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REVIEW 4 major objections 4 minor 81 references

In a two-way traversable wormhole, a radial φ⁴ kink released at rest repeatedly crosses the throat, emitting scalar wave packets with each traverse and slowly losing amplitude like a damped oscillator.

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2026-08-03 14:04 UTC pith:2KLSM7VA

load-bearing objection A clean numerical demonstration that kinks can oscillate through a traversable wormhole while shedding wave packets, but the damping envelope is likely contaminated by reflections off the finite domain. the 4 major comments →

arxiv 2512.22281 v3 pith:2KLSM7VA submitted 2025-12-25 gr-qc

Dynamics of kinks in a traversable wormhole

Tian-Chi Ma , Hai-Qing Zhang This is my paper
classification gr-qc
keywords radial kinksdomain wallsSimpson-Visser wormholetraversable wormholeφ⁴ modelscalar wave emissiontopological defects in curved spacetimedamped oscillation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper asks what happens to a topological defect—a domain-wall kink in a φ⁴ double-well field—when it lives in a two-way traversable wormhole instead of flat space. By evolving the field numerically on the Simpson-Visser background, it finds that a radial kink released at rest does not fall in or disappear; it repeatedly traverses the throat, moving from one asymptotic region to the other and back. The throat parameter a governs how far the kink can roam: wide throats allow large-amplitude oscillations, while near-critical throats confine the kink to the throat vicinity. Each crossing emits a scalar wave packet, so the kink loses energy and its oscillation amplitude decays gradually, like a damped oscillator. The kink nevertheless persists, protected by the wormhole topology—unlike in boson-star backgrounds, where the kink eventually dissolves.

Core claim

In the Simpson-Visser two-way traversable wormhole (a > 2M), a spherically symmetric φ⁴ kink with zero initial velocity executes damped oscillations between the two asymptotic regions. The kink crosses the throat repeatedly; with every traverse it sheds a scalar wave packet into the background, transferring away a fraction of its energy, which shows up as a slow decrease of the oscillation amplitude in r_k(t). Larger throat parameter a means a wider throat and larger oscillation range, while a approaching 2M confines the kink near the throat. The paper argues that the kink's persistence is a topological effect of the wormhole geometry, in contrast with compact stars, and that the regular wav

What carries the argument

The central object is the Simpson-Visser metric ds² = -A dt² + A⁻¹ dr² + (r²+a²)dΩ², with A = 1 - 2M/√(r²+a²), whose parameter a > 2M gives a two-way timelike throat. The field is a real scalar with a double-well potential V = (φ²-1)²/4, and the kink is the radial tanh profile φ(0,r) = tanh[(r - r_k(0))/√(2(1-v²))] with v = 0. The equation of motion (Eq. 9) is solved on a fixed background with Dirichlet boundaries at r = ±100; the kink position r_k(t) is tracked by the zero of φ. The throat acts as the scattering and emission site: each crossing excites outgoing wave packets that drain energy from the kink.

Load-bearing premise

The metric is treated as a fixed background with no backreaction, and the numerical grid has reflecting boundaries at r = ±100; if the scalar field's own gravity or boundary-reflected radiation changes the late-time motion, the observed persistent oscillation and amplitude decay could be artifacts rather than wormhole-topology effects.

What would settle it

Run the same evolution with absorbing (outgoing) boundary conditions or with a much larger domain and track total energy versus time; if the amplitude decay vanishes or the kink eventually stops or pinches off when boundaries are moved or radiation is absorbed, then the claimed geometry-driven damping and topological persistence are numerical artifacts. Alternatively, couple the scalar to the metric and check whether the throat parameter a changes significantly during the first few crossings.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • If the claim is right, a topological defect crossing a wormhole throat emits regular scalar wave packets, providing a possible observational signature that distinguishes wormholes from black-hole-like compact objects.
  • The persistence of the kink at late times means wormhole topology can protect defects that would dissolve around ordinary compact stars; a high-tension domain wall could shuttle between two asymptotic regions, potentially carrying information or altering conditions across the throat.
  • The confinement near the throat as a → 2M predicts a sharp transition in defect behavior as the throat changes from timelike to null or spacelike.
  • The amplitude decay, while reminiscent of a damped oscillator, is not exactly that; the mechanism is discrete wave-packet shedding per crossing, so energy loss is episodic rather than continuous.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If backreaction were included, the shed wave packets might leave an imprint on the wormhole itself; the test-field approximation likely underestimates long-term decay and ignores possible throat dynamics, so the claimed topological protection is a prediction to be tested in a dynamical spacetime.
  • The regular periodic emission suggests a possible analogy to quasinormal ringing or gravitational-wave echoes; the repetition period and amplitude decrement could be mapped to the parameters a and M as a search template.
  • Extending this to asymmetric or rotating wormholes, as the paper suggests, could turn the oscillation into one-way transport or add frame-dragging precession, changing the wave-packet cadence; the same numerical setup could test this.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper studies the dynamics of spherically symmetric radial φ^4 kinks on a fixed Simpson-Visser traversable wormhole background with a > 2M. The authors numerically evolve the scalar-field equation (9) from a flat-space tanh initial profile with zero velocity, and report that the kink oscillates back and forth through the throat. They find that the throat parameter a controls the oscillation amplitude: larger a gives wider traversals, while a near 2M confines the kink near the throat. They further claim that each throat crossing emits scalar wave packets, causing a gradual decrease of the oscillation amplitude reminiscent of a damped oscillator, and contrast this with kink behavior around boson stars. The main quantitative evidence is the kink-position time series in Fig. 4 and snapshots in Figs. 3 and 5.

Significance. If the reported behavior is robust, this is the first detailed numerical study of radial kink dynamics in a traversable wormhole, and the proposed contrast with boson stars could be of interest for distinguishing wormholes from other compact objects. The numerical framework is standard, the equations are clearly stated, and the qualitative features visible in the figures are plausible. However, the paper's central quantitative claims—irreversible energy loss and amplitude damping—are not yet backed by energy diagnostics or boundary-effect controls. The fixed-background (test-field) approximation is acceptable for a first study, but the reflecting outer boundaries require explicit treatment before the damping statement can be trusted.

major comments (4)
  1. [Sec. III.A, Fig. 4] The simulation imposes Dirichlet conditions φ(t,±100)=±1 and evolves to t=800. For a=9M, the first emitted packet is at r≈−97 at t=151, so it reaches the r=−100 boundary at t≈152–155 and can return to the throat region by t≈220–230. The apparent gradual amplitude decrease in Fig. 4 may therefore be contaminated by boundary-reflected radiation; no energy leaves the domain, so the total energy is conserved and the observed 'damping' could be a redistribution artifact. Please add absorbing boundary layers or sponge regions, or alternatively demonstrate domain-size convergence, and include a flux diagnostic at extraction surfaces to separate irreversible emission from boundary echoes.
  2. [Sec. III.B] The paper qualitatively attributes the amplitude decrease to wave-packet emission, but no quantitative energy budget is provided. There is no time series of the kink's energy, the radiated energy, or the total energy; the damping is only inferred from visual inspection of r_k(t). To support the 'reminiscent of a damped oscillator' claim, please compute and plot the kink energy and the energy carried by emitted packets as functions of time, and if possible fit the amplitude envelope or extracted damping rate.
  3. [Sec. II.B, Eq. (10)] The initial profile (10) is the flat-spacetime kink, not a stationary solution of the curved-space equation (9). On the wormhole background it will relax and emit radiation even in the absence of a throat-crossing interaction. The paper attributes all observed ripples to throat interactions, but does not attempt to separate the initial transient. Please compare with a flat-spacetime evolution using the same initial data, or monitor radiation before the first throat crossing, to substantiate the emission mechanism.
  4. [Sec. III.A, Fig. 4, footnote 1] Footnote 1 states that for a=2.02M the kink position is 'hard to track' and that the curve in Fig. 4 uses an 'averagely approximate range' because complex oscillatory modes are superimposed. Yet Fig. 4 shows a definite curve and the confinement conclusion is drawn from it. Please define the tracking procedure, quantify the ambiguity, or show the actual field configuration at late times. As written, the quantitative content of the a=2.02M result is unclear.
minor comments (4)
  1. [Sec. II.B, Eq. (11)] The energy density expression uses h_ab and √−g_tt without defining these objects. Please specify the induced metric and the coordinate conventions used.
  2. [Fig. 3 caption] The caption says 'the solid line (in the upper part) represents the kink moving leftwards, while the dashed line (in the lower part) represents the kink moving rightwards.' It would be clearer to label the panels by time or by line type directly, since each panel already contains multiple solid/dashed curves.
  3. [Footnote 1] The footnote references 'this link' but no URL is given. Either provide the link or describe where the animations can be obtained.
  4. [References] Reference [55] is the authors' companion paper on boson stars; please confirm it is publicly available or cite the relevant published version if applicable.

Circularity Check

1 steps flagged

Core wormhole kink simulation is self-contained; minor self-citation in the boson-star contrast does not feed back into the derivation.

specific steps
  1. self citation load bearing [Sec. IV (Conclusions, last paragraph, citing refs. [54,55])]
    "In contrast, in the backgrounds of boson stars and neutron stars, the kink ultimately transfers all of its energy to the background through oscillations, and eventually the kink disappears into the background [54, 55]."

    Ref. [55] is the authors' own companion paper (T.-C. Ma, X.-Y. Wang, and H.-Q. Zhang, 'Radial kinks in the boson stars', arXiv:2510.13923). The paper's advertised 'sharp contrast' between wormholes and compact objects rests on this self-citation. This is not a reduction of the wormhole PDE evolution to its inputs, so the core simulation is not circular; however, the comparative claim is supported only by the authors' own unverified companion result within this manuscript.

full rationale

The central result—kink oscillation through the wormhole throat, wave-packet emission at each crossing, and dependence on the throat parameter a—is obtained by direct forward integration of Eq. (9) in the fixed Simpson-Visser background. The throat parameter a is scanned, not fitted; the kink position is read off from the condition phi(t,r_k)=0 rather than imposed; and no parameter is tuned to reproduce the reported amplitude decay. Hence there is no fitted-input-called-prediction or self-definitional circularity. The only self-citation relevant to a headline claim is [55], used in the conclusions to contrast wormhole persistence with boson-star dissipation; this is a real but minor self-citation for the comparative claim, and it does not feed back into the wormhole simulation itself. The reflecting Dirichlet boundaries at r=+-100 and the fixed-background test-field approximation are numerical/correctness risks that could contaminate the quantitative 'damping oscillator' envelope, but they are not circular steps. The paper's footnote about the a=2.02M curve being an 'averagely approximate' location is an acknowledged measurement limitation, again not a constructional circularity. Overall, the derivation chain is self-contained; score 2 reflects the minor self-cited comparison.

Axiom & Free-Parameter Ledger

0 free parameters · 5 axioms · 0 invented entities

The central claim rests on standard-but-unflagged modeling choices: a fixed non-dynamical wormhole background, a toy double-well potential, spherical reduction, and hand-chosen initial data. No constants are fitted to produce the result; the throat parameter a is scanned. The fixed-background approximation is the main unverified assumption, since no backreaction or stability analysis is provided.

axioms (5)
  • domain assumption The Simpson-Visser metric with a>2M is a fixed traversable wormhole background.
    Used in Eq. (1); the spacetime is taken as static and non-dynamical, ignoring the scalar field's backreaction on the geometry.
  • domain assumption The φ^4 double-well potential V = 1/4(φ^2−1)^2 is the matter model.
    Introduced in Eq. (7); a standard toy potential, not derived from fundamental physics.
  • domain assumption Spherical symmetry: the kink depends only on (t,r), and angular derivatives drop out of Eq. (9).
    Assumed in Sec. II.B; only radial kinks are considered.
  • ad hoc to paper The flat-spacetime tanh kink (Eq. 10) is a valid initial configuration on the curved background.
    The initial data is not a stationary solution of the curved-space equations; any transient is attributed to physical evolution.
  • standard math The finite-difference discretization (4th-order RK, 6th-order spatial differences) resolves the dynamics without significant numerical error.
    Convergence checks with other step sizes reported in Sec. III.A, but no rigorous error bound.

reviewed 2026-08-03 · how reviews work

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Cite this review

Pith. "Pith review of Dynamics of kinks in a traversable wormhole." pith.science (2026). https://pith.science/paper/2KLSM7VA

@misc{pith2026251222281,
  author       = {Pith},
  title        = {Pith review of: Dynamics of kinks in a traversable wormhole},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2KLSM7VA}},
  note         = {Machine review of arXiv:2512.22281}
}
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read the original abstract

We investigate the dynamics of spherically symmetric radial domain walls (or kinks) in a traversable Simpson-Visser wormhole. By solving the scalar field in a double-well potential, we find that the parameter $a$ has a strong impact on the kink dynamics: larger $a$ allows the kink to go through the throat back and forth, while smaller $a$ strongly confines the kink nearby the throat. In addition, each traverse of the kink through the throat is accompanied with the emission of scalar wave packets, resulting in a gradual decrease of the oscillation amplitude reminiscent of a damping oscillator. This oscillatory behavior between the two sides of the wormhole is in sharp contrast to its counterpart in compact objects, such as boson stars. Our findings uncover how wormhole geometry will influence the dynamics of topological defects and may provide new insights for distinguishing wormholes from ordinary compact objects.

Figures

Figures reproduced from arXiv: 2512.22281 by Hai-Qing Zhang, Tian-chi Ma.

Figure 1
Figure 1. Figure 1: FIG. 1: The metric function [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Three-dimensional plot of rotations of the embedding function [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Time evolution of the scalar field [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Time evolution of the kink’s position [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Configurations of the scalar field [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The time evolution of the position of the radial kink for [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

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Reference graph

Works this paper leans on

81 extracted references · 4 linked inside Pith

  1. [1]

    For smaller values ofa, the reduction in oscillation amplitude becomes more pronounced

    It is evident that the kink oscillates back and forth between the two sides of the wormhole, with the oscillation amplitude decreasing over time. For smaller values ofa, the reduction in oscillation amplitude becomes more pronounced. This behavior reminds us of the dynamics of a damped oscillator, although quantitatively this behavior does not fully align...

  2. [2]

    Topological defects and structure formation,

    R. H. Brandenberger, “Topological defects and structure formation,”International Journal of Modern Physics A, vol. 9, no. 13, pp. 2117–2189, 1994

    1994

  3. [3]

    Topological defects in symmetry-protected topological phases,

    J. C. Teo and T. L. Hughes, “Topological defects in symmetry-protected topological phases,” Annual Review of Condensed Matter Physics, vol. 8, no. 1, pp. 211–237, 2017

    2017

  4. [4]

    Nobel lecture: Topological defects and phase transitions,

    J. M. Kosterlitz, “Nobel lecture: Topological defects and phase transitions,”Reviews of Modern Physics, vol. 89, no. 4, p. 040501, 2017

    2017

  5. [5]

    L. M. Pismen,Vortices in nonlinear fields: From liquid crystals to superfluids, from non- equilibrium patterns to cosmic strings, vol. 100. Oxford University Press, 1999. 11

    1999

  6. [6]

    Manton and P

    N. Manton and P. Sutcliffe,Topological solitons. Cambridge University Press, 2004

    2004

  7. [7]

    Y. M. Bunkov and H. Godfrin,Topological defects and the non-equilibrium dynamics of symmetry breaking phase transitions, vol. 549. Springer Science & Business Media, 2000

    2000

  8. [8]

    Phase transitions in the early universe,

    T. W. B. Kibble and G. In, “Phase transitions in the early universe,”Quantum Structure of Space and Time, p. 391, 1982

    1982

  9. [9]

    Vilenkin, A

    A. Vilenkin, A. Vilenkin, and E. Shellard,Cosmic strings and other topological defects. Cambridge University Press, 1994

    1994

  10. [10]

    Vachaspati,Kinks and domain walls: An introduction to classical and quantum solitons

    T. Vachaspati,Kinks and domain walls: An introduction to classical and quantum solitons. Cam- bridge University Press, 2006

    2006

  11. [11]

    Dynamical evolution of domain walls in an expanding universe,

    W. H. Press, B. S. Ryden, and D. N. Spergel, “Dynamical evolution of domain walls in an expanding universe,”Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 347, Dec. 15, 1989, p. 590-604. Research supported by NASA and Alfred P. Sloan Foundation., vol. 347, pp. 590–604, 1989

    1989

  12. [12]

    Dynamics of domain wall networks with junctions,

    P. Avelino, C. Martins, J. Menezes, R. Menezes, and J. Oliveira, “Dynamics of domain wall networks with junctions,”Physical Review D—Particles, Fields, Gravitation, and Cosmology, vol. 78, no. 10, p. 103508, 2008

    2008

  13. [13]

    Domain walls as dark energy,

    A. Friedland, H. Murayama, and M. Perelstein, “Domain walls as dark energy,”Physical Review D, vol. 67, no. 4, p. 043519, 2003

    2003

  14. [14]

    Topology of cosmic domains and strings,

    T. W. Kibble, “Topology of cosmic domains and strings,”Journal of Physics A: Mathematical and General, vol. 9, no. 8, p. 1387, 1976

    1976

  15. [15]

    Cosmic strings and domain walls in models with goldstone and pseudo-goldstone bosons,

    A. Vilenkin and A. E. Everett, “Cosmic strings and domain walls in models with goldstone and pseudo-goldstone bosons,”Physical Review Letters, vol. 48, no. 26, p. 1867, 1982

    1982

  16. [16]

    Cosmic strings and domain walls,

    A. Vilenkin, “Cosmic strings and domain walls,”Physics reports, vol. 121, no. 5, pp. 263–315, 1985

    1985

  17. [17]

    Hunting for topological dark matter with atomic clocks,

    A. Derevianko and M. Pospelov, “Hunting for topological dark matter with atomic clocks,”Nature Physics, vol. 10, no. 12, pp. 933–936, 2014

    2014

  18. [18]

    Search for domain wall dark matter with atomic clocks on board global positioning system satellites,

    B. M. Roberts, G. Blewitt, C. Dailey, M. Murphy, M. Pospelov, A. Rollings, J. Sherman, W. Williams, and A. Derevianko, “Search for domain wall dark matter with atomic clocks on board global positioning system satellites,”Nature communications, vol. 8, no. 1, p. 1195, 2017

    2017

  19. [19]

    Extracting dark matter signatures from atomic clock stability mea- surements,

    T. Kalaydzhyan and N. Yu, “Extracting dark matter signatures from atomic clock stability mea- surements,”Physical Review D, vol. 96, no. 7, p. 075007, 2017

    2017

  20. [20]

    Interaction of cosmological domain walls with large classical objects, like planets and satellites, and the flyby anomaly,

    D.-C. Dai, D. Minic, and D. Stojkovic, “Interaction of cosmological domain walls with large classical objects, like planets and satellites, and the flyby anomaly,”Journal of High Energy Physics, vol. 2022, no. 3, pp. 1–17, 2022

    2022

  21. [21]

    Searching for topological defect dark matter via nongravitational signatures,

    Y. Stadnik and V. Flambaum, “Searching for topological defect dark matter via nongravitational signatures,”Physical review letters, vol. 113, no. 15, p. 151301, 2014

    2014

  22. [22]

    The global network of optical magne- tometers for exotic physics (gnome): A novel scheme to search for physics beyond the standard model,

    S. Pustelny, D. F. Jackson Kimball, C. Pankow, M. P. Ledbetter, P. Wlodarczyk, P. Wcislo, M. Pospelov, J. R. Smith, J. Read, W. Gawlik,et al., “The global network of optical magne- tometers for exotic physics (gnome): A novel scheme to search for physics beyond the standard model,”Annalen der Physik, vol. 525, no. 8-9, pp. 659–670, 2013

    2013

  23. [23]

    Search for topological defect dark matter with a global network of optical magnetometers,

    S. Afach, B. C. Buchler, D. Budker, C. Dailey, A. Derevianko, V. Dumont, N. L. Figueroa, I. Gerhardt, Z. D. Gruji´ c, H. Guo,et al., “Search for topological defect dark matter with a global network of optical magnetometers,”Nature Physics, vol. 17, no. 12, pp. 1396–1401, 2021. 12

    2021

  24. [24]

    Constraining domain wall dark matter with a network of superconducting gravimeters and ligo,

    R. L. McNally and T. Zelevinsky, “Constraining domain wall dark matter with a network of superconducting gravimeters and ligo,”The European Physical Journal D, vol. 74, no. 4, p. 61, 2020

    2020

  25. [25]

    Laser interferometers as dark matter detectors,

    E. D. Hall, R. X. Adhikari, V. V. Frolov, H. M¨ uller, and M. Pospelov, “Laser interferometers as dark matter detectors,”Physical Review D, vol. 98, no. 8, p. 083019, 2018

    2018

  26. [26]

    Novel signatures of dark matter in laser-interferometric gravitational- wave detectors,

    H. Grote and Y. Stadnik, “Novel signatures of dark matter in laser-interferometric gravitational- wave detectors,”Physical Review Research, vol. 1, no. 3, p. 033187, 2019

    2019

  27. [27]

    Probing dark matter clumps, strings and domain walls with gravitational wave detectors,

    J. Jaeckel, S. Schenk, and M. Spannowsky, “Probing dark matter clumps, strings and domain walls with gravitational wave detectors,”The European Physical Journal C, vol. 81, no. 9, p. 828, 2021

    2021

  28. [28]

    Planar and radial kinks in nonlinear klein-gordon models: Existence, stability, and dynamics,

    P. G. Kevrekidis, I. Danaila, J.-G. Caputo, and R. Carretero-Gonz´ alez, “Planar and radial kinks in nonlinear klein-gordon models: Existence, stability, and dynamics,”Physical Review E, vol. 98, no. 5, p. 052217, 2018

    2018

  29. [29]

    Kink–antikink stripe interactions in the two-dimensional sine– gordon equation,

    R. Carretero-Gonz´ alez, L. Cisneros-Ake, R. Decker, G. Koutsokostas, D. J. Frantzeskakis, P. Kevrekidis, and D. J. Ratliff, “Kink–antikink stripe interactions in the two-dimensional sine– gordon equation,”Communications in Nonlinear Science and Numerical Simulation, vol. 109, p. 106123, 2022

    2022

  30. [30]

    Radial sine-gordon kinks as sources of fast breathers,

    J.-G. Caputo and M. P. Sørensen, “Radial sine-gordon kinks as sources of fast breathers,”Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, vol. 88, no. 2, p. 022915, 2013

    2013

  31. [31]

    The large-n limit of superconformal field theories and supergravity,

    J. Maldacena, “The large-n limit of superconformal field theories and supergravity,”International journal of theoretical physics, vol. 38, no. 4, pp. 1113–1133, 1999

    1999

  32. [32]

    Anti de sitter space and holography,

    E. Witten, “Anti de sitter space and holography,”arXiv preprint hep-th/9802150, 1998

    Pith/arXiv arXiv 1998

  33. [33]

    From black hole to one-dimensional chain: Parity sym- metry breaking and kink formation,

    Z.-H. Li, H.-Q. Shi, and H.-Q. Zhang, “From black hole to one-dimensional chain: Parity sym- metry breaking and kink formation,”Physical Review D, vol. 108, no. 10, p. 106015, 2023

    2023

  34. [34]

    Universal critical holography and domain wall formation,

    T.-C. Ma, H.-Q. Shi, H.-Q. Zhang, and A. del Campo, “Universal critical holography and domain wall formation,”Physical Review Research, vol. 7, no. 1, p. 013096, 2025

    2025

  35. [35]

    Expansion in the width and collective dynamics of a domain wall,

    H. Arodz, “Expansion in the width and collective dynamics of a domain wall,”Nuclear Physics B, vol. 509, no. 1-2, pp. 273–293, 1998

    1998

  36. [36]

    Construction of curved domain walls,

    T. Dobrowolski, “Construction of curved domain walls,”Physical Review E—Statistical, Nonlin- ear, and Soft Matter Physics, vol. 77, no. 5, p. 056608, 2008

    2008

  37. [37]

    Kink motion in a curved josephson junction,

    T. Dobrowolski, “Kink motion in a curved josephson junction,”Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, vol. 79, no. 4, p. 046601, 2009

    2009

  38. [38]

    Modeling kink dynamics in the sine–gordon model with position dependent dispersive term,

    J. Gatlik and T. Dobrowolski, “Modeling kink dynamics in the sine–gordon model with position dependent dispersive term,”Physica D: Nonlinear Phenomena, vol. 428, p. 133061, 2021

    2021

  39. [39]

    Kink propaga- tion and trapping in a two-dimensional curved josephson junction,

    C. Gorria, Y. B. Gaididei, M. P. Sørensen, P. L. Christiansen, and J. G. Caputo, “Kink propaga- tion and trapping in a two-dimensional curved josephson junction,”Physical Review B, vol. 69, no. 13, p. 134506, 2004

    2004

  40. [40]

    Topologically protected metastable states in classical dynamics,

    H.-Q. Shi, T.-C. Ma, and H.-Q. Zhang, “Topologically protected metastable states in classical dynamics,”Chaos, Solitons & Fractals, vol. 182, p. 114789, 2024

    2024

  41. [41]

    Introducing the black hole,

    R. Ruffini and J. A. Wheeler, “Introducing the black hole,”Physics today, vol. 24, no. 1, pp. 30– 41, 1971

    1971

  42. [42]

    Frolov and I

    V. Frolov and I. Novikov,Black hole physics: Basic concepts and new developments, vol. 96. Springer Science & Business Media, 2012. 13

    2012

  43. [43]

    The physics of neutron stars,

    J. M. Lattimer and M. Prakash, “The physics of neutron stars,”science, vol. 304, no. 5670, pp. 536–542, 2004

    2004

  44. [44]

    Neutron stars,

    J. M. Lattimer, “Neutron stars,”General Relativity and Gravitation, vol. 46, no. 5, p. 1713, 2014

    2014

  45. [45]

    Boson stars,

    P. Jetzer, “Boson stars,”Physics Reports, vol. 220, no. 4, pp. 163–227, 1992

    1992

  46. [46]

    General relativistic boson stars,

    F. E. Schunck and E. W. Mielke, “General relativistic boson stars,”Classical and Quantum Gravity, vol. 20, no. 20, p. R301, 2003

    2003

  47. [47]

    Wormholes in spacetime,

    S. W. Hawking, “Wormholes in spacetime,”Physical Review D, vol. 37, no. 4, p. 904, 1988

    1988

  48. [48]

    Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity,

    M. S. Morris and K. S. Thorne, “Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity,”American Journal of Physics, vol. 56, no. 5, pp. 395–412, 1988

    1988

  49. [49]

    How to form a wormhole,

    D.-C. Dai, D. Minic, and D. Stojkovic, “How to form a wormhole,”The European Physical Journal C, vol. 80, no. 12, p. 1103, 2020

    2020

  50. [50]

    Thick domain walls and charged dilaton black holes,

    R. Moderski and M. Rogatko, “Thick domain walls and charged dilaton black holes,”Physical Review D, vol. 67, no. 2, p. 024006, 2003

    2003

  51. [51]

    Thick domain walls around a black hole,

    Y. Morisawa, D. Ida, A. Ishibashi, and K.-i. Nakao, “Thick domain walls around a black hole,” Physical Review D, vol. 67, no. 2, p. 025017, 2003

    2003

  52. [52]

    Reissner-nordstr¨ om black holes and thick domain walls,

    R. Moderski and M. Rogatko, “Reissner-nordstr¨ om black holes and thick domain walls,”Physical Review D, vol. 69, no. 8, p. 084018, 2004

    2004

  53. [53]

    Thick domain walls in ads black hole spacetimes,

    R. Moderski and M. Rogatko, “Thick domain walls in ads black hole spacetimes,”Physical Review D—Particles, Fields, Gravitation, and Cosmology, vol. 74, no. 4, p. 044002, 2006

    2006

  54. [54]

    Planar domain walls in black hole spacetimes,

    F. Ficek and P. Mach, “Planar domain walls in black hole spacetimes,”Physical Review D, vol. 97, no. 4, p. 044012, 2018

    2018

  55. [55]

    Radial kinks in a schwarzschild- like geometry,

    J.-G. Caputo, T. Dobrowolski, J. Gatlik, and P. G. Kevrekidis, “Radial kinks in a schwarzschild- like geometry,”Physical Review D, vol. 110, no. 12, p. 125025, 2024

    2024

  56. [56]

    Radial kinks in the boson stars,

    T.-C. Ma, X.-Y. Wang, and H.-Q. Zhang, “Radial kinks in the boson stars,”arXiv preprint arXiv:2510.13923, 2025

    arXiv 2025

  57. [57]

    Wormholes supported by a kink-like configuration of a scalar field,

    S. V. Sushkov and S.-W. Kim, “Wormholes supported by a kink-like configuration of a scalar field,”Classical and Quantum Gravity, vol. 19, no. 19, p. 4909, 2002

    2002

  58. [58]

    Sine-gordon on a wormhole,

    P. Bizo´ n, M. Dunajski, M. Kahl, and M. Kowalczyk, “Sine-gordon on a wormhole,”Nonlinearity, vol. 34, no. 8, p. 5520, 2021

    2021

  59. [59]

    Kinks of the sine-gordon equation on a wormhole,

    B. A. D ´ ıaz Arias, “Kinks of the sine-gordon equation on a wormhole,”Thesis in UNIVERSI- DAD DE CHILE, (2023) https://repositorio.uchile.cl/bitstream/handle/2250/193976/Kinks-of- the-Sine-Gordon-equation-on-a-wormhole.pdf?sequence=1&isAllowed=y

    2023

  60. [60]

    Theϕ 4 kink on a wormhole spacetime,

    A. Waterhouse, “Theϕ 4 kink on a wormhole spacetime,”arXiv preprint arXiv:1908.09650, 2019

    Pith/arXiv arXiv 1908

  61. [61]

    Phantom wormholes in einstein–maxwell-dilaton theory,

    P. Goulart, “Phantom wormholes in einstein–maxwell-dilaton theory,”Classical and Quantum Gravity, vol. 35, no. 2, p. 025012, 2017

    2017

  62. [62]

    The particle problem in the general theory of relativity,

    A. Einstein and N. Rosen, “The particle problem in the general theory of relativity,”Physical Review, vol. 48, no. 1, p. 73, 1935

    1935

  63. [63]

    Ether flow through a drainhole: A particle model in general relativity,

    H. G. Ellis, “Ether flow through a drainhole: A particle model in general relativity,”Journal of Mathematical Physics, vol. 14, no. 1, pp. 104–118, 1973

    1973

  64. [64]

    Wormholes, time machines, and the weak energy condition,

    M. S. Morris, K. S. Thorne, and U. Yurtsever, “Wormholes, time machines, and the weak energy condition,”Physical Review Letters, vol. 61, no. 13, p. 1446, 1988

    1988

  65. [65]

    Characterising exotic matter driving wormholes,

    M. Chianese, E. Di Grezia, M. Manfredonia, and G. Miele, “Characterising exotic matter driving wormholes,”The European Physical Journal Plus, vol. 132, no. 4, p. 164, 2017. 14

    2017

  66. [66]

    Spin, torsion and violation of null energy condition in traversable wormholes,

    E. Di Grezia, E. Battista, M. Manfredonia, and G. Miele, “Spin, torsion and violation of null energy condition in traversable wormholes,”The European Physical Journal Plus, vol. 132, no. 12, p. 537, 2017

    2017

  67. [67]

    Generalized uncertainty principle corrections in rastall–rainbow casimir wormholes,

    E. Battista, S. Capozziello, and A. Errehymy, “Generalized uncertainty principle corrections in rastall–rainbow casimir wormholes,”The European Physical Journal C, vol. 84, no. 12, p. 1314, 2024

    2024

  68. [68]

    New wormhole solution in de sitter space,

    D.-C. Dai, D. Minic, and D. Stojkovic, “New wormhole solution in de sitter space,”Physical Review D, vol. 98, no. 12, p. 124026, 2018

    2018

  69. [69]

    Reconstructing wormhole solu- tions in curvature based extended theories of gravity,

    V. De Falco, E. Battista, S. Capozziello, and M. De Laurentis, “Reconstructing wormhole solu- tions in curvature based extended theories of gravity,”The European Physical Journal C, vol. 81, no. 2, p. 157, 2021

    2021

  70. [70]

    Testing wormhole solutions in extended gravity through the poynting-robertson effect,

    V. De Falco, E. Battista, S. Capozziello, and M. De Laurentis, “Testing wormhole solutions in extended gravity through the poynting-robertson effect,”Physical Review D, vol. 103, no. 4, p. 044007, 2021

    2021

  71. [71]

    General relativistic poynting- robertson effect to diagnose wormholes existence: static and spherically symmetric case,

    V. De Falco, E. Battista, S. Capozziello, and M. De Laurentis, “General relativistic poynting- robertson effect to diagnose wormholes existence: static and spherically symmetric case,”Physical Review D, vol. 101, no. 10, p. 104037, 2020

    2020

  72. [72]

    Observing a wormhole,

    D.-C. Dai and D. Stojkovic, “Observing a wormhole,”Physical Review D, vol. 100, no. 8, p. 083513, 2019

    2019

  73. [73]

    Astrophysical wormholes,

    C. Bambi and D. Stojkovic, “Astrophysical wormholes,”Universe, vol. 7, no. 5, p. 136, 2021

    2021

  74. [74]

    Can wormholes mirror the quasinormal mode spectrum of schwarzschild black holes?,

    C. De Simone, V. De Falco, and S. Capozziello, “Can wormholes mirror the quasinormal mode spectrum of schwarzschild black holes?,”Physical Review D, vol. 111, no. 6, p. 064021, 2025

    2025

  75. [75]

    Epicyclic frequencies in static and spherically symmetric wormhole geometries,

    V. De Falco, M. De Laurentis, and S. Capozziello, “Epicyclic frequencies in static and spherically symmetric wormhole geometries,”Physical Review D, vol. 104, no. 2, p. 024053, 2021

    2021

  76. [76]

    Static and spherically symmetric wormholes in metric-affine theories of gravity,

    V. De Falco and S. Capozziello, “Static and spherically symmetric wormholes in metric-affine theories of gravity,”arXiv preprint arXiv:2308.05440, 2023

    Pith/arXiv arXiv 2023

  77. [77]

    Black-bounce to traversable wormhole,

    A. Simpson and M. Visser, “Black-bounce to traversable wormhole,”Journal of Cosmology and Astroparticle Physics, vol. 2019, no. 02, p. 042, 2019

    2019

  78. [78]

    Some implications of a cosmological phase transition,

    T. W. Kibble, “Some implications of a cosmological phase transition,”Physics Reports, vol. 67, no. 1, pp. 183–199, 1980

    1980

  79. [79]

    Cosmological experiments in superfluid helium?,

    W. H. Zurek, “Cosmological experiments in superfluid helium?,”Nature, vol. 317, no. 6037, pp. 505–508, 1985

    1985

  80. [80]

    Asymmetric symmetry breaking: Unequal probabilities of vacuum selection,

    T.-C. Ma, H.-Q. Shi, and H.-Q. Zhang, “Asymmetric symmetry breaking: Unequal probabilities of vacuum selection,”arXiv preprint arXiv:2405.05168, 2024

    Pith/arXiv arXiv 2024

Showing first 80 references.

This paper was first reviewed by deepseek-v4-flash on August 3, 2026.