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Traversable Asymptotically Flat Wormholes with Short Transit Times

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Pith's one-line read Quantum fluctuations of a cosmic string can render a classical flat-space wormhole traversable, with a minimum transit time approaching the separation of its mouths.

desk verdict A solid, careful extension of the perturbative traversable wormhole program with a genuinely new short-transit-time result; the main caveat is that the negative energy relies on a free-CFT model for string fluctuations with no estimate of bulk-field contributions. read the letter →

arxiv 1908.03273 v2 pith:P2HLBKYR submitted 2019-08-08 hep-th gr-qc

Zicao Fu , Brianna Grado-White , Donald Marolf This is my paper · ORCID
classification hep-thgr-qc
keywords traversablewormholesquantumback-reactioncosmicstringsHartle-HawkingstatenullenergyconditionReissner-NordströmblackholesWeylanomalytransittime
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 aims to show that a classical, non-traversable wormhole in asymptotically flat spacetime can be made traversable by the perturbative back-reaction of quantum fields in the Hartle-Hawking state (the natural vacuum for a black hole), without exotic matter or a cosmological constant. The concrete setting is a pair of oppositely charged black holes connected by a throat and held apart by cosmic strings; the quantum fluctuations of a compact cosmic string threading the throat act as 1+1-dimensional massless scalar fields and produce negative integrated null energy on the horizon. Because this energy is exponentially small in the mouth separation $d$, the paper emphasizes that traversability is exponentially fragile, yet a carefully timed signal can still cross with minimum transit time $t_{\min} = d + \text{logs}$. In the large-$d$ limit $t_{\min}/d \to 1$, which is more than a factor of two faster than the eternally traversable MMP wormholes and, at least in higher dimensions, saturates the speed limit implied by the generalized second law. A de Sitter analogue is computed as a counterpoint, where the same negative energy makes the wormhole harder to traverse.

What carries the argument

The load-bearing object is a $\mathbb{Z}_2$ quotient of a charged Bach–Weyl spacetime: two oppositely charged, Reissner–Nordström-like black holes connected by a non-traversable throat and held apart by cosmic strings, with a compact cosmic string threading the throat. Fluctuations of that compact string are modeled as $N$ copies of a 1+1-dimensional massless free scalar field, giving central charge $c=2N$. A conformal transformation from the string worldsheet to a standard cylinder maps the Hartle-Hawking state to the cylinder vacuum, and the Weyl anomaly fixes the horizon null-null stress tensor as $T_{u_c u_c} = -c/(64\pi)$, which integrates to the exponentially small negative energy of Eq. (2.20). The perturbation is fed into the linearized Einstein equations, inverted with a Green's function on the two-sphere (Eq. 3.15), to give the horizon displacement and finally the transit-time formula (Eq. 3.17). The same conformal-map machinery applied to $dS_d/\mathbb{Z}_2$ yields the opposite-sign cosmological counterpoint.

What would settle it

Compute the integrated null stress-energy on the horizon using the full Nambu–Goto string worldsheet theory, or include one-loop graviton and Maxwell contributions; if the result is not negative, or if its magnitude is not exponentially small in $\kappa_+ d$, then the predicted $t_{\min}=d+\text{logs}$ transit time does not follow. A more direct check would be to evolve the linearized Einstein equations with an independent numerical stress-tensor computation and test whether the horizon shift $\Delta V$ of Eq. (3.7) is negative as claimed.

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Extended reading notes

Core claim

The central claim is that perturbative back-reaction of quantum fields in the Hartle-Hawking state converts an almost-traversable, null-energy-condition-respecting wormhole in four-dimensional asymptotically flat spacetime into a traversable one, but only inside an exponentially fragile window. The governing quantity is the integrated affine null stress-energy along the classical horizon, computed by conformally mapping the compact cosmic string worldsheet to a cylinder: $\langle \int T_{UU}\,dU\rangle = -e^{-\kappa_+ x_0^*}\, c\kappa_+/16$ with $c=2N$, which at large separation $d$ is of order $-N\kappa_+ e^{-\kappa_+ d/2}$. This negative energy produces a horizon shift $\Delta V$ (Eq. 3.7), and the optimally timed geodesic crosses the wormhole in $t_{\min\,\mathrm{transit}} = d + \text{logs}$ (Eq. 3.17), so $t_{\min}/d \to 1$ as $d\to\infty$. The paper stresses that for non-extremal backgrounds the exponential smallness makes traversability highly sensitive to perturbations, including a signal's own back-reaction, and that the near-extremal limit is where perturbation theory breaks down and a non-perturbative eternally traversable wormhole of the MMP type is expected to emerge. The same computation on $dS_d/\mathbb{Z}_2$ has the opposite sign, so Hartle-Hawking negative energy there produces a time delay instead of a time advance.

Load-bearing premise

The construction stands on treating the compact cosmic string's quantum fluctuations as a set of 1+1-dimensional massless free scalar fields; if real string fluctuations are not well approximated by free fields, or if bulk fields and gravitons contribute energy of comparable size, the negative null energy that opens the wormhole could change sign or disappear.

Editorial extensions

If this is right

  • For widely separated mouths the minimum transit time is $d$ plus logarithmic corrections, so $t_{\min}/d \to 1$; in $D \ge 5$ this approaches the fastest-causal-curve bound derived from the generalized second law.
  • Because the integrated null energy is of order $e^{-\kappa_+ d/2}$, any positive-energy perturbation of that size — including, in realistic couplings, the signal's own back-reaction — can close the wormhole; the required care relaxes only after a time of order $d$.
  • In the near-extremal limit $\kappa_+ \to 0$, perturbative back-reaction diverges, which the paper reads as evidence that a full non-perturbative treatment should yield an eternally traversable wormhole along the lines of the MMP construction.
  • With a sufficiently large number $N$ of compact strings, fluctuations of the integrated null energy are suppressed by $1/\sqrt{N}$, so the semiclassical expectation-value calculation is reliable and bulk fields and linearized gravitons can be neglected.
  • The $dS_d/\mathbb{Z}_2$ counterpoint shows that the same kind of Hartle-Hawking negative energy can produce a time delay instead of a time advance, so the direction of the back-reaction depends on the background.

Reading between the lines

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

  • Editorial inference: The exponential fragility likely dominates practical questions: ambient radiation, gravitational waves, or the gravitational field of the signal itself would generically supply the exponentially small positive kick needed to shut the wormhole, making the $d+\text{logs}$ timing a property of an extremely isolated laboratory rather than a usable shortcut.
  • Editorial inference: Because the conformal-map derivation ties the result mainly to the $\mathbb{Z}_2$ quotient and the causal structure, the same exponential suppression and $t_{\min}/d\to 1$ behavior should reappear for other charged or rotating black-hole pairs, making this a general feature of perturbative near-NEC wormholes rather than a special property of the Bach–Weyl family.
  • Editorial inference: A testable extension is to replace the free-field model of string fluctuations with the full Nambu–Goto worldsheet theory, or to include one-loop graviton and Maxwell contributions; the sign and size of the integrated null energy is the first place such a correction could flip the traversability conclusion.
  • Editorial inference: The de Sitter counterpoint suggests that "negative quantum energy opens wormholes" is not a universal rule; a systematic survey of which backgrounds respond with time advance versus time delay would clarify where perturbative traversability is possible.
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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

2 major / 5 minor

Summary. This paper studies perturbatively traversable wormholes in four-dimensional asymptotically flat spacetime, continuing the framework of Gao-Jafferis-Wall and the authors' earlier work. The classical background is a Bach-Weyl-type dihole: two oppositely charged Reissner-Nordström-like black holes connected by a non-traversable wormhole, held apart by cosmic strings, with an additional compact cosmic string wrapped through the wormhole. The compact string's quantum fluctuations are modeled as 2N free 1+1-dimensional massless scalars, and a Weyl-anomaly computation under a conformal map to a cylinder yields a negative integrated null stress tensor on the horizon, Eq. (2.20), whose magnitude is exponentially small in the mouth separation d. Linearized Einstein equations and a closed-form Green's function on the sphere then give the null geodesic displacement and a minimal transit time t_min_transit = d + O(log d), Eq. (3.17), so t_min_transit/d tends to 1 for large d, improving on the MMP wormholes by more than a factor of two. The authors stress that, for non-extremal backgrounds, traversability is exponentially fragile and only available to appropriately timed signals, and an appendix analyzes the contrasting dS_d/Z2 'cosmological wormhole' in which negative null energy makes traversal harder.

Significance. If correct, the central result is a concrete four-dimensional asymptotically flat example in which quantum back-reaction renders a NEC-respecting classical wormhole traversable with a transit-time ratio approaching 1, saturating (in D >= 5) the conjectured lower bound and surpassing the eternally traversable MMP construction by more than a factor of two. The paper has genuine strengths: the conformal-map/Weyl-anomaly derivation of (2.20) is explicit and parameter-free; the Green's function (3.15)-(3.16) is given in closed form; the fragility of non-extremal traversability is discussed carefully, including the signal's own back-reaction (footnote 6) and fluctuation estimates (footnote 7); and the appendix provides an exact, self-contained dS_d/Z2 computation for arbitrary scalar masses. No parameter is fitted to the target result. The main qualifications are real but local: the string-fluctuation model is an assumption, bulk fields are neglected, and the minimal-transit-time formula is singular on the string core; these are fixable within the manuscript's scope.

major comments (2)
  1. [Section 2, Eq. (2.20), and Section 4] The negative integrated null energy (2.20) is computed by modeling compact cosmic string fluctuations as N free 1+1-dimensional massless scalars (c = 2N), and the paper states explicitly that bulk fields are ignored. Because (2.20) is exponentially small, of order N e^{-kappa_+ d/2}, any bulk-field method-of-images contribution that is only algebraically suppressed in d, or that has the opposite sign, would dominate for sufficiently large d at fixed N. The large-N defense in Section 4 would require N to grow faster than e^{kappa_+ d}, a condition that is not stated and that conflicts with the asymptotic claim t_min_transit/d -> 1 at fixed parameters. The authors should either bound or estimate the bulk-field (including linearized graviton) contributions to the integrated null energy, or explicitly restrict the traversability claim to the regime kappa_+ d less than or similar to ln N.
  2. [Section 3, Eqs. (3.15)-(3.17)] The Green's function H(theta) in (3.15) diverges logarithmically at theta = 0, which is the location of the compact cosmic string and the point where the paper claims the minimal transit time is achieved. Because H(theta) enters inside a logarithm in (3.17), t_min_transit(theta) tends to -infinity as theta tends to 0, so the claimed minimal transit time is singular at the quoted minimum, and the linearized geodesic-displacement formula (3.6) is not valid at that point. The remark in Section 3.2 that the divergence is 'rather small' because it is inside another logarithm does not remove the singularity. The authors should introduce a UV regulator at the string core (for example a finite string thickness or a cutoff theta_core), compute the regulated geodesic displacement and transit time, and show that d + logs is the regulator-independent result for geodesics outside the core.
minor comments (5)
  1. [Section 1, paragraph 3] The phrase 'non-contractable cycle' should read 'non-contractible cycle'.
  2. [Figure 4 caption] 'The spacetimes has two bifurcation surfaces' should read 'The spacetime has two bifurcation surfaces'.
  3. [Section 4, first paragraph] 'Fluctuations in the locations of the of cosmic strings' contains a duplicated 'of the'; one should be deleted.
  4. [Section 3.2, Eqs. (3.15)-(3.16)] For parameter ranges with 8 kappa_+ r_+ > 1, the degree lambda in (3.15) is complex and the closed form is not manifestly real or positive, whereas the spectral representation (3.16) is manifestly real and positive for all kappa_+ r_+ > 0; the intended domain of validity of each form should be stated.
  5. [Section 4, transit-time discussion] Since (3.17) implies that t_min_transit - d is a d-independent constant plus O(ln d), the paper should state explicitly whether the ratio t_min_transit/d approaches 1 from above or from below, given that the bounds of Refs. [8,9] prohibit the wormhole from providing the fastest causal curve between distant points.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the integrated null energy and transit time are derived from an explicit CFT calculation and a fixed coordinate normalization, not from fitted inputs or self-citation chains.

full rationale

The central negative-energy input, Eq. (2.20), is computed rather than fitted: string fluctuations are explicitly modeled as 1+1 massless free fields with c = 2N, and the integrated null energy follows from the Weyl anomaly of the conformal map (2.8) to a cylinder, with the numerical coefficient fixed by (2.14)–(2.18). No parameter in this computation is adjusted to produce the stated transit time or traversability. The back-reaction step uses the same authors' earlier perturbative framework [15], but that framework is a general method for almost-traversable wormholes applied here to a new charged Bach-Weyl background with a compact cosmic string; the cited framework is not equivalent to the specific claim and is not the target result. The choice x0* = d/2 + O(ln d/r+) is a coordinate normalization matching the standard Reissner-Nordström Kruskal coordinate to the geometric separation d defined in (2.2), not a fit to the target result, and the final t_min formula (3.17) is a derived consequence of the geodesic-displacement computation in those fixed coordinates. Self-citations are present but not load-bearing in a circular sense: the cited results are either re-derived or serve as background framework, and no step reduces to a definitional identity, a fitted input renamed as a prediction, or a self-citation chain that alone forces the conclusion. Modeling assumptions such as free-field string fluctuations and neglect of bulk fields are physical assumptions posing correctness risk, not circularity.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard QFT in curved spacetime, a specific modeling assumption for string fluctuations, and an approximation of the throat as Reissner-Nordstrom. The hand-chosen parameters are N and mu, chosen to validate the semiclassical and free-field approximations.

free parameters (2)
  • N, number of compact cosmic strings = large, with N G_N mu much less than 1 and mu r_0^2 much greater than 1
    Chosen by hand to suppress quantum fluctuations and justify the semiclassical treatment; central charge c = 2N enters the integrated null energy (2.20).
  • cosmic string tension mu = regime mu r_0^2 much greater than 1 and G_N mu much less than 1
    Chosen so string fluctuations linearize while conical deficit is negligible; this is a parameter regime, not a fit to data.
assumptions (6)
  • ad hoc to paper Cosmic string fluctuations are described by 1+1-dimensional massless free scalar fields with central charge c = 2N.
    Introduced in Section 2 to model quantum stress-energy; not derived from a specific string action; determines the negative null energy result (2.20).
  • domain assumption There exists a Hartle-Hawking state on the quotient spacetime M = tilde(M)/Z2 obtainable by the method of images from the Killing-invariant state on tilde(M).
    Used in Sections 1 and 2 to compute <T_kk>_M as cross-terms involving a point x and its image Jx.
  • domain assumption The charged Bach-Weyl and black-dihole solution of references [22-24] provides the classical background with two oppositely charged black holes held by cosmic strings.
    The paper relies on this solution as the starting geometry and does not rederive it; cited in Section 2.
  • domain assumption For d much greater than r+, the throat geometry is approximately Reissner-Nordstrom, so linearized perturbation about Reissner-Nordstrom captures the geodesic back-reaction.
    Used in Section 3.1 to derive the geodesic displacement formula (3.7) and the transit time formula (3.17).
  • standard math The Weyl anomaly formula (2.12) for null-null stress tensor under a conformal map is valid.
    Standard CFT result quoted from references [30,31]; used to obtain the horizon stress-energy (2.18).
  • domain assumption Bulk fields and linearized gravitons can be neglected relative to a large number N of cosmic strings.
    Stated in Section 2 to justify keeping only cosmic-string fluctuations in the stress-energy.

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Pith. "Pith review of Traversable Asymptotically Flat Wormholes with Short Transit Times." pith.science (2026). https://pith.science/paper/P2HLBKYR

@misc{pith2026190803273,
  author       = {Pith},
  title        = {Pith review of: Traversable Asymptotically Flat Wormholes with Short Transit Times},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P2HLBKYR}},
  note         = {Machine review of arXiv:1908.03273}
}
abstract

We construct traversable wormholes by starting with simple four-dimensional classical solutions respecting the null energy condition and containing a pair of oppositely charged black holes connected by a non-traversable wormhole. We then consider the perturbative back-reaction of bulk quantum fields in Hartle-Hawking states. Our geometries have zero cosmological constant and are asymptotically flat except for a cosmic string stretching to infinity that is used to hold the black holes apart. Another cosmic string wraps the non-contractible cycle through the wormhole, and its quantum fluctuations provide the negative energy needed for traversability. Our setting is closely related to the non-perturbative construction of Maldacena, Milekhin, and Popov (MMP), but the analysis is complementary. In particular, we consider cases where back-reaction slows, but fails to halt, the collapse of the wormhole interior, so that the wormhole is traversable only at sufficiently early times. For non-extremal backgrounds, we find the integrated null energy along the horizon of the classical background to be exponentially small, and thus traversability to be exponentially fragile. Nevertheless, if there are no larger perturbations, and for appropriately timed signals, a wormhole with mouths separated by a distance $d$ becomes traversable with a minimum transit time $t_{\text{min transit}} = d + \text{logs}$. Thus $\frac{t_{\text{min transit}}}{d}$ is smaller than for the eternally traversable MMP wormholes by more than a factor of 2, and approaches the value that, at least in higher dimensions, would be the theoretical minimum. For contrast we also briefly consider a `cosmological wormhole' solution where the back-reaction has the opposite sign, so that negative energy from quantum fields makes the wormhole harder to traverse.

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