The null energy condition in dynamic wormholes

David Hochberg (LAEFF); Matt Visser (Washington University)

REVIEW

The null energy condition in dynamic wormholes

David Hochberg (LAEFF), Matt Visser (Washington University)

General Relativity and Quantum Cosmology · Submitted 18 Feb 1998 · 22 references

Pith's verdict: A correct, compact Letter: the weak-violation theorem is airtight and checkable, the two-throat observation is the real contribution, and the strict-violation upgrade is asserted and deferred to the companion paper.

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arXiv IDgr-qc/9802048 (version 3)

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CitationDavid Hochberg (LAEFF), Matt Visser (Washington University). "The null energy condition in dynamic wormholes." arXiv:gr-qc/9802048 (1998). https://pith.science/paper/WOVGKFEZ

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Editor's note

read the letter

The thing to know up front: the three-line argument is right, and the two-throat observation is the genuine contribution. Everything past Eq. (8) is a promissory note to gr-qc/9802046, and the authors say so themselves. The classifier found no stated limitations in the abstract, but the body is candid about where the argument thins out — read the body, not the abstract, for the caveats. What is new: the static non-symmetric theorem was already theirs in Refs. [8] and [9]. Here they extend to fully time-dependent, non-symmetric spacetimes, and the sharp structural point is that a surface extremal for l+ need not be extremal for l-, so a dynamic wormhole has two throats. Eq. (6) makes the static coalescence transparent via l± = (V ± n)/2. That reframing is useful and explains a lot of the confusion in the earlier time-dependent literature. The weak result (Eqs. 1-8) I can check line by line: θ = 0, dθ/du ≥ 0, twist zero for an orthogonal congruence, σ² ≥ 0, so R_ab l^a l^b ≤ 0, and Einstein gives T_ab l^a l^b ≤ 0. No assumptions beyond Raychaudhuri. That is the load-bearing part and it holds. Soft spots, in order of weight. First, the upgrade to strict violation in Eq. (13): the step from the integrated constraint (11) to pointwise positivity (12) is one sentence — 'this constraint further implies' — and it is a localization argument (take f → δ, use continuity and compactness of Σ) that is not carried out. The authors flag it as messy and point to [11,14]. Acceptable for a Letter, but the strict claim rests on the companion paper. Second, the 'only static' half of [abstract:s2]: Eq. (6) proves static implies coalescence; the converse — coalescence implies a timelike Killing vector — is asserted, not shown. That is the one place the abstract outruns the text. Third, the universality claim depends on condition (9) being satisfiable for every wormhole one would want to call traversable; the paper treats it as a definitional refinement excluding degenerate cases. Reasonable, but it narrows the theorem relative to the Discussion's 'any configuration that deserves to be called a wormhole.' On the stress test: it mostly lands, but one part overreaches. The paper is explicit that claim (2) is weak (≤ 0) at the throat and only claim (3) is strict on an open neighborhood. The abstract's 'generic and universal' is consistent with that; don't fault them for a bait-and-switch they did not commit. Minor: the Discussion's line about a 'distressing number of papers' marred by computational error, with no names, is unverifiable. Rhetoric, not a defect. Who should read it: anyone working on energy conditions or wormhole solutions, and anyone who has been tripped up by spatial-embedding throat definitions in dynamic spacetimes — the paragraph on why embedding fails is worth the read on its own. Recommendation: send it out. It is a correct, standard-setting Letter. Referees should press on the localization step and on the converse in the two-throat claim.

Referee report

Significance

If correct, this is a genuine no-go theorem of broad scope: it removes the symmetry, asymptotic-flatness, and causality assumptions that limited both the original Morris–Thorne argument and the topological-censorship route of Friedman–Schleich–Witt, and it reduces the question to local geometry at a two-surface. The observation that time-dependent wormholes carry two distinct throats is a real conceptual contribution, and it explains a family of confusions in the earlier literature about what it means to 'pass through' an expanding or contracting wormhole. The result is parameter-free and purely geometric, with no free constants or fitted quantities, and it is falsifiable in the precise sense that any claimed NEC-satisfying traversable wormhole must violate one of the stated hypotheses (compactness and two-sidedness of Σ, vanishing expansion, strict local minimality of area, or the strict flare-out refinement of Eq. (9)). The paper is also commendably explicit about which steps are routine and which are technical, and it correctly credits Page's anti-trapped-surface idea as the source of the throat definition.

Major objections (2)

[Eqs. (11)–(12)] The step from the integrated constraint Eq. (11) to the pointwise positivity Eq. (12) is the one place in the Letter where the chain to the strict result of Eq. (13) is not self-contained. The text states only that 'this constraint further implies the existence of another open neighborhood ... such that dθ±/du± > 0', and then characterizes the remaining work as 'these messy technical details'. The intended argument is presumably a localization one — take f in Eq. (11) to approximate a delta function supported near a point of Σ, use continuity of the integrand and compactness of Σ — but as written the reader cannot check it. Since claim (3) of the introduction is one of the paper's four headline results, I would ask the authors to give that localization argument in three or four explicit lines, or, if space forbids, to state it as a named lemma with a precise pointer to the section of [11] where it is proved. I note that the authors are careful to say the open set 'may include the hypersurface Σ(0) itself but does not necessarily have to do so, its closure must however certainly intersect Σ(0)', which is consistent with claim (2) being only the marginal statement T_ab l^a l^b ≤ 0 at the throat itself; the manuscript is internally consistent on this point, and the concern is about checkability rather than about an error.
[Introduction, claim (4); footnote [14]] Claim (4) — that the transverse-averaged NEC is violated throughout an open interval — is announced in the introduction as one of the four central results, but the body gives no derivation sketch at all, only 'the fourth result follows from appropriate modifications of the integrated constraint Eq. (11). See [11,14] for details.' Footnote [14] additionally flags that the averaged flare-out condition 'must be carefully formulated to remain invariant under arbitrary affine reparametrizations of the null geodesic congruence', which is exactly the kind of subtlety that a reader of the Letter cannot resolve from the Letter. Either sketch the modification of Eq. (11) that yields claim (4), or move claim (4) out of the enumerated list of central results and present it as a corollary established in the companion paper. As it stands the enumerated list promises more than the body delivers.

Minor objections (6)

[Eq. (6)] The factor of 1/4 in θ± = ±(1/4) Tr[L_n γ] depends on the normalization l± = (V ± n)/2 and on the convention for Tr over the two-metric; a parenthetical note fixing the convention would save the reader a recomputation. The conclusion that θ+ and θ− vanish simultaneously in the static case is unaffected.
[Text following Eq. (1)] The statement that 'the twist ω± is automatically zero for any orthogonal geodesic congruence' is correct but is asserted rather than justified; one clause invoking hypersurface orthogonality (Frobenius) would make the derivation of Eq. (7) fully self-contained.
[Definition of throat, Eqs. (3) and (9)] It would help to say explicitly, in one sentence, that Eq. (9) is a definitional strengthening of the throat notion rather than a property derived from Eq. (3), and to note the consequence: configurations whose extremal surfaces are only weak minima of area are excluded from claim (3) but remain covered by claim (2). The text implies this but does not state it in one place.
[Abstract] The abstract speaks of 'violations of the null energy condition' without qualification, whereas claim (2) of the introduction is careful to say 'violated or on the verge of being violated on the throat itself'. Given that the strict statement holds only on an open region whose closure meets the throat, the abstract would be more accurate if it said 'violations at or near the throat', matching the phrase the authors themselves note is ubiquitous.
[Discussion, paragraph on semantic games] The remark that 'a distressing number of papers addressing this topic are marred by actual computational error' is not tied to any specific citation, unlike the surrounding discussion of semantic redefinitions, which does cite [15]. Either name the papers concerned or soften the sentence; an unverifiable blanket charge against unnamed work is not something a reader can act on.
[References] Reference [6] gives 'J.L Friedmann' while the text gives 'Friedman'; reference [16] gives 'B. Bahwal', presumably 'B. Bhawal'. The displayed set-theoretic expression in the introduction uses '⁄= φ' where '≠ ∅' is meant.

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The paper

The paper claims

Any wormhole throat, however time-dependent or lopsided, must violate the null energy condition in an open region around it.

The reading

The paper asks whether the link between traversable wormholes and exotic, energy-condition-violating matter survives when every simplifying assumption is dropped. Earlier proofs assumed static, spherically symmetric geometry, or relied on global theorems that demand asymptotic flatness and causality conditions. Hochberg and Visser define a wormhole throat purely locally: a compact two-surface whose cross-sectional area is a strict local minimum for light rays passing through it along one null direction, and they then apply the Raychaudhuri equation at that surface. The payoff is that no wormhole of any symmetry, any time dependence, and any asymptotic structure escapes the conclusion. A reader should care because it turns a folklore expectation into a general local theorem: if you want a shortcut between two regions, you must pay for it with stress-energy that no ordinary matter supplies.

What carries the argument

The load-bearing tool is the Raychaudhuri equation applied to the two null geodesic congruences orthogonal to the candidate throat, $dtheta_pm/du_pm = -1/2 theta_pm^2 - sigma_pm^{ab} sigma_pm^{ab} + omega_pm^{ab} omega_pm^{ab} - R_{cd} l_pm^c l_pm^d$. Every term except the curvature term is signed: the twist vanishes for an orthogonal congruence, the shear squared is non-negative, and $theta_pm = 0$ with $dtheta_pm/du_pm >= 0$ at the throat. The curvature term is therefore forced negative, and Einstein's equations pass that sign straight to the stress-energy tensor. The definition of the throat itself — area extremal and flaring out along the null direction, with at least one variation that strictly increases the area — is what keeps apparent horizons and bifurcation surfaces out of the theorem's scope.

Extended reading notes

Core claim

The central claim is that for a compact two-surface that is a strict local minimum of cross-sectional area along a null geodesic congruence, the null energy condition fails not merely at the surface but throughout an open neighbourhood whose closure meets it. The argument runs: at the throat the expansion $theta_+$ vanishes and the flare-out condition $dtheta_+/du_+ >= 0$ holds; the congruence is orthogonal so its twist vanishes and its shear squared is non-negative; the Raychaudhuri equation then gives $R_{ab} l_+^a l_+^b <= 0$, and Einstein's equations convert this into $T_{ab} l_+^a l_+^b <= 0$. A strengthened flare-out condition, requiring at least one infinitesimal area variation that strictly increases the area, upgrades the weak inequality to the strict one, $T_{ab} l_+^a l_+^b < 0$, on an open set. The second half of the result is structural: a time-dependent wormhole has two throats, one for each direction of travel, defined by the zero of $theta_+$ and the zero of $theta_-$ respectively, and these two surfaces coalesce into one only when a timelike Killing vector exists.

Load-bearing premise

The step from 'the null energy condition is saturated or violated at the throat' to 'it is strictly violated on an open region' rests on the strengthened flare-out condition — that at least one infinitesimal deformation of the throat strictly increases its area — and the authors themselves call the resulting technical steps messy and defer the details to the companion paper.

Editorial extensions

If this is right

No traversable wormhole, whatever its symmetry, time dependence, or asymptotic structure, can be supported by matter obeying the null energy condition.
A dynamic wormhole's two throats are physically distinct surfaces, so 'passing through the centre' is not the same as passing a throat: for an expanding wormhole the throat comes before the centre, for a contracting one after.
Definitions of wormhole throats built from spatial embedding diagrams in a chosen time slice can miss the throat entirely or mislocate it in the dynamic case.
Claims that time dependence temporarily suspends the energy-condition violation are reinterpreted: the violation can be moved around, but a traveller who reaches the far side must have crossed a throat where it occurs.
Any proposed wormhole solution in a modified gravity theory still has a total stress-energy tensor that violates the condition, even if the violation is shuffled into a scalar or exotic component.

Reading between the lines

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

Because the theorem is local, it should apply verbatim to throat-like surfaces in analogue gravity and condensed-matter systems that mimic Lorentzian geometry, giving a laboratory-independent statement about which effective spacetimes can support two-way shortcuts.
The result is a statement about the total stress-energy tensor, so it does not by itself rule out a wormhole whose exotic component is small in magnitude; quantifying how small the violation can be made for a given throat size and traversal time is a separate question the letter does not address.
If the two throats of a dynamic wormhole can be causally disconnected, as the authors note, then there should be configurations that are one-way traversable only; classifying which throat orderings give which causal structure looks like a tractable follow-up.
The same extremal-area-plus-flare-out definition could be used to sharpen the statement of topological censorship, replacing its global assumptions with a local energy-condition hypothesis.

Original abstract

We extend previous proofs that violations of the null energy condition (NEC) are a generic and universal feature of traversable wormholes to completely non-symmetric time-dependent wormholes. We show that the analysis can be phrased purely in terms of local geometry at and near the wormhole throat, and do not have to make any technical assumptions about asymptotic flatness or other global properties. A key aspect of the analysis is the demonstration that time-dependent wormholes have two throats, one for each direction through the wormhole, and that the two throats coalesce only for the case of a static wormhole.

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We extend previous proofs that violations of the null energy condition (NEC) are a generic and universal feature of traversable wormholes to completely non-symmetric time-dependent wormholes. We show that the analysis can be phrased purely in terms of local geometry at and near the wormhole throat, and do not have to make any technical assumptions about asymptotic flatness or other global properties. A key aspect of the analysis is the demonstration that time-dependent wormholes have two throats, one for each direction through the wormhole, and that the two throats coalesce only for the case of a static wormhole.

background contribution method result interpretation main claim

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We extend previous proofs that violations of the null energy condition (NEC) are a generic and universal feature of traversable wormholes to completely non-symmetric time-dependent wormholes.	contribution 0.99	0.91	0.72	asserted 0.99
s1	We show that the analysis can be phrased purely in terms of local geometry at and near the wormhole throat, and do not have to make any technical assumptions about asymptotic flatness or other global properties.	contribution 0.53	0.91	0.15	asserted 1.00
s2	A key aspect of the analysis is the demonstration that time-dependent wormholes have two throats, one for each direction through the wormhole, and that the two throats coalesce only for the case of a static wormhole.	result 0.86	0.91	0.20	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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References

Works cited (22)

[8]

D. Hochberg and M. Visser, Phys. Rev. D. 56, 4745 (1997)

View on Pith 1997
[9]

M. Visser and D. Hochberg, “Generic Wormhole Throats”, in The Internal Structure of Black Holes and Spacetime Singularities, ed. L.M. Burko and A. Ori, (In- stitute of Physics, Bristol, 1997)

View on Pith 1997
[11]

D. Hochberg and M. Visser, Dynamic wormholes, anti- trapped surfaces, and energy conditions , gr-qc/9802046

View on Pith Pith review arXiv
[14]

The averaged ﬂare-out condition places a constraint on the putative throat by asking that the extremal surface be outward-ﬂaring over at least half its area and must be carefully formulated to remain invariant under arbitrary aﬃne reparametrizations of the null geodesic congruence. See [11] for more details

View on Pith
[1]

M.S. Morris and K.S. Thorne, Am. J. Phys. 56, 395 (1988)

View on Pith 1988
[2]

M.S. Morris, K.S. Thorne and U. Yurtsever, Phys. Rev. Lett. 61, 1446 (1988)

View on Pith 1988
[3]

M. Visser, Lorentzian Wormholes: From Einstein to Hawking (American Institute of Physics, New York, 1995)

View on Pith 1995
[4]

M. Visser, Phys. Rev. D 39, 3182 (1989)

View on Pith 1989
[5]

M. Visser, Nucl. Phys. B 328, 203 (1989)

View on Pith 1989
[6]

J.L Friedmann, K. Schleich and D.M. Witt, Phys. Rev. Lett. 71, 1486 (1993)

View on Pith 1993
[7]

D. Hochberg, A. Popov and S.V. Sushkov, Phys. Rev. Lett. 78, 2050 (1997)

View on Pith 1997
[10]

D. Page, cited as a note-added-in-proof in [1]

View on Pith
[12]

S.W. Hawking and G.F.R. Ellis, The Large Scale Struc- ture of Space-Time (Cambridge University Press, Cam- bridge, England, 1973)

View on Pith 1973
[13]

R.M. Wald, General Relativity (University of Chicago Press, Chicago, 1984)

View on Pith 1984
[15]

P.S. Letelier and A. Wang, Phys. Rev. D 48, 631 (1993); A. Agnese and M. LaCamera, Phys. Rev. D 51, 2011 (1995); L.A. Anchordoqui, S.E. Perez Bergliaﬀa and D.F. Torres, Phys. Rev. D 55, 5226 (1997); K.K. Nandi, B. Bhattacharjee, S.M.K. Alam, and J. Evans, Phys. Rev. D57, 823 (1998)

View on Pith 1993
[16]

B. Bahwal and S. Kar, Phys. Rev. D. 46, 2464 (1992)

View on Pith 1992
[17]

T. Roman, Phys. Rev. D. 47, 1370 (1993)

View on Pith 1993
[18]

D. Hochberg and T. Kephart, Phys. Rev. Lett. 70, 2665 (1993)

View on Pith 1993
[19]

S. Kar, Phys. Rev. D. 49, 862 (1994)

View on Pith 1994
[20]

S. Kar and D. Sahdev, Phys. Rev. D. 53, 722 (1996)

View on Pith 1996
[21]

A. Wang and P.S. Letelier, Prog. Theor. Phys. 94, 137 (1995)

View on Pith 1995
[22]

L.A. Anchordoqui, D.F. Torres, M.L. Trobo, and S.E. Perez Bergliaﬀa, Phys. Rev. D 57, 829 (1998). 4

View on Pith 1998

Forward citations

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How the literature uses it

42 arXiv papers cite this in 48 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 1 paper

A class of exact solutions of the Einstein field equations representing non-static wormholes that obey the {\em weak and dominant energy conditions } is presented.

Dynamic wormholes and Energy Conditions · 0.85

Papers citing it · 38 sentences without a confident label

Uses its method or tool 1 paper

However, for a covariant treatment we follow the analysis by Hochberg and Visser [ref] .

Exotic solutions in General Relativity: Traversable wormholes and 'warp drive' spacetimes · The mathematics of embedding and generic static throat · 1.00

Compares with it 1 paper

However, it does not describe a dynamical wormhole throat of the kind described in e.g. [ref] .

Black bounces to traversable wormholes from pure gravity in four and higher dimensions · Dynamic wormholes and black bounces · 0.93

Cites it as background 7 papers

Traversability of WHs is subjected to the fulfilment of the flaring outward condition [ref] which, depending on the underlying theory of gravity, can be achieved by considering exotic matter [ref] or topological defects [ref] .

Testing wormhole solutions in extended gravity through the Poynting-Robertson effect · Geometrical proprieties · 0.85
They constructed smooth traversable wormholes with exotic matter that violates the null energy condition [ref] .

Traversable Thin-shell Wormhole in the 4D Einstein-Gauss-Bonnet Theory · Introduction · 0.84
Hochberg-Visser and Hayward: Hochberg and Visser gave several definitions for the wormhole throat with different strengths [ref] .

Trapping Horizons of the Evolving Charged Wormhole and Black Bounce · Wormhole throats · 1.00

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [8]

D. Hochberg and M. Visser, Phys. Rev. D. 56, 4745 (1997)

View on Pith 1997

[2] [9]

M. Visser and D. Hochberg, “Generic Wormhole Throats”, in The Internal Structure of Black Holes and Spacetime Singularities, ed. L.M. Burko and A. Ori, (In- stitute of Physics, Bristol, 1997)

View on Pith 1997

[3] [11]

D. Hochberg and M. Visser, Dynamic wormholes, anti- trapped surfaces, and energy conditions , gr-qc/9802046

View on Pith Pith review arXiv

[4] [14]

The averaged ﬂare-out condition places a constraint on the putative throat by asking that the extremal surface be outward-ﬂaring over at least half its area and must be carefully formulated to remain invariant under arbitrary aﬃne reparametrizations of the null geodesic congruence. See [11] for more details

View on Pith

[5] [1]

M.S. Morris and K.S. Thorne, Am. J. Phys. 56, 395 (1988)

View on Pith 1988

[6] [2]

M.S. Morris, K.S. Thorne and U. Yurtsever, Phys. Rev. Lett. 61, 1446 (1988)

View on Pith 1988

[7] [3]

M. Visser, Lorentzian Wormholes: From Einstein to Hawking (American Institute of Physics, New York, 1995)

View on Pith 1995

[8] [4]

M. Visser, Phys. Rev. D 39, 3182 (1989)

View on Pith 1989

[9] [5]

M. Visser, Nucl. Phys. B 328, 203 (1989)

View on Pith 1989

[10] [6]

J.L Friedmann, K. Schleich and D.M. Witt, Phys. Rev. Lett. 71, 1486 (1993)

View on Pith 1993

[11] [7]

D. Hochberg, A. Popov and S.V. Sushkov, Phys. Rev. Lett. 78, 2050 (1997)

View on Pith 1997

[12] [10]

D. Page, cited as a note-added-in-proof in [1]

View on Pith

[13] [12]

S.W. Hawking and G.F.R. Ellis, The Large Scale Struc- ture of Space-Time (Cambridge University Press, Cam- bridge, England, 1973)

View on Pith 1973

[14] [13]

R.M. Wald, General Relativity (University of Chicago Press, Chicago, 1984)

View on Pith 1984

[15] [15]

P.S. Letelier and A. Wang, Phys. Rev. D 48, 631 (1993); A. Agnese and M. LaCamera, Phys. Rev. D 51, 2011 (1995); L.A. Anchordoqui, S.E. Perez Bergliaﬀa and D.F. Torres, Phys. Rev. D 55, 5226 (1997); K.K. Nandi, B. Bhattacharjee, S.M.K. Alam, and J. Evans, Phys. Rev. D57, 823 (1998)

View on Pith 1993

[16] [16]

B. Bahwal and S. Kar, Phys. Rev. D. 46, 2464 (1992)

View on Pith 1992

[17] [17]

T. Roman, Phys. Rev. D. 47, 1370 (1993)

View on Pith 1993

[18] [18]

D. Hochberg and T. Kephart, Phys. Rev. Lett. 70, 2665 (1993)

View on Pith 1993

[19] [19]

S. Kar, Phys. Rev. D. 49, 862 (1994)

View on Pith 1994

[20] [20]

S. Kar and D. Sahdev, Phys. Rev. D. 53, 722 (1996)

View on Pith 1996

[21] [21]

A. Wang and P.S. Letelier, Prog. Theor. Phys. 94, 137 (1995)

View on Pith 1995

[22] [22]

L.A. Anchordoqui, D.F. Torres, M.L. Trobo, and S.E. Perez Bergliaﬀa, Phys. Rev. D 57, 829 (1998). 4

View on Pith 1998