker":"[33]"},{"why":"Shows unique continuation for stationary vacuum spacetimes, a predecessor of the hyperbolic approach.","marker":"[7]"}],"fun_headline_variants":["Boundary patch data uniquely fix AdS-Einstein-Maxwell near the edge","With Maxwell fields, AdS boundary data still force unique bulk","Near-boundary uniqueness proved for coupled Einstein-Maxwell in AdS","AdS-EM: identical holographic data imply isometric spacetimes near boundary","Unique continuation from conformal boundary holds for Einstein-Maxwell"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is the generalised null convexity criterion on the boundary domain $D$: existence of a positive function $\\eta$ vanishing on $\\partial D$ with $(\\mathrm{D}^2\\eta - \\eta\\, g_{(2)})(X,X)>c\\,\\eta\\,h(X,X)$ along every $g_{(0)}$-null vector $X$; without it the wave Carleman estimate is unavailable and the paper's own earlier linear counterexamples show unique continuation fails generically.","fun_headline_variants_meta":{"raw":{"variants":["Boundary patch data uniquely fix AdS-Einstein-Maxwell near the edge","With Maxwell fields, AdS boundary data still force unique bulk","Near-boundary uniqueness proved for coupled Einstein-Maxwell in AdS","AdS-EM: identical holographic data imply isometric spacetimes near boundary","Unique continuation from conformal boundary holds for Einstein-Maxwell"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000425,"raw_usage":{"total_tokens":2225,"prompt_tokens":1040,"completion_tokens":1185,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":656,"completion_tokens_details":{"reasoning_tokens":1087}},"tokens_in":656,"tokens_out":1185,"duration_ms":10846,"temperature":1.0,"reasoning_tokens":1087,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T19:15:49.840728+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A concrete observation that would refute the central claim is a pair of smooth Maxwell-FG-aAdS solutions whose holographic data are gauge-equivalent on a domain $D$ satisfying the GNCC but whose metrics are not isometric in any neighbourhood of $\\{0\\}\\times D$; Theorem 4.51 asserts no such pair exists, so one explicit counterexample would settle the question negatively. A more computational check is to verify the claimed cancellation of the $\\mathrm{D}^2\\delta g$ terms in Proposition 4.29: locating a missed term with the same weight as the left-hand side of (4.49) would break the Carleman closing argument.","supporting_citations":[{"cited_title":"The near-boundary geometry of Einstein-vacuum a symptotically Anti-de Sitter space- times","cited_arxiv_id":null,"evidence_quote":"Supplies the vacuum near-boundary Fefferman–Graham expansion in finite regularity that Section 3 extends to the coupled Maxwell system."},{"cited_title":"The bulk-boundary correspondenc e for the Einstein equations in asymp- totically Anti-de Sitter spacetimes","cited_arxiv_id":null,"evidence_quote":"Gives the vacuum bulk-boundary correspondence and the renormalised-difference method that Section 4 adapts to the Einstein–Maxwell differences."},{"cited_title":"A gauge-invariant unique continua tion criterion for waves in asymp- totically Anti-de Sitter spacetimes","cited_arxiv_id":null,"evidence_quote":"Proves the gauge-invariant wave Carleman estimate (Theorem 4.43) used for the difference fields."},{"cited_title":"On counterexamples to unique co ntinuation for critically singu- lar wave equations","cited_arxiv_id":null,"evidence_quote":"Provides linear counterexamples to unique continuation when the GNCC fails, marking the condition as the sharp threshold."},{"cited_title":"Unique continuation from infinity in asy mptotically Anti-de Sitter spacetimes","cited_arxiv_id":null,"evidence_quote":"Establishes unique continuation from infinity for tensorial wave equations in asymptotically AdS spacetimes, the linear foundation."},{"cited_title":"Unique continuation from infinity in asy mptotically Anti-de Sitter spacetimes II: Non-static boundaries","cited_arxiv_id":null,"evidence_quote":"Extends the linear unique continuation to non-static boundary geometries, informing the boundary-geometry hypotheses."},{"cited_title":"Null geodesics and improved unique contin uation for waves in asymptot- ically Anti-de Sitter spacetimes","cited_arxiv_id":null,"evidence_quote":"Relates null-pseudoconvexity to the absence of near-boundary null geodesics and gives the geometric content of the GNCC."},{"cited_title":"Unique continuation and extensions of Killing vectors for stationary vacuum space-times","cited_arxiv_id":null,"evidence_quote":"Shows unique continuation for stationary vacuum spacetimes, a predecessor of the hyperbolic approach."}],"review_version":1}