Einstein-Maxwell-Dilaton Wormholes that meet the Energy Conditions

Leonel Bixano; Tonatiuh Matos

REVIEW 3 major objections 4 minor 19 references

Einstein-Maxwell-Dilaton Wormholes that meet the Energy Conditions

T0 review · 3 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read Exact rotating wormhole solutions of Einstein-Maxwell-dilaton gravity satisfy the null energy condition.

desk verdict Genuinely new λN1 branch and coherent exact-solution work, but the energy-conditions claim is not proven: only one null direction and two boundary slices are checked. read the letter →

arxiv 2502.07206 v1 pith:77KGX5ZG submitted 2025-02-11 gr-qc

Leonel Bixano , Tonatiuh Matos This is my paper · ORCID

classification gr-qc MSC 83C1583C2283C75

keywords Einstein-Maxwell-dilatontraversablewormholenullenergyconditionexactrotatingsolutionringsingularitycosmiccensorshiptidalforcesgeodesics

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

This paper claims to have constructed explicit, stationary, axisymmetric solutions of the Einstein-Maxwell-dilaton equations that represent traversable wormholes. The branch called $\lambda_5$ is asymptotically flat and, when the scalar field is dilatonic rather than phantom, the combination density minus radial pressure is nonnegative, so the wormhole does not require the exotic matter usually invoked for traversable wormholes. The spacetime carries a ring singularity at $x=y=0$, but the paper argues that the geometry deflects geodesics before they reach it, making the singularity causally disconnected. The second branch, $\lambda_{N1}$, is asymptotically flat only for a phantom scalar field, which does not satisfy the null energy condition, so the authors single out $\lambda_5$ as the physically feasible case. They also give concrete sizes for solar-mass, pulsar-like, and supermassive versions of the wormhole.

What carries the argument

The machinery is the five-potential formulation of the Einstein-Maxwell-dilaton equations on oblate spheroidal coordinates $(x,y)$, with $y=\cos\theta$ and $Lx=r-l_1$. The potentials are taken to be functions of a single harmonic seed $\lambda$ satisfying Laplace's equation, and the two seeds $\lambda_5$ and $\lambda_{N1}$ generate explicit metric and electromagnetic potentials through the integration formulas (12). The $\lambda_5$ seed produces metric (13), whose key properties are: $k(x,y)$ decays as $x\to\pm\infty$, giving asymptotic flatness; the Ricci and Kretschmann invariants stay finite except at $x=y=0$; and the combination $\rho-\varrho = (R_{\hat t\hat t}+R_{\hat x\hat x})/(8\pi)$, evaluated in the comoving frame used for wormhole analysis, is nonnegative for the dilatonic choice of $k_0$. The $\lambda_5$ branch is the load-bearing object of the paper; $\lambda_{N1}$ serves as a contrasting second family that is asymptotically flat only in the phantom case.

What would settle it

Evaluate the two remaining null projections, $T_{\hat t\hat t}+T_{\hat y\hat y}$ and $T_{\hat t\hat t}+T_{\hat\varphi\hat\varphi}$, in the comoving frame for the $\lambda_5$ dilatonic solution over $x\in\mathbb{R}$ and $y\in[-1,1]$; if either combination is negative at any point, the null energy condition is not satisfied.

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Extended reading notes

Core claim

The central discovery is that the Einstein-Maxwell-dilaton system admits a harmonic seed $\lambda_5 = \lambda_0 x/(x^2+y^2)+m_0$ that, after integrating the metric functions, yields the exact rotating wormhole metric (13). In that spacetime the invariants $R$ and the Kretschmann scalar tend to zero at spatial infinity and diverge only on the ring $x=y=0$, giving a ring singularity; the energy-momentum combination $\rho-\varrho$ is nonnegative for the dilatonic field, which the paper identifies with compliance with the null energy condition. Numerical geodesic integration shows that trajectories aimed at the ring are deflected back or around it, so the singularity is not in causal contact with the wormhole, a property the authors call wormhole cosmic censorship. The authors conclude that $\lambda_5$ is the physically viable branch and that the rotation, throat size, electric and magnetic fields can be matched to stellar-mass and supermassive objects.

Load-bearing premise

The energy-condition claim rests on checking one lightlike direction, straight through the throat in the comoving frame, and assuming that single check represents all lightlike directions; if transverse pressures turn negative anywhere, the title claim fails.

Editorial extensions

If this is right

If the $\lambda_5$ solution is correct, there are exact asymptotically flat rotating wormholes in Einstein-Maxwell-dilaton theory that satisfy the null energy condition, so traversability does not force exotic matter in this class.
The ring singularity at $x=y=0$ is unreachable by geodesics in the numerical solutions shown, extending the paper's wormhole cosmic censorship idea to this family.
For the $\lambda_5$ wormhole, tidal forces stay survivable near the poles and the equatorial plane for non-relativistic crossing, and a traveller can pass at constant $\theta$ without changing direction.
The parameter estimates give concrete values of throat size, angular velocity, electric and magnetic fields for Sun-mass, magnetar-like, and supermassive black-hole-mass wormholes; the $\lambda_{N1}$ branch, by contrast, predicts a throat of about one meter and becomes inconsistent for larger sizes.
The $\lambda_{N1}$ branch is asymptotically flat only with a phantom scalar field, which does not satisfy the null energy condition, so the paper's physical feasibility claim rests entirely on $\lambda_5$.

Reading between the lines

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

The paper checks the null energy condition through the single projection $T_{\hat t\hat t}+T_{\hat x\hat x}$ in the comoving frame; a reader extending the calculation would still need to verify the transverse projections $T_{\hat t\hat t}+T_{\hat y\hat y}$ and $T_{\hat t\hat t}+T_{\hat\varphi\hat\varphi}$ over the full domain to claim the condition holds for all null vectors.
The paper does not analyse linear or nonlinear stability; an exact NEC-satisfying rotating wormhole would become substantially stronger evidence for the rotating-wormhole stability conjecture if shown stable, but that remains an open question beyond this paper.
The SI-unit tables imply throat magnetic fields of order $10^7$ tesla for the solar-mass $\lambda_5$ example; an observational extension would be to ask whether such field strengths and rotation rates leave detectable lensing or polarization signatures, which the paper does not address.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: this is a legitimate exact-solutions paper with a genuinely new λN1 branch, but the headline claim—that these wormholes satisfy the energy conditions—is not established by the text as written. The missing work is probably doable, but it is missing.

What is new and good: The λN1 harmonic (11b) and metric (14) are new, and the substitution into the EMD field equations is coherent; constraint (16) determines k0 cleanly from the theory parameters, and Table I is consistent. The λ5 branch is inherited from the authors' own [4], and [13] already reported energy-condition-satisfying rotating wormholes, so the novelty is incremental but real. The embedding, tidal-force components, and the asymptotic-flatness discussion are worked out in enough detail to be useful to someone studying wormhole geodesics and traversability. The SI-unit estimates, while rough, are a sensible attempt to connect the solutions to astrophysical objects.

Where it falls short: Section IV claims the NEC but only evaluates T_μν l^μ l^ν for the single null vector l = e_t + e_x, and then only at y=0 and y=1. The y and φ null directions are never checked, and no argument is given that ρ+p_y or ρ+p_φ are nonnegative. In a stationary axisymmetric spacetime that is not automatic. The bracket in (24) can in principle change sign for intermediate y; boundary values don't settle it. This is the central claim, so this is a load-bearing gap, not a cosmetic one. The cosmic-censorship claim is supported by selected numerical geodesics with the y0=0 case explicitly excluded from the plots; the note in Fig 7 that the y0=0 geodesic rebounds without contact is not backed by a shown curve. Citations to the same group's earlier papers are not a substitute for a proof for these branches. The SI section also leaves the normalization √f0/(2κ0) unspecified, so Tables II and III are not independently reproducible as printed; and Table III contains a negative Q^2_L+H^2_L entry, which the conclusions attribute to the λN1 class being unphysical—fine, but it belongs in the main NEC discussion.

None of this suggests the construction is wrong. The exact solution is very likely salvageable; the NEC might hold for the dilatonic branch, and the paper just needs to prove it. But as submitted, the title oversells what is demonstrated.

Who it's for and what I'd do: worth sending to a serious referee—exact solutions with a new branch deserve that—but I would not accept it as is. Ask for a full NEC check (all null directions, or the orthonormal-frame pressure inequalities), a positivity proof or semi-analytic bound over the full domain for (24)-(25), and a clearer geodesic statement for y0=0. Then it could be a solid contribution.

Referee Report

3 major / 4 minor

Summary. The paper constructs two stationary, axisymmetric solutions of the Einstein-Maxwell-dilaton system in oblate spheroidal coordinates, labeled λ5 and λN1, using a potential-space ansatz. It claims that the λ5 solution is an exact, asymptotically flat traversable wormhole that satisfies the energy conditions for a dilatonic scalar field, has a ring singularity that geodesics cannot reach, and has tidal forces that allow safe traversal near the poles and equator. The λN1 solution is claimed to be asymptotically flat only for a phantom scalar and is judged less physical. The paper closes with SI-unit estimates of rotation, electromagnetic fields, and throat sizes for solar-mass, magnetar-type, and supermassive examples.

Significance. If the claims were established, the λ5 solution would be a useful explicit example of a rotating wormhole with non-exotic matter in a dilatonic theory, together with a concrete mechanism for singularity avoidance. The paper has real strengths: the metric functions, electromagnetic potentials, and scalar field are given in closed form, the field equations are reduced to the single constraint (16), and the presentation includes numerical geodesic plots and astrophysical unit conversions. However, the central claims are not supported by the calculations as presented: the energy-condition check is incomplete, the singularity-avoidance claim rests on numerical integrations that exclude the most dangerous initial condition, and some of the plotted curves appear to violate the timelike normalization condition.

major comments (3)

[Sec. IV, Eqs. (21)-(27)] The null energy condition is not established. The paper computes T_{\hat\mu\hat\nu} l^\hat\mu l^\hat\nu only for the single null vector l = e_{\hat t}+e_{\hat x}, and then analyzes that expression only at y=0 and y=1. The NEC requires non-negativity for every null vector; for a general axisymmetric stress tensor this also requires combinations involving T_{\hat y\hat y} and T_{\hat\phi\hat\phi}, and the possible off-diagonal T_{\hat t\hat\phi} component, none of which are computed. Even for the single direction considered, the sign of the bracketed polynomial in Eq. (24) is not proved on the full domain x\in(-\infty,\infty), y\in[-1,1]; the boundary values at y=0 and y=1 are insufficient because the polynomial contains mixed terms such as x^2 y^2[4k0(y^2-2)/(4k0+1) - ...] whose coefficient changes with y. Thus the abstract and title claim that the solutions "satisfy the energy conditions" is unsupported; in fact, the paper only discusses the NEC and never checks the weak, strong, or dominant energy conditions.
[Sec. VII and Fig. 7] The claim that geodesics cannot reach the ring singularity is not demonstrated. The numerical integrations are performed only for y(0) in {0.01, 0.25, 0.50, 0.75, 0.95}; the y0=0 case, which is the one aimed directly at the equatorial ring singularity, is explicitly excluded because of "extreme sensitivity" near the singularity. The caption of Fig. 7 then states that the y0=0 geodesic approaches the ring without contact and rebounds, which contradicts the exclusion stated in the text. A convergent numerical or analytic treatment of the equatorial case is required before the cosmic-censorship statement in the abstract can be accepted. In addition, the initial data t'(0)=1, x'(0)=-1, y'(0)=0, \phi'(0)=0 do not satisfy the timelike normalization g_{\mu\nu}\dot{x}^\mu\dot{x}^\nu=-1 for the stated parameters; for example, with L=10 and x=25, the spatial part is of order g_{xx}\approx 10^2. The plotted curves therefore may not be physical timelike geodesics.
[Sec. III, Eqs. (17b) and (18b)] The singularity and asymptotic-flatness analysis depends on polynomials that are never given. Eq. (17b) defines the Kretschmann scalar for λ5 in terms of an unspecified polynomial F5(x,y), and Eq. (18b) defines it for λN1 in terms of an unspecified FN1(x,y). Without these expressions, the central singularity claim for λ5 and the asymptotic behavior of both solutions cannot be independently verified from the manuscript.

minor comments (4)

[Sec. VI, Figs. 5 and 6] The captions of Figs. 5 and 6 describe the components as "associated with λ5", while Section VI.B presents the same component list as the λN1 solution; this mismatch needs correction.
[Throughout] There are numerous typographical and formatting errors, including "Eintein-Maxwell" in Eq. (2), the garbled coordinate parenthesis in Eq. (5), "throt" in the Fig. 2 caption, and inconsistent notation such as "Rˆµˆtˆµˆt" versus "R\hat\mu\hat t\hat\mu\hat t".
[Sec. III, Eq. (18b)] The sign of the Kretschmann scalar in Eq. (18b) is written with a leading minus sign, which is unusual for a sum of squares; the authors should confirm that kN is actually positive for the parameter ranges used.
[Sec. IV, Eq. (27a)] The text says that in all cases except (27a) the sign is determined by the bracket, but for λN1 at y=0 the expression is positive regardless of k0; this is consistent but should be stated explicitly.

Circularity Check

0 steps flagged · score 2.0 of 10

No construction-level circular reduction found: k0 is fixed by the EMD field equations, and the NEC sign follows algebraically; the main weaknesses are an incomplete NEC check and self-cited WHCCC support, not circularity.

full rationale

I walked the derivation chain. The starting ansatz (f=f0, κ=κ0 e^λ, ψ=√f0 κ0^{-1} e^{-λ}+ψ0, etc.) is imported from [4], but the paper then substitutes the λ5 and λN1 potentials into the EMD equations and obtains the constraint α0²(4k0+1)−4ϵ0=0 (Eq. 16). This fixes k0; it is not fitted to make ρ−ϱ positive. The NEC expression (24) contains the factor (4k0+1), and with Eq. (16) this factor equals 4ϵ0/α0², so the dilatonic choice ϵ0=1 makes it positive. That is an algebraic consequence of the field equations, not a parameter fitted to the claimed result. The NEC analysis is incomplete as a proof 'for all lμ': Eq. (21) only uses l=e_t+e_x and Eqs. (26)-(27) only evaluate y=0 and y=1; this is a correctness gap, not a circularity. The ring-singularity censorship claim is supported by in-paper numerical geodesics and by same-group citations [7],[13], and Section VII excludes y0=0; reliance on prior work by the same authors is visible, but the paper does not define the censorship result in terms of its own input or rename a fit as a prediction. No step reduces to its input by construction. Score 2 reflects the visible same-group citation load, which is below the threshold for construction-level circularity.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central construction rests on the harmonic-ansatz technique from [4], on an unverified single-null-vector NEC check, on the transfer of the WHCCC result from prior same-group papers, and on a black-hole-analogue unit identification. No new particles or forces are introduced. Freely chosen parameters λ0, L, f0 and the unspecified field scale √f0/(2κ0) control the displayed plots and tables.

free parameters (5)

λ0 = 1/100 or 1/1000 in displayed plots/tables
Integration constant for the harmonic functions λ5 and λN1; chosen by hand, sets rotation and field strength scales.
L = 10 in plots; 10^1 to 10^5 meters in Tables II/III
Length scale associated with the wormhole throat; chosen by hand for visualization and astrophysical examples.
k0 = 3/4, 1/12, 0, or (4-n)/4n for dilatonic field
Integration constant in k(x,y), fixed by the constraint α0^2(4k0+1)-4ε0=0 (Eq. 16); not fitted, but the choice of a dilatonic field is needed for the NEC result.
√f0/(2κ0) = not stated numerically
Overall scale of the electromagnetic four-potential in SI units (Eq. 41); its numerical value is needed for Tables II/III but is never reported.
f0 = 1
Metric function f is set to 1 in both solution families (Eqs. 13a, 14a), removing the gravitational potential; this is a simplifying ansatz.

assumptions (4)

domain assumption Harmonic ansatz (Y_A)^T = (Y_A(λ))^T with λ satisfying Laplace's equation (9) is sufficient to solve the EMD field equations (8).
Inherited from the authors' prior paper [4]; the present work does not re-derive why this ansatz is general or why f0=1 covers the solution space.
domain assumption The single null combination ρ − ϱ = T_tt + T_xx in the comoving frame controls the null energy condition.
Section IV checks only l^μ = e_t + e_x; this assumes the energy-momentum tensor is diagonal or that this is the extremal null direction, without proof.
domain assumption The geodesic-avoidance (WHCCC) proof from [6,7] applies unchanged to the new λ5 and λN1 metrics.
The paper concludes geodesics cannot touch the ring singularity by citing [7,13] and showing selected numerical geodesics; no analytic proof for these specific branches is included.
domain assumption The black-hole analogue relations (46)-(51) correctly identify constants L, l1, J, Q, H with astrophysical quantities.
Section VIII adopts these relations to build the solar-mass, pulsar, and SMBH examples; they are justified only by analogy with black holes, not derived from the wormhole solution.

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Cite this review

Pith. "Pith review of Einstein-Maxwell-Dilaton Wormholes that meet the Energy Conditions." pith.science (2026). https://pith.science/paper/77KGX5ZG

@misc{pith2026250207206,
  author       = {Pith},
  title        = {Pith review of: Einstein-Maxwell-Dilaton Wormholes that meet the Energy Conditions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/77KGX5ZG}},
  note         = {Machine review of arXiv:2502.07206}
}

read the original abstract

One of the latest predictions of Einstein's theory is the existence of Wormholes (WH). In this work, we present exact solutions of the Einstein-Maxwell-Dilaton equations representing traversable Wormholes. These solutions satisfy the energy conditions and have a ring singularity satisfying the cosmic censorship of WHs, i.e. we show that, as in previous solutions, geodesics cannot touch the singularity. We find that the most optimal input regions for the first class of solutions traversing these wormholes are near the poles and near the equatorial plane for the second class. We also find that the solution associated with the first class is physically feasible, while for the second class it presents the problem of not being asymptotically flat when considering a dilatonic-type scalar field. Finally, we give examples of realistic astrophysical objects that could fulfill these conditions.

Figures

Figures reproduced from arXiv: 2502.07206 by the authors.

**Figure 4.** FIG. 4: Graphs of the cross elements [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** FIG. 5: The graphical representations of elements [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗

Figures from the paper (2 more)

**Figure 6.** Figure 6: FIG. 6: Graphs of the cross elements [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]

**Figure 7.** Figure 7: FIG. 7: The values for [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

19 extracted references · 16 canonical work pages

[4]

Einstein-Maxwell-Dilaton Wormholes that meet the Energy Conditions

we give a new formulation for finding new exact so- lutions of the Einstein-Maxwell-Dilaton (EMD) system and find the first families of exact rotational solutions [5]. This work is, after all, a recipe for finding new exact stationary and axially symmetric solutions of the EMD system. Some of these families contain a ring singular- ity which makes these s...

work page Pith review arXiv 2025
[13]

Taken from the article [4]

work page
[1]

M. S. Morris and K. S. Thorne, Wormholes in space-time and their use for interstellar travel: A tool for teaching general relativity, Am. J. Phys. 56, 395 (1988)

1988
[2]

(27b) For all cases except (27a), the expression within the brackets will determine the satisfaction of the null en- ergy condition (NEC)

(27a) • (λN 1) y = 1: ρ − ϱ = λ2 0e−2k(x,1) 2L2 4k0 + 1 . (27b) For all cases except (27a), the expression within the brackets will determine the satisfaction of the null en- ergy condition (NEC). Upon examination of Table [I], we can conclude that, as expected, the NEC is satisfied only when a dilatonic scalar field is chosen. 6 V. WORMHOLE GEOMETR Y To ...

work page
[3]

(28) This hypersurface is embedded in a cylindrical space that can be parameterized using the given coordinates (x, y)

− ω(x, y0)2 dφ2. (28) This hypersurface is embedded in a cylindrical space that can be parameterized using the given coordinates (x, y). ds2 = dρ2 + dz2 + ρ2dφ2 = ( dρ dx 2 + dz dx 2) dx2 + ρ(x, y0)2dφ2. (29) Subsequent to the embedding process, we derived the following equations, which can only be solved using nu- merical methods, given the initial condi...

work page
[5]

(30b) By numerically solving and obtaining ρ(x) and z(x), we can plot z(ρ) against a given value of y = cos θ = y0

− ω(x, y0)2, (30a) dρ dx 2 + dz dx 2 = L2 (x2 + y2 0) x2 + 1 e2k(x,y0). (30b) By numerically solving and obtaining ρ(x) and z(x), we can plot z(ρ) against a given value of y = cos θ = y0. A. Solution λ5 The geometry of the wormhole corresponding to λ5 for a specific y0 is illustrated in Figure [1a]. As shown, the choice of scalar field, whether phantom or...

work page
[6]

indicate that it is not feasible to access the center of the wormhole without succumbing to tidal forces, partic- ularly when relativistic velocities are considered. Finally, considering all components and their respec- tive magnitudes, that is, the orders of magnitude among them, it is possible to conclude that the safest angles of entry for both relativ...

work page 2024
[7]

J. A. Gonzalez, F. S. Guzman, and O. Sarbach, Insta- bility of wormholes supported by a ghost scalar field. I. Linear stability analysis, Class. Quant. Grav. 26, 015010 (2009), arXiv:0806.0608 [gr-qc]. 17

arXiv 2009

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Matos and D

T. Matos and D. Nunez, Rotating scalar field worm- hole, Class. Quant. Grav. 23, 4485 (2006), arXiv:gr- qc/0508117

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Matos, Class of Einstein-Maxwell Phantom Fields: Rotating and Magnetised Wormholes, Gen

T. Matos, Class of Einstein-Maxwell Phantom Fields: Rotating and Magnetised Wormholes, Gen. Rel. Grav. 42, 1969 (2010), arXiv:0902.4439 [gr-qc]

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Matos, D

T. Matos, D. Nunez, and M. Rios, Class of Einstein- Maxwell dilatons, an ansatz for new families of rotating solutions, Class. Quant. Grav. 17, 3917 (2000), arXiv:gr- qc/0008068

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Matos, L

T. Matos, L. A. Urena-Lopez, and G. Miranda, Worm- hole Cosmic Censorship, Gen. Rel. Grav. 48, 61 (2016), arXiv:1203.4801 [gr-qc]

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J. C. Del ´Aguila and T. Matos, Gravitational pertur- bations in the Newman-Penrose formalism: Applica- tions to wormholes, Phys. Rev. D 103, 084033 (2021), arXiv:2102.09160 [gr-qc]

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S. Hans, K. Dietrich, M. MacCallum, C. Hoenselaers, and E. Herlt, Exact Solutions of Einstein ’s Field Equations , 2nd ed. (Cambridge University Press, 2009)

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For a comprehensive derivation, refer to [14]
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The Hermite method is a high-order interpolation method suitable for smooth solutions, automatically se- lected in NDSolve when the equations and integration do- main meet specific smoothness and stability conditions
[17]

There exists a transcendental condition, L < 2l1, i.e., the throat is situated within the area defined by the Schwarzschild radius
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J. C. Del ´Aguila, T. Matos, and G. Miranda, Exact Ro- tating Magnetic Traversable Wormholes satisfying the Energy Conditions, Phys. Rev. D 99, 124045 (2019), arXiv:1507.02348 [gr-qc]

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Matos, D

T. Matos, D. Nunez, G. Estevez, and M. Rios, Rotat- ing 5-D Kaluza-Klein space-times from invariant trans- formations, Gen. Rel. Grav. 32, 1499 (2000), arXiv:gr- qc/0001039

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

[1] [4]

Einstein-Maxwell-Dilaton Wormholes that meet the Energy Conditions

we give a new formulation for finding new exact so- lutions of the Einstein-Maxwell-Dilaton (EMD) system and find the first families of exact rotational solutions [5]. This work is, after all, a recipe for finding new exact stationary and axially symmetric solutions of the EMD system. Some of these families contain a ring singular- ity which makes these s...

work page Pith review arXiv 2025

[2] [13]

Taken from the article [4]

work page

[3] [1]

M. S. Morris and K. S. Thorne, Wormholes in space-time and their use for interstellar travel: A tool for teaching general relativity, Am. J. Phys. 56, 395 (1988)

1988

[4] [2]

(27b) For all cases except (27a), the expression within the brackets will determine the satisfaction of the null en- ergy condition (NEC)

(27a) • (λN 1) y = 1: ρ − ϱ = λ2 0e−2k(x,1) 2L2 4k0 + 1 . (27b) For all cases except (27a), the expression within the brackets will determine the satisfaction of the null en- ergy condition (NEC). Upon examination of Table [I], we can conclude that, as expected, the NEC is satisfied only when a dilatonic scalar field is chosen. 6 V. WORMHOLE GEOMETR Y To ...

work page

[5] [3]

(28) This hypersurface is embedded in a cylindrical space that can be parameterized using the given coordinates (x, y)

− ω(x, y0)2 dφ2. (28) This hypersurface is embedded in a cylindrical space that can be parameterized using the given coordinates (x, y). ds2 = dρ2 + dz2 + ρ2dφ2 = ( dρ dx 2 + dz dx 2) dx2 + ρ(x, y0)2dφ2. (29) Subsequent to the embedding process, we derived the following equations, which can only be solved using nu- merical methods, given the initial condi...

work page

[6] [5]

(30b) By numerically solving and obtaining ρ(x) and z(x), we can plot z(ρ) against a given value of y = cos θ = y0

− ω(x, y0)2, (30a) dρ dx 2 + dz dx 2 = L2 (x2 + y2 0) x2 + 1 e2k(x,y0). (30b) By numerically solving and obtaining ρ(x) and z(x), we can plot z(ρ) against a given value of y = cos θ = y0. A. Solution λ5 The geometry of the wormhole corresponding to λ5 for a specific y0 is illustrated in Figure [1a]. As shown, the choice of scalar field, whether phantom or...

work page

[7] [6]

indicate that it is not feasible to access the center of the wormhole without succumbing to tidal forces, partic- ularly when relativistic velocities are considered. Finally, considering all components and their respec- tive magnitudes, that is, the orders of magnitude among them, it is possible to conclude that the safest angles of entry for both relativ...

work page 2024

[8] [7]

J. A. Gonzalez, F. S. Guzman, and O. Sarbach, Insta- bility of wormholes supported by a ghost scalar field. I. Linear stability analysis, Class. Quant. Grav. 26, 015010 (2009), arXiv:0806.0608 [gr-qc]. 17

arXiv 2009