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REVIEW 3 major objections 5 minor 83 references

Bondi accretion disk luminosity around neutral and charged Simpson-Visser spacetimes

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that the Simpson-Visser regularization length ℓ and electric charge Q shift the Bondi sonic radius, accretion rate, and luminosity of inflowing gas, offering a double observational marker to distinguish regular black…

desk verdict The exponential-density branch is a sound extension of Bondi accretion to Simpson-Visser spacetimes, but the barotropic branch, which drives the headline marker claim, has no valid sonic point and its reported radii are artifacts. read the letter →

arxiv 2507.21580 v1 pith:WHBVTDJL submitted 2025-07-29 gr-qc astro-ph.HE

Serena Gambino , Roberto Giambò , Orlando Luongo This is my paper
classification gr-qcastro-ph.HE MSC 83C5783C15 PACS 04.20.Dw04.70.-s04.50.Kd97.10.Gz
keywords BondiaccretionSimpson-Visserspacetimeregularblackholeswormholeschargedsonicpointluminositybarotropicfluid
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper investigates spherical Bondi accretion in the Simpson-Visser family of spacetimes, which uses a single parameter ℓ to interpolate between Schwarzschild black holes, regular black holes, extremal black holes, and traversable wormholes, and in a charged extension between Reissner-Nordström and charged regular solutions. It derives the relativistic conservation equations for accretion, identifies the critical (sonic) point where inflow becomes supersonic, and integrates velocity, density, and pressure profiles for two fluid models: a barotropic fluid with $P=w\rho$ and a fluid with an exponential (Sofue) density profile. The central finding is that the sonic radius, mass accretion rate, and disk luminosity shift systematically with ℓ and, more modestly, with charge $Q$, while near-horizon inflow velocities stay nearly the same across geometries. The authors argue that these shifts, which reach roughly 18–36% in the wormhole regime for exponential-density fluids, could serve as a double observational marker for distinguishing regular black holes and wormholes from their Schwarzschild and Reissner-Nordström counterparts.

What carries the argument

The machinery is the relativistic Bondi–Michel critical point system. From the conservation of energy flux and mass flux, the velocity equation is written in terms of the variable $V^2=d\ln(P+\rho)/d\ln\rho-1$, and the critical (sonic) point is fixed by the simultaneous vanishing of the two brackets, giving $V_c^2=1/(2\sqrt{x^2+\ell^2}/M-3)$ and $u_c^2=M/(2\sqrt{x^2+\ell^2})$ for the neutral case, with charged generalizations involving $Q$. Equating these critical quantities with the fluid-specific velocity law—$u^2=C_4^2/(1+w)^2-A(x)$ for the barotropic fluid, $u=C_3/(\rho(x^2+\ell^2))$ for the exponential profile—locates the sonic radius $x_c$, which is then converted into the mass accretion rate $\dot M=-4\pi(x^2+\ell^2)(P+\rho)u\sqrt{u^2+A}$ and the luminosity $L=\eta_{\rm eff}\dot M$. This chain from metric to velocity profile to observable is what carries the claim that ℓ and $Q$ leave measurable fingerprints in accretion flows.

What would settle it

Compute $V^2=d\ln(P+\rho)/d\ln\rho-1$ for $P=w\rho$: since the specific enthalpy $(P+\rho)/\rho=1+w$ is constant, $V^2\equiv 0$, and the first critical condition $V_c^2=u_c^2/(u_c^2+A)$ then forces $u_c=0$, so no finite sonic point exists. Solving the authors' equations (14a)–(14b) directly with $V^2=0$ for the constants in Tables I and IV and checking whether any positive $x_c$ remains would settle whether the barotropic sonic radii and the claimed barotropic shifts are physical; the exponential-density results are unaffected by this check.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the Bondi accretion observables encode the regularization parameter ℓ and the electric charge $Q$. Solving the Michel-type critical point system for the neutral Simpson-Visser metric $A(x)=1-2M/\sqrt{x^2+\ell^2}$, the authors find sonic radii that decrease slightly with ℓ for the barotropic fluid (deviations below roughly 1.5% from Schwarzschild) but shift substantially for the exponential density profile, reaching about 18% at $\rho_0=0.5\,\mathrm{AU}^{-2}$ and 36% at $\rho_0=1.0\,\mathrm{AU}^{-2}$ in the wormhole regime $\ell=2.5$. In the charged spacetime $A(x)=1-2M/\sqrt{x^2+\ell^2}+Q^2/(x^2+\ell^2)$ with $Q=0.3$, the sonic radius shifts by fractions of a percent for the black-hole cases and by up to about 8% (barotropic, $w=0$) or 35% (exponential, $\rho_0=1$) in the wormhole case relative to Reissner-Nordström. The critical inflow velocity $u_c$ is unchanged to numerical precision in every configuration, and near-horizon velocities are similar across solutions, whereas ℓ acts mainly on the critical point's position and $Q$ slightly dampens the near-horizon inflow velocity in the barotropic case. The paper concludes that ℓ and $Q$ together provide a double observational marker to distinguish these spacetimes from standard black holes.

Load-bearing premise

The load-bearing premise is that the standard Michel-type critical point system, which locates the sonic point by equating critical and fluid velocities, remains valid for a constant-$w$ barotropic fluid with $P=w\rho$; if that system does not admit a finite nonzero sonic radius for the chosen constants, then the barotropic critical radii reported in the tables would be artifacts rather than physical predictions.

Editorial extensions

If this is right

  • A measured sonic radius that deviates from the Schwarzschild value by more than a few percent cannot be produced by the barotropic fluid models considered, but is naturally produced by an exponential-density flow in the wormhole regime, so the fluid model matters for interpreting any observed shift.
  • If the accretion flow around a candidate compact object is consistent with an exponential density profile, deviations in $x_c$ of order 18–36% in the wormhole regime would indicate Simpson-Visser-type regularization rather than a Schwarzschild or Reissner-Nordström geometry.
  • Because $Q$ shifts the sonic radius by only fractions of a percent in black-hole cases, a measurement of $x_c$ alone cannot fix $Q$; the combination of $x_c$ and the near-horizon inflow velocity (damped by $Q$ in the barotropic case) is needed to separate the two parameters.
  • The insensitivity of the critical inflow velocity $u_c$ to both ℓ and $Q$ means velocity measurements at the sonic point are not a diagnostic; the diagnostic power lies in the location of the sonic point and in the luminosity and accretion-rate profiles.
  • For barotropic fluids, the near-overlap of all solutions (deviations below about 1.5%) implies that if the accreting matter is stiff or dust-like, standard and regular black holes are hard to separate with Bondi observables alone.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • One extension the paper does not pursue is testing how sensitive these shifts are to the specific choice of regular geometry; repeating the same Bondi calculation for Bardeen or Hayward metrics would show whether the ℓ-induced sonic shifts are a generic feature of regular black holes or specific to the Simpson-Visser coordinate choice.
  • The exponential-density results are the more robust channel for the proposed marker, because the constant-$w$ barotropic critical point construction can degenerate (for $P=w\rho$ the sound-speed combination vanishes identically); an independent derivation of the sonic condition for such fluids would clarify whether the barotropic trend is physical or an artifact of the chosen integration constants
  • A practical test of the double marker would be to fit the predicted luminosity and sonic-radius patterns to low-luminosity galactic nuclei, using the exponential profile as a proxy for dark-matter-contaminated environments; real accretion disks add angular momentum, magnetic fields, and radiative transfer that the spherically symmetric Bondi model omits, so the observed luminosity would need de-pr
  • If the near-horizon velocity insensitivity holds, spectral or interferometric measurements of inflow speed would be blind to ℓ and $Q$, pushing observational searches toward the sonic point location and bolometric luminosity instead.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript studies relativistic Bondi accretion in neutral and charged Simpson-Visser spacetimes, treating two fluid models: a constant-w barotropic fluid (P = wρ) and a fluid with an exponential density profile. The authors derive conservation equations, locate critical (sonic) points, integrate velocity/density/pressure profiles, and compute accretion rates and luminosities for Schwarzschild, regular black hole, and wormhole regimes. They conclude that the regularization parameter ℓ and the charge Q shift the sonic radius and modify accretion observables, proposing these shifts as a double observational marker for distinguishing regular black holes and wormholes from Schwarzschild and Reissner-Nordström solutions.

Significance. The core question—whether Bondi accretion observables can distinguish Simpson-Visser geometries from their classical counterparts—is timely and, if answered correctly, would be a useful contribution to the phenomenology of regular black holes. The manuscript presents a clear derivation of the conservation equations and an extensive set of numerical results, and the exponential-density branch appears internally consistent: a direct evaluation of V² at the tabulated exponential critical points satisfies the critical-point condition. However, the barotropic branch, which underpins the double-marker claim, is invalid because a constant-w equation of state makes the sound-speed variable V² vanish identically, so the critical-point system admits no finite positive-radius solution. The reported barotropic critical radii, accretion-rate deviations, and luminosity deviations are therefore artifacts rather than physical predictions, and the central observational claim is unsupported.

major comments (3)
  1. [§III.A, Eqs. (12)–(14); Tables I and IV] For the assumed equation of state P = wρ with constant w, the variable defined in Eq. (12) is identically zero: V² = d ln(P+ρ)/d ln ρ − 1 = d ln((1+w)ρ)/d ln ρ − 1 = 1 − 1 = 0. With V_c² = 0, Eq. (14a) forces u_c² = 0, and Eq. (14b) reduces to A′(x_c) = 0. For the neutral Simpson-Visser metric A′(x) = 2Mx/(x²+ℓ²)^{3/2}, which vanishes only at x = 0 (and is non-zero at x=0 for ℓ=0); for the charged metric with Q = 0.3 and the tabulated ℓ values, A′ also does not vanish at any positive radius used in the tables. Thus the critical radii reported in Tables I and IV do not solve the critical-point system derived by the authors. The barotropic columns of these tables and the corresponding figures are not supported by the equations in the paper.
  2. [Eq. (20); Table I] Equation (20) is algebraically inconsistent with the condition it claims to encode, namely the equality of Eq. (15b) and Eq. (18) at x = x_c. A direct derivation yields r_c = 3M(1+w)²/[2((1+w)² − C4²)], which is negative for the values used in Table I (C4 > 1+w), so no positive-radius solution exists for those constants. For ℓ=0, w=1, C4=2.09, the printed Eq. (20) gives x_c ≈ 4.04, whereas Table I reports 16.13; for w=0, C4=1.05, Eq. (20) gives x_c ≈ 3.82, again not 16.13. The tabulated values appear to come from the unsquared expression with an additional sign error. The barotropic critical radii, critical velocities, and all downstream accretion-rate and luminosity deviations are therefore not credible.
  3. [§V–§VI; Tables I–VI] The comparison of different geometries is not controlled with respect to the integration constants. The text states that the constants C_i are chosen to ensure the existence of a physical sonic point, and indeed C4 differs between the w=0 and w=1 cases (Tables I and IV) and C3 differs between the two exponential-density cases (Tables II and V). Since the critical radius depends sensitively on these constants, the percentage deviations in Tables III and VI cannot be attributed to ℓ and Q alone; they partly reflect the different boundary conditions chosen for each configuration. Even setting aside the barotropic inconsistency, the claim of a 'double observational marker' requires a common asymptotic boundary condition across the geometries being compared, which is not specified or implemented. This affects the quantitative predictions in both fluid models.
minor comments (5)
  1. [§V.A, paragraph after Fig. 2] The sentence 'from Eq. (21), it appears clear that the dependence on w is very weak' cites the wrong equation: Eq. (21) is the exponential-density velocity, not the barotropic expression; the dependence on w for the barotropic case should be discussed via Eq. (18).
  2. [Table II caption] The caption says 'C=10, C4 = 2.1', but the symbol C is not defined and the text uses C1 for the energy-flux constant; this should read C1=10.
  3. [Eq. (27) and §V] The luminosity formula in Eq. (27) uses η_eff, while the text and tables use η = 0.1; the notation should be unified.
  4. [§IV and §V] The units are inconsistent as written: M = 1 AU, Q = 0.3 (presumably in units of M but not stated), and ρ0 is given in AU^{-2}; please state the unit conventions explicitly for Q and ρ0.
  5. [Figures in Appendix A] The figure legends are missing the ℓ symbol (e.g., '=0.5, w=0.0' instead of 'ℓ=0.5, w=0.0'), which makes the plots difficult to read.

Circularity Check

2 steps flagged · score 6.0 of 10

Barotropic critical radii are artifacts: with P=wρ, V²≡0 makes the critical-point system unsolvable, and the reported x_c values are produced by hand-tuned constants C4, so the claimed ℓ/Q markers are not independent predictions.

  1. fitted input called prediction [Sec. III A 'Critical points', Eq. (20); Sec. V, Tables I]
    "V 2 = d ln(P + ρ) d ln ρ − 1 ... P (x) = wρ(x) ... To find the critical point ... equate the expression of the velocity at the critical point, Eq. (15b), with its generic counterpart for the barotropic case, Eq. (18), evaluated at x = xc ... The result reads xc = ± s 3M 2(1 + w)2 2(C2 4 − (1 + w)2) ! − ℓ2 ... All integration constants, denoted by Ci, are chosen to ensure the existence of a physical sonic (critical) point."

    For constant w, P+ρ=(1+w)ρ, so Eq. (12) gives V²=1−1=0 identically. The paper's own critical-point system (14a)-(14b) then forces u_c=0 and A′(x_c)=0, which has no finite solution for the Simpson-Visser or Reissner-Nordström metrics. The barotropic critical radius is instead obtained from the separate velocity equality defining Eq. (20), not from the critical-point system. Since C4 is freely chosen per (ℓ,w) 'to ensure the existence of a physical sonic point', the tabulated x_c values in Table I are not predictions of the spacetime model: they are restatements of the fitted C4 values.

  2. fitted input called prediction [Sec. IV A 'Barotropic fluid', Eq. (30); Sec. VI, Table IV]
    "Barotropic fluid. Equating u2 c to the barotropic velocity expression, Eq. (18), leads to ... which has to be solved numerically for each ( ℓ, w) couple, since the presence of Q does not allow for analytical outcomes."

    The charged barotropic branch inherits the same inconsistency: P=wρ with constant w makes V² in Eq. (12) vanish identically, so the charged critical-point condition (29a) cannot be satisfied at any finite radius. Equation (30) is again an imposed equality between the critical velocity expression and the barotropic velocity, not a solution of the critical-point system. With C4 already selected to force sonic points in the uncharged case, the additional 'modest shifts' attributed to Q in Table IV are generated by solving an equation that the model itself says has no critical point. Hence the claimed double observational marker (ℓ plus Q) is not an independent derivation but a consequence of the imposed velocity equality and hand-picked constants.

full rationale

The paper's general Bondi conservation equations and the exponential-density-profile branch are self-contained: the exponential critical radii are obtained by solving the stated algebraic conditions for each fixed C3, and no self-citation chain is load-bearing. However, the central barotropic claims fail internal consistency: for P=wρ, Eq. (12) gives V²=0 identically, which makes the critical-point system (14a)-(14b) unsolvable at finite radius. The paper bypasses this by imposing a separate velocity equality (Eqs. 20 and 30) and by tuning C4 per (ℓ,w) to 'ensure the existence of a physical sonic point'. The reported barotropic critical radii, velocities, accretion rates, luminosities, and the ℓ/Q shifts derived from them therefore reduce to the chosen integration constants rather than to predictions of the spacetime geometry. This is partial circularity concentrated in the barotropic sector, hence score 6 rather than 0-2; the exponential sector and the formal framework are not similarly compromised.

Assumptions & free parameters 9 free parameters · 4 assumptions · 0 invented entities

The central results depend on a large set of hand-chosen parameters (ℓ, w, ρ0, r0, Q, η, and integration constants C1, C3, C4). No parameter is fitted to observational data; the constants are selected to ensure the existence of critical points. The fluid models themselves, particularly the exponential density profile, are assumed rather than derived. No new physical entities are introduced.

free parameters (9)
  • Simpson-Visser length ℓ = 0.5, 1.5, 2.5 (plus 0 for Schwarzschild/RN)
    Central geometry parameter; chosen values span regular black hole, extremal, and wormhole regimes.
  • Barotropic EoS parameter w = 0 and 1
    Chosen to represent dust and stiff matter.
  • Exponential density profile amplitude ρ0 = 0.5 and 1.0 AU⁻²
    Central density amplitude, chosen; lower values yield no physical critical points in their setup.
  • Exponential density profile radius r0 = 10 AU
    Core radius of the assumed exponential density profile.
  • Integration constant C4 (barotropic) = 2.09, 1.05, 2.10, 1.12 (varies by case)
    Chosen to 'ensure the existence of a physical sonic point'; directly sets the critical radius via Eq. (20).
  • Integration constant C3 (mass flux) = 1.9, 2.1, 3.0 (varies by case)
    Appears in the continuity equation and the exponential critical point condition Eq. (23).
  • Charge Q = 0.3
    Chosen as a moderate charge satisfying Q≤M.
  • Efficiency parameter η = 0.1
    Used to convert accretion rate to luminosity in Eq. (27).
  • Mass M = 1 AU
    Normalization of the central object.
assumptions (4)
  • domain assumption Stationary, radial, spherically symmetric perfect fluid accretion
    Invoked throughout Section II B; the four-velocity is taken to have only t and x components.
  • domain assumption Mass flux conservation J^µ = ρ u^µ is assumed
    The continuity equation Eq. (10) treats ρ u^µ as conserved, which is not equivalent to baryon number conservation for a general barotropic fluid but follows standard Bondi literature.
  • ad hoc to paper The Michel critical point system with V² as defined applies to each fluid
    For P=wρ with constant w, V²=0 identically, so the system is unsolvable; the paper nevertheless uses it to extract critical radii, which is internally inconsistent.
  • domain assumption The exponential density profile is a complete fluid model
    The density profile Eq. (17) is assumed and the pressure is derived from the Bernoulli equation rather than specified by an equation of state, so the resulting flow need not satisfy standard energy conditions.

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Cite this review

Pith. "Pith review of Bondi accretion disk luminosity around neutral and charged Simpson-Visser spacetimes." pith.science (2026). https://pith.science/paper/WHBVTDJL

@misc{pith2026250721580,
  author       = {Pith},
  title        = {Pith review of: Bondi accretion disk luminosity around neutral and charged Simpson-Visser spacetimes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WHBVTDJL}},
  note         = {Machine review of arXiv:2507.21580}
}
abstract

We investigate relativistic Bondi accretion in the Simpson-Visser spacetime, which, via a single parameter $\ell$, interpolates between the Schwarzschild, regular black hole, extremal and wormhole regimes. First, we analyze the neutral Simpson-Visser geometry, recovering Schwarzschild at $\ell=0$, and then its charged extension of the Reissner-Nordstr\"om metric. In both these cases, we derive the conservation equations and analyze two representative fluid models: a barotropic perfect fluid and a constituent with an exponential density profile. By varying the parameters across regimes, we locate critical (sonic) points and integrate velocity, density and pressure profiles. While near-horizon inflow velocities are similar across the different solutions, we find that the critical radius and the resulting accretion rates and luminosities severely change, depending on the value of the parameter and type of fluid. Remarkably, the barotropic and exponential cases exhibit different trends in the outer regions. Moreover, by extending the analysis to the charged SV spacetime, we find that the presence of a central charge $Q$ produces additional, albeit modest, shifts in the sonic radius which, in combination with those induced by the regularization parameter $\ell$, could provide a double observational marker. In particular, while $\ell$ acts predominantly on the position of the critical point, in the barotropic fluid case, the electromagnetic contribution of $Q$ slightly dampens the inflow velocity near the horizon.

Figures

Figures reproduced from arXiv: 2507.21580 by the authors.

Figure 1
Figure 1. Barotropic EoS (p = wρ) profiles w.r.t. x/M: (a) radial velocity u(x), (b) density ρ(x), (c) pressure P(x), (d) accretion rate M˙ (x), and (e) luminosity L(x), for ℓ = 0.5, 1.5 and w = 0, 1. Critical radii are marked with filled circles in panel (a). 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 x 1.1 1.0 0.9 0.8 0.7 0.6 0.5 u(x) (a) 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 x 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 (x) (b) 2.5 5.0… view at source ↗
Figure 2
Figure 2. Comparison between Schwarzschild (ℓ = 0, black lines) and RBHs solutions for a barotropic EoS (p = wρ) profiles w.r.t. x/M: (a) radial velocity u(x), (b) density ρ(x), (c) pressure P(x), (d) accretion rate M˙ (x), and (e) luminosity L(x), for ℓ = 0.5, 1.5 and w = 0, 1. Critical radii are marked with filled circles in panel (a) [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Exponential density profile model w.r.t. x/M: (a) radial velocity u(x), (b) density ρ(x), (c) pressure P(x), (d) accretion rate M˙ (x), and (e) luminosity L(x), for ℓ = 0.5, 1.5 and ρ0 = 0.5, 1.0AU−2 . The critical points are marked in the velocity panel. 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 x 1.2 1.0 0.8 0.6 0.4 0.2 0.0 u(x) (a) 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 (x) (b) 2.5 5.0 … view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: Comparison between Schwarzschild (ℓ = 0, black lines) and RBHs solutions for an exponential density profile model w.r.t. x/M: (a) radial velocity u(x), (b) density ρ(x), (c) pressure P(x), (d) accretion rate M˙ (x), and (e) luminosity L(x), for ℓ = 0.5, 1.5 and ρ0 = 0.…
Figure 5
Figure 5. Figure 5: Barotropic EoS (p = wρ) profiles w.r.t. x/M: (a) radial velocity u(x), (b) density ρ(x), (c) pressure P(x), (d) accretion rate M˙ (x), and (e) luminosity L(x), for ℓ = 2.5 and w = 0, 1. Critical radii are marked with filled circles in panel (a). 20 15 10 5 0 5 10 15 20…
Figure 6
Figure 6. Figure 6: Comparison between Schwarzschild (ℓ = 0, black lines) and RBHs solutions for a barotropic EoS (p = wρ) profiles w.r.t. x/M: (a) radial velocity u(x), (b) density ρ(x), (c) pressure P(x), (d) accretion rate M˙ (x), and (e) luminosity L(x), for ℓ = 2.5 and w = 0, 1. Crit…
Figure 7
Figure 7. Figure 7: Exponential density profile model w.r.t. x/M: (a) radial velocity u(x), (b) density ρ(x), (c) pressure P(x), (d) accretion rate M˙ (x), and (e) luminosity L(x), for ℓ = 2.5 and ρ0 = 0.5, 1.0AU−2 . The critical points are marked in the velocity panel. 20 15 10 5 0 5 10 …
Figure 8
Figure 8. Figure 8: Comparison between Schwarzschild (ℓ = 0, black lines) and RBHs solutions for an exponential density profile model w.r.t. x/M: (a) radial velocity u(x), (b) density ρ(x), (c) pressure P(x), (d) accretion rate M˙ (x), and (e) luminosity L(x), for ℓ = 2.5 and ρ0 = 0.5, 1.…
Figure 9
Figure 9. Figure 9: Barotropic EoS (p = wρ) profiles w.r.t. x/M: (a) radial velocity u(x), (b) density ρ(x), (c) pressure P(x), (d) accretion rate M˙ (x), and (e) luminosity L(x), for ℓ = 0.5, 1.5, w = 0, 1 and Q = 0.3. Critical radii are marked with filled circles in panel (a). 2.5 5.0 7…
Figure 10
Figure 10. Figure 10: Comparison between RN (ℓ = 0, Q = 0.3, black lines) and charged RBHs solutions for a barotropic EoS (p = wρ) profiles w.r.t. x/M: (a) radial velocity u(x), (b) density ρ(x), (c) pressure P(x), (d) accretion rate M˙ (x), and (e) luminosity L(x), for ℓ = 0.5, 1.5, w = 0…
Figure 11
Figure 11. Figure 11: Exponential density profile model w.r.t. x/M: (a) radial velocity u(x), (b) density ρ(x), (c) pressure P(x), (d) accretion rate M˙ (x), and (e) luminosity L(x), for ℓ = 0.5, 1.5, ρ0 = 0.5, 1.0AU−2 and Q = 0.3. The critical points are marked in the velocity panel. 2.5 …
Figure 12
Figure 12. Figure 12: Comparison between RN (ℓ = 0, black lines) and RBHs solutions for an exponential density profile model w.r.t. x/M: (a) radial velocity u(x), (b) density ρ(x), (c) pressure P(x), (d) accretion rate M˙ (x), and (e) luminosity L(x), for , ρ0 = 0.5, 1.0AU−2 and Q = 0.3. T…
Figure 13
Figure 13. Figure 13: Barotropic EoS (p = wρ) profiles w.r.t. x/M: (a) radial velocity u(x), (b) density ρ(x), (c) pressure P(x), (d) accretion rate M˙ (x), and (e) luminosity L(x), for ℓ = 2.5, w = 0, 1 and Q = 0.3. Critical radii are marked with filled circles in panel (a). 20 15 10 5 0 …
Figure 14
Figure 14. Figure 14: Comparison between RN (ℓ = 0, Q = 0.3, black lines) and charged wormholes solutions for a barotropic EoS (p = wρ) profiles w.r.t. x/M: (a) radial velocity u(x), (b) density ρ(x), (c) pressure P(x), (d) accretion rate M˙ (x), and (e) luminosity L(x), for ℓ = 2.5, w = 0…
Figure 15
Figure 15. Figure 15: Exponential density profile model w.r.t. x/M: (a) radial velocity u(x), (b) density ρ(x), (c) pressure P(x), (d) accretion rate M˙ (x), and (e) luminosity L(x), for ℓ = 2.5, ρ0 = 0.5, 1.0AU−2 and Q = 0.3. The critical points are marked in the velocity panel. 20 15 10 …
Figure 16
Figure 16. Figure 16: Comparison between Schwarzschild (ℓ = 0, Q = 0.3, black lines) and charged wormholes solutions for an exponential density profile model w.r.t. x/M: (a) radial velocity u(x), (b) density ρ(x), (c) pressure P(x), (d) accretion rate M˙ (x), and (e) luminosity L(x), for ℓ…

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Reference graph

Works this paper leans on

83 extracted references · 38 canonical work pages

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    Exponential density profile 9

  2. [2]

    Bondi accretion for charged Simpson-Visser spacetime 10 A

    Quantifying deviations from the Schwarzschild solution 10 VI. Bondi accretion for charged Simpson-Visser spacetime 10 A. Regular black hole accretion 11 Barotropic equation of state 11 Exponential density profile 12 B. Wormholes accretion 12

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    Barotropic equation of state 12

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    Exponential density profile 13 arXiv:2507.21580v1 [gr-qc] 29 Jul 2025 2

    work page Pith review arXiv 2025

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    Final outlooks 14 Acknowledgments 15 A

    Deviations from the Reissner-Nordstr¨ om solution 14 VII. Final outlooks 14 Acknowledgments 15 A. Numerical trends for charged and uncharged Simpson-Visser solutions 16 References 24 I. INTRODUCTION Black holes (BHs) are among the most intriguing ob- jects predicted by general relativity and solutions to Einstein’s equations. While many observations in re...

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    Inflow velocity, density, and pressure profiles, shown in panels (a), (b), and (c), respectively, begin to diverge near the center

    The classical solution, depicted by black lines, closely resembles the RBH cases with small ℓ. Inflow velocity, density, and pressure profiles, shown in panels (a), (b), and (c), respectively, begin to diverge near the center. The critical radius increases by up to∼ 6 for moderate values of ℓ. Unlike the barotropic model, the exponential profile is less s...

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    Notably, the Schwarzschild profiles nearly coincide with the wormhole ones in the dust case, w = 0, albeit not for stiff matter

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    Exponential density profile The wormhole case with an exponential density profile is shown in Fig. 7. The inflow velocity, panel (a), is again split into two sets of curves depending on the value of ρ0. The velocity decreases outward and remains symmetrical with respect to the throat. Near x = 0, the falloff is smoother than in BH cases, especially for hi...

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.