{"id":"ff735e0e-cf88-42e1-a689-c5746c92281c","arxiv_id":"2506.08341","paper_version":4,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"For Kerr-Newman black holes, the Vlasov gas distribution depends only on constants of motion, and computed accretion rates push the hole toward Schwarzschild.","lead":"This paper models gases that almost never collide as they fall into rotating, charged black holes, and finds which particles get eaten and which escape. It shows such accretion spins the black hole down and neutralizes its charge, pushing it toward a simpler Schwarzschild shape.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Absorption/scattering domains derived for equatorial-periastron orbits are applied at all θ, biasing the accretion rates that support the central evolution-to-Schwarzschild claim.","rationale":"The reader's conditional verdict is appropriate, but their formal weakest_assumption (the Q3 elimination) is not the most load-bearing concern. The paper's Eq. (29) allowing a linear Q3 term is a byproduct of an incomplete Hamiltonian vector field in Eq. (27); the original Vlasov equation (8) already forces f to be independent of all angle variables, so Eq. (30) is correct even without the 'thermodynamic equilibrium at infinity' axiom. The genuinely fragile step is the transfer of the equatorial-periastron critical parameters to all θ in the domain integrals. The paper itself flags the restriction, but then uses those domains in the θ-integrated accretion rates. If the off-equatorial boundary is materially different, the quantitative claims in Sec. 5.2 and the qualitative evolution-to-Schwarzschild conclusion in Sec. 5.3 lose their support. A single recomputation with the general boundary, as proposed in concrete_test, would settle whether the approximation is numerically harmless. The backreaction/evolution inference is also overreaching for a fixed-background calculation, but the domain issue is more directly testable and affects the headline accretion numbers. Therefore the reader's CONDITIONAL verdict stands, with the requested revision focused on restricting or correcting the off-equatorial domain treatment.","tokens_in":13596,"tokens_out":16071,"duration_ms":196074,"concrete_test":"Recompute the Kerr (Q=0, a=0.9) mass accretion rate parameter ˙M∆ by replacing the equatorial E_c and \\bar{L}_c in Eqs. (53)-(56) with the general θ-, σ-dependent critical boundary obtained from solving R=0 and R'=0 in Eqs. (38)-(42) without imposing θ=π/2, then integrating over θ as in Eq. (75). If the normalized ˙M∆ changes by more than ~5% relative to Fig. 4a, the equatorial-periastron domain is load-bearing for the paper's accretion conclusions.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing assumption is not the Q3 elimination in Eq. (29) but the phase-space domain construction. Eqs. (49)-(50) define D_abs and D_scat using E_c and \\bar{L}_c from Eq. (47), whose derivation the text explicitly restricts to trajectories with periastron on the equatorial plane: \"It is crucial to emphasize that this analysis specifically addresses particle trajectories whose periastron lies on the equatorial plane (θ=π/2)\" (Sec. 3). Yet the momentum-space integrals (53)-(56) and the horizon accretion-rate integrals (75)-(77) evaluate these domains at arbitrary θ and integrate σ∈[0,2π]. For θ≠π/2, the critical energy and angular momentum for capture depend on θ and σ through the general periastron equations (41)-(42), so the equatorial boundary misclassifies orbits. This biases the normalized mass/energy accretion rates and the angular-momentum rate in Figs. 4-5, and thereby the Sec. 5.3 inference that accretion drives Kerr-Newman toward Schwarzschild. The Q3 issue, by contrast, is not load-bearing: a linear Q3 term in Eq. (29) does not satisfy the Vlasov equation because Q3 advances along the Hamiltonian flow, so Eq. (30) survives even if the 'thermodynamic equilibrium at infinity' argument is dropped.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies collisionless Vlasov gas in Kerr-Newman spacetime. Section 2 claims that spacetime symmetries constrain the one-particle distribution function to the form f=f(m,E,L_z,L) (Eq. (30)), with the dependence on the angle variable Q^3 eliminated. Section 3 analyzes charged-particle trajectories, derives periastron conditions, and defines absorption and scattering domains in momentum space (Eqs. (49)-(50)). Section 4 computes particle flux, energy-momentum tensor, LNRF-frame observables, asymptotic quantities at infinity, and horizon-regularized accretion rates for a Jüttner-distributed two-species plasma. Section 5 presents numerical profiles and accretion rates for Kerr, Reissner-Nordström, and extremal Kerr-Newman black holes, and concludes that accretion of weakly charged plasma drives a Kerr-Newman black hole toward a Schwarzschild configuration. The central quantitative claims, including the evolution-to-Schwarzschild conclusion, rest on the phase-space domain construction and on the numerical evaluation of the accretion integrals.","tokens_in":13883,"tokens_out":9271,"duration_ms":125330,"significance":"If the analysis were fully correct, the paper would provide a useful analytic framework for kinetic accretion in stationary axisymmetric charged spacetimes: explicit absorption/scattering boundaries, LNRF observables, and asymptotic formulas that recover the Schwarzschild Jüttner-gas limits. The paper does contain genuinely useful components: the periastron conditions (41)-(42), the first-order-in-κ expressions (44)-(46), the regularized horizon quantities (74), and the closed-form asymptotic results (70)-(73). The numerical exploration over a,Q∈[0,1] for multiple black-hole families is also a reasonable first survey. However, the load-bearing domain construction is restricted to equatorial-plane periastrons and is then applied at arbitrary θ, which directly affects the accretion rates and the main evolutionary conclusion. The symmetry derivation in Sec. 2.3 also overstates what is proven, since the elimination of all Q^3 dependence is an equilibrium assumption rather than a consequence of the Vlasov equation or Killing symmetries.","major_comments":[{"comment":"The critical boundaries E_c and \\bar L_c are derived only for trajectories whose periastron lies on the equatorial plane. The text states this explicitly: \"It is crucial to emphasize that this analysis specifically addresses particle trajectories whose periastron lies on the equatorial plane (θ=π/2)\" (Sec. 3, after Eq. (46)), and Fig. 1 is restricted to θ=π/2. Nevertheless, the domains D_abs and D_scat in Eqs. (49)-(50) are used in the momentum-space integrals (53)-(56) and in the horizon accretion integrals (75)-(77) at arbitrary θ with σ∈[0,2π]. For θ≠π/2, the general periastron conditions (41)-(42) show that the capture threshold depends on θ and σ, so the equatorial boundary misclassifies orbits. This biases the number/energy density profiles and, more importantly, the mass, energy, and angular-momentum accretion rates in Figs. 4-5, on which the Sec. 5.3 conclusion that accretion drives Kerr-Newman toward Schwarzschild is based. The authors must either restrict the entire analysis and conclusions to equatorial-plane periastrons or solve the general θ-dependent capture boundary and use it in all integrals.","section":"Sec. 3, Eqs. (47)-(50)"},{"comment":"The derivation of f=f(m,E,L_z,L) is not as conclusive as the abstract and Sec. 2.3 claim. The Vlasov equation and the Killing constraints (28) eliminate dependence on Q^0, Q^1, Q^2, but they do not eliminate dependence on Q^3. The linear term Q^3 \\hat f in Eq. (29) is excluded only by the additional \"natural physical conditions\" that the distribution be a steady state depending solely on action variables; the text itself uses phrases like \"we argue\" and \"natural choice\". Single-valuedness on the invariant torus excludes the linear term, but it does not exclude a periodic function of Q^3, which would satisfy the stated equations and be a single-valued function on phase space. Thus the statement in the abstract that the distribution function is \"shown\" to depend solely on (m,E,L_z,L) overstates the result. Since the subsequent Jüttner model is assumed, the accretion calculations are not invalidated, but the symmetry section should be reframed as an assumption or supplemented with a rigorous argument (e.g., a steady-state/ergodic condition) that rules out all Q^3 dependence.","section":"Sec. 2.3, Eqs. (27)-(30)"},{"comment":"The notation for the capture threshold in the domain definitions is ambiguous in a way that can change all results. In Eqs. (49)-(50), D_abs and D_scat list the radial-momentum bound simply as \\bar L_c, but Eq. (47) defines \\bar L_c as a function of the critical energy E_c(r), not as a function of the integration variable E. In the integrals (53)-(56), the lower (or upper) limit must be the capture angular momentum \\bar L_c(E) evaluated at the energy E being integrated, not a fixed number determined by E_c(r) at some radius. If the numerical implementation used a constant \\bar L_c, then the domains are mis-specified. The authors should write \\bar L_c(E) explicitly in (49)-(50) and clarify how the mapping E↦\\bar L_c(E) is obtained from (41)-(42).","section":"Sec. 4, Eqs. (49)-(56)"},{"comment":"The numerical results underlying the main physical conclusion lack convergence tests and error estimates. The accretion integrals (75)-(77) contain the singular factor 1/√Δ, and the regularization \\dot Q_Δ = lim_{r→r_H} √Δ \\dot Q in Eq. (78) requires careful numerical extrapolation. No grid-resolution studies, tolerance values, or estimated relative errors are reported for the curves in Figs. 4-5, even though the claim of identical functional dependence of mass and energy accretion rates and the monotonic trends in a and Q depend on the accuracy of these integrals. The authors should provide a convergence check (e.g., doubling the radial/angular/momentum grid and reporting the change) and state the numerical precision of the plotted quantities.","section":"Sec. 5, Figs. 4-5"}],"minor_comments":[{"comment":"Eq. (56) contains a typographical error: the second integral is written as ∫_{E_c}^{+∞} d\\bar L, but it should be ∫_{E_c}^{+∞} dE, consistent with Eq. (54) and with the following integration variable \\bar L in the third integral.","section":"Sec. 4.1, Eq. (56)"},{"comment":"The regularization of the energy density is defined as \\tilde ε ≡ e^{2ν} ε in Eq. (74), which is the correct finite combination near the horizon, but the caption of Fig. 3 writes \\tilde ε ≡ e^{-2ν} ε. The caption should be corrected to match Eq. (74).","section":"Sec. 4.5, Eq. (74) and Fig. 3 caption"},{"comment":"In the line \\bar L_c = g_{\\bar L}(a,Q,θ,E_c,σ,q), the symbol E_c appears both as the critical energy and as the argument of the function g. Since Eq. (47) defines E_c as a function of r, the notation is confusing; the authors should write \\bar L_c = g_{\\bar L}(a,Q,θ,E_c(r),σ,q) and explain how this gives the boundary curve \\bar L_c(E) used in the domains.","section":"Sec. 3, Eq. (47)"},{"comment":"The factor 2 in the scattering integrals is said to account for \"the symmetric treatment of pre- and post-scattering trajectories\" but this is not explained. For a periastron-passing trajectory, the radial momentum changes sign at the turning point; the factor 2 is correct only if the two branches have equal weight, which should be stated explicitly.","section":"Sec. 4.1, Eqs. (54)-(56)"},{"comment":"The quantity \\dot M is called the mass accretion rate, but J^a defined in Eq. (51) is the particle-number current. Since the Jüttner model in Eq. (69) has f∝δ(P_0−m), the identification \\dot M = m∫_S J^a \\bar n_a holds only if the particle mass is set to unity. The text should state this convention explicitly to avoid a dimensionful inconsistency.","section":"Sec. 4.3, Eq. (67)"}],"recommendation":"major_revision","confidential_remarks":"The main blocker is the domain construction: the paper derives capture thresholds only for equatorial-plane periastrons and then integrates over all θ and σ. This is not a stylistic issue but a correctness issue for the accretion rates and for the Sec. 5.3 evolutionary claim. The symmetry section's overstatement in Eq. (30) should also be corrected, but it is less damaging because the Jüttner distribution is an assumed input. The numerical section needs convergence evidence before the quantitative claims can be trusted. If the general-θ periastron solution is analytically intractable, an acceptable alternative would be to restrict the entire paper to equatorial-plane accretion and temper the conclusions accordingly. The paper is within scope for the journal and is a reasonable extension of prior Vlasov-accretion work, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nRead the Vlasov-in-Kerr-Newman paper. It does two things: restates the standard Jeans-style result that f depends only on the conserved quantities (m,E,Lz,L), and then builds a new calculation of absorption/scattering domains and accretion rates for charged gas around a rotating, charged black hole. The latter is the actual contribution. The analytic expressions for the domains and the LNRF observables, including the charge coupling κ, are not in the earlier Kerr-equatorial papers, so there is real new material here.\n\nThe paper is also honest in places. The footnote about the two-species plasma being a toy model for identical particles is a good caveat. The asymptotic expressions at infinity correctly reduce to the Schwarzschild values. The numerical work covers a sensible range of a and Q.\n\nThe soft spot, and it is load-bearing, is the phase-space domain. In Sec. 3 the critical energy and angular momentum E_c and \\bar L_c are derived from periastron conditions that the paper itself restricts to the equatorial plane (θ=π/2). A few pages later, these same boundaries are used in the momentum-space integrals and in the horizon accretion-rate integrals, which integrate over all θ and σ. For θ≠π/2 the capture boundary can be different, so the accretion rates in Figs. 4 and 5 are likely biased. That bias feeds directly into the Sec. 5.3 claim that accretion drives Kerr-Newman toward Schwarzschild. The conclusion may be qualitatively right, but the quantitative support is not there yet.\n\nThe symmetry part is a lesser issue. The derivation through the elimination of Q3 is convoluted and leans on an equilibrium-at-infinity argument, but the final form f=f(m,E,Lz,L) is the standard Jeans' theorem result for an integrable system, so the conclusion is correct. The Q3 term is not actually the problem.\n\nAlso, the numerical results would benefit from convergence checks, and the evolution-to-Schwarzschild statement should be softened to a fixed-background test-field regime rather than a universal dynamical result.\n\nWho should read this: kinetic-theory people working on black hole accretion, especially those who want explicit formulas for charged gas around Kerr-Newman. It deserves a serious referee; with a fix to the domain construction (either full θ-dependent boundaries or a clear justification that the equatorial approximation is valid off-equator), it could be a solid paper. As it stands, I would not cite the numerical accretion rates without reservation.\n\nRecommendation: send to peer review, but flag the domain issue as a major revision.","headline":"Useful extension of Vlasov accretion to Kerr-Newman with charged particles, but the phase-space domains are computed for equatorial periastron and then applied at all angles, which likely skews the accretion rates and the Schwarzschild-evolution conclusion.","tokens_in":14399,"tokens_out":11394,"would_cite":false,"duration_ms":129158,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83C57","83C10"],"pacs":["04.70.-s","05.20.Dd"],"model":"deepseek-v4-flash","headline":"A collisionless charged gas around a rotating, charged black hole has a distribution function fixed by mass, energy, axial angular momentum, and total angular momentum; the resulting accretion drives the hole toward a neutral…","keywords":["Vlasov gas","kinetic theory","black hole accretion","Kerr-Newman metric","Carter constant","hidden symmetries","accretion rate","Jüttner distribution"],"falsifier":"A concrete check is to start a kinetic simulation with a distribution function that has a non-zero linear $Q^3$ dependence and see whether the steady-state accretion rate onto a Kerr–Newman black hole differs from the rates computed here; a different result would show that Eq. (30) is not generic. Equivalently, a direct calculation of $\\mathcal{L}_{Z_{L^2}} f$ for a physically motivated source at infinity that gives $\\mathcal{L}_{Z_{L^2}} f \\neq 0$ would falsify the reduction.","tokens_in":13391,"feed_emoji":"🕳️","tokens_out":15045,"duration_ms":146761,"temperature":0.7,"pith_summary":"This paper builds a kinetic description of a collisionless, charged Vlasov gas around a Kerr–Newman black hole. It argues that the spacetime's symmetries—stationarity, axisymmetry, and the hidden Carter symmetry—reduce the one-particle distribution function to a function of only the four constants of motion, $f=f(m,E,L_z,L)$, provided the gas is sourced from thermodynamic equilibrium at infinity. With that form, the paper analytically separates captured from scattered trajectories and computes number density, energy density, principal pressures, and mass, energy, and angular momentum accretion rates in the Locally Non-Rotating Frame. For a Jüttner-distributed neutral plasma, accretion of weakly charged gas removes both charge and spin from the hole, so a Kerr–Newman black hole evolves toward a Schwarzschild configuration.","feed_headline":"Accretion of charged gas drives black holes to Schwarzschild","feed_subtitle":"Kinetic model shows accreting plasma removes both charge and spin, leaving a static hole.","key_machinery":"The load-bearing object is the reduced distribution function $f=f(m,E,L_z,L)$ of Eq. (30). It rests on three pieces: the Killing symmetries giving energy $E$ and axial angular momentum $L_z$; Carter's Killing tensor $C_{ab}=2\\rho^2 l_{(a}k_{b)}+r^2 g_{ab}$, whose hidden symmetry supplies the Carter constant $L^2$ and completes integrability; and the action-angle coordinates $(P_0,P_1,P_2,P_3)=(\\sqrt{-2H},E,L_z,L)$ with conjugate variables $Q^\\mu$, in which the Vlasov equation forces $\\partial f/\\partial Q^0=\\partial f/\\partial Q^1=\\partial f/\\partial Q^2=0$, leaving at most linear dependence on $Q^3$. The equilibrium-at-infinity argument eliminates the $Q^3$ term. This reduced distribution, together with the periastron conditions $R=0$, $R'=0$ that define the absorption and scattering domains, carries all later computations of fluxes, densities, pressures, and accretion rates.","core_discovery":"The paper's central claim is Eq. (30): in Kerr–Newman spacetime the distribution function of a collisionless Vlasov gas depends solely on the constants of motion, $f=f(m,E,L_z,L)$. The Killing vectors $\\partial_t$ and $\\partial_\\varphi$ provide $E$ and $L_z$, while Carter's Killing tensor provides the hidden constant $L$; complete integrability then permits action-angle variables in which the Vlasov equation forces the distribution to be independent of three of the four angle coordinates. The remaining angle $Q^3$ is dropped by the steady-state/equilibrium-at-infinity argument, leaving the reduced form on which every later integral is built. From this foundation the paper derives the critical energy and angular momentum separating absorption from scattering, computes the densities and principal pressures in the LNRF with horizon-regularized quantities, and obtains analytic accretion rates. Numerical evaluation for a charge-symmetric Jüttner plasma shows the normalized mass and energy accretion rates are equal functions of $(a,Q)$ and are suppressed by both spin and charge, while the magnitude of the negative angular momentum accretion rate grows with $a$ and falls with $Q$; together these trends push the hole toward neutrality and zero spin.","pith_inferences":["If the equilibrium-at-infinity assumption is relaxed, the distribution function can retain a linear $Q^3$ term; a natural test is to build a steady-state gas with a non-trivial $Q^3$ dependence and compute whether the accretion rates shift. This is an editorial extension, not a claim in the paper.","The charge-asymmetric density profiles (negative charges enhanced, positive charges suppressed) imply a net electric current into the hole; the paper fixes the background geometry, so the back-reaction of the induced electromagnetic field on the gas is left for future work.","The exact coincidence of the mass and energy accretion rate functions likely comes from the exponential $e^{-zE}$ form of the Jüttner distribution; other distribution families should break the coincidence and could provide a kinetic diagnostic of the phase-space distribution.","If the Schwarzschild attractor behavior holds dynamically, the coupled system $\\dot M$, $\\dot a$, $\\dot Q$ could be integrated to give the neutralization and spin-down timescales, connecting kinetic accretion to the 'no-hair' relaxation of black holes."],"forward_implications":["For a Jüttner-distributed neutral plasma the normalized mass and energy accretion rates of a Kerr–Newman black hole are identical functions of the spin parameter $a$ and charge $Q$, and both decrease as $a$ or $Q$ increases.","The magnitude of the angular momentum accretion rate, which is negative, increases with spin $a$ and decreases with charge $Q$, so rotating holes lose angular momentum through accretion.","A Kerr–Newman black hole accreting weakly charged plasma evolves toward smaller charge and smaller spin, i.e., toward a Schwarzschild black hole, across the parameter range including extremal cases.","Pressure anisotropy ($P_1\\neq P_2\\simeq P_3$) and radial-pressure suppression at the horizon are intrinsic features of collisionless dynamics: they persist in Schwarzschild spacetime and are not caused by rotation or charge.","The analytic absorption and scattering domains provide closed-form integration boundaries, so all reported observables can be reproduced without orbit-by-orbit ray tracing."],"supporting_citations":[{"why":"Carter's Killing tensor supplies the hidden symmetry and the Carter constant $L^2$ that make charged-particle motion integrable and put $L$ among the arguments of $f$.","marker":"[39]"},{"why":"The action-angle construction gives the canonical coordinates $Q^\\mu$ conjugate to the constants of motion, used to show the distribution is independent of angle variables.","marker":"[40]"},{"why":"The geometric Vlasov framework on the cotangent bundle supplies the lifted symmetries and the equation $\\mathcal{L}_{\\hat T}f=0$ used throughout.","marker":"[17]"},{"why":"The locally non-rotating frame tetrad defines the measured number density, energy density, and principal pressures that are computed in the paper.","marker":"[41]"},{"why":"The Jüttner distribution ansatz and the Schwarzschild Vlasov-accretion baseline come from this work; the paper's asymptotic results reduce to its Schwarzschild limits.","marker":"[21]"},{"why":"The equatorial-plane Kerr accretion analysis with critical orbits supplies the periastron conditions and boundary curves adapted here to Kerr–Newman.","marker":"[32]"},{"why":"The demonstration that black-hole charge suppresses mass accretion is the result this paper extends and reproduces in its Kerr–Newman numerics.","marker":"[30]"}],"fun_headline_variants":["Vlasov gas reveals black hole accretion strips spin and charge","Charged particle accretion pushes Kerr-Newman holes to Schwarzschild","Kinetic model: accretion erases black hole spin and charge","Symmetry constraints on Vlasov gas determine black hole accretion","Accretion of Vlasov gas strips Kerr-Newman black holes of spin and charge"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The reduction to $f=f(m,E,L_z,L)$ depends on the assumption that a gas sourced from thermodynamic equilibrium at infinity must have a phase-space distribution function independent of the angle variable $Q^3$; if that equilibrium condition fails, the distribution can carry a linear $Q^3$ term and every accretion rate computed from the reduced form would change.","fun_headline_variants_meta":{"raw":{"variants":["Vlasov gas reveals black hole accretion strips spin and charge","Charged particle accretion pushes Kerr-Newman holes to Schwarzschild","Kinetic model: accretion erases black hole spin and charge","Symmetry constraints on Vlasov gas determine black hole accretion","Accretion of Vlasov gas strips Kerr-Newman black holes of spin and charge"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000603,"raw_usage":{"total_tokens":2880,"prompt_tokens":1075,"completion_tokens":1805,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":691,"completion_tokens_details":{"reasoning_tokens":1710}},"tokens_in":691,"tokens_out":1805,"duration_ms":15879,"temperature":1.0,"reasoning_tokens":1710,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T05:14:56.988625+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A concrete check is to start a kinetic simulation with a distribution function that has a non-zero linear $Q^3$ dependence and see whether the steady-state accretion rate onto a Kerr–Newman black hole differs from the rates computed here; a different result would show that Eq. (30) is not generic. Equivalently, a direct calculation of $\\mathcal{L}_{Z_{L^2}} f$ for a physically motivated source at infinity that gives $\\mathcal{L}_{Z_{L^2}} f \\neq 0$ would falsify the reduction.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Carter's Killing tensor supplies the hidden symmetry and the Carter constant $L^2$ that make charged-particle motion integrable and put $L$ among the arguments of $f$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The action-angle construction gives the canonical coordinates $Q^\\mu$ conjugate to the constants of motion, used to show the distribution is independent of angle variables."},{"cited_title":"Proc.1548134–155","cited_arxiv_id":null,"evidence_quote":"The geometric Vlasov framework on the cotangent bundle supplies the lifted symmetries and the equation $\\mathcal{L}_{\\hat T}f=0$ used throughout."},{"cited_title":"J.178347–370 14","cited_arxiv_id":null,"evidence_quote":"The locally non-rotating frame tetrad defines the measured number density, energy density, and principal pressures that are computed in the paper."},{"cited_title":"Quantum Grav.34095007","cited_arxiv_id":null,"evidence_quote":"The Jüttner distribution ansatz and the Schwarzschild Vlasov-accretion baseline come from this work; the paper's asymptotic results reduce to its Schwarzschild limits."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The equatorial-plane Kerr accretion analysis with critical orbits supplies the periastron conditions and boundary curves adapted here to Kerr–Newman."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The demonstration that black-hole charge suppresses mass accretion is the result this paper extends and reproduces in its Kerr–Newman numerics."}],"review_version":1}