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arxiv: 2604.10379 · v1 · submitted 2026-04-11 · 🌀 gr-qc

Quantum Entanglement of Circular Strings as a Probe for Topologically Charged Spacetimes

Ai-chen Li , Xin-Fei Li , Xuanting Ji This is my paper

Pith reviewed 2026-05-10 15:07 UTC · model grok-4.3

classification 🌀 gr-qc
keywords quantum entanglementcircular stringtopological defectsglobal monopolewormholedeficit anglevon Neumann entropysqueezed-state formalism
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The pith

A circular string's quantum entanglement distinguishes spacetimes with topological charges by responding to their deficit angles.

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

The paper develops a framework for embedding a circular string as a quantum probe in spherically symmetric curved spacetimes. Quadratic fluctuations of the string are quantized using the squeezed-state formalism to produce two-mode states and compute their von Neumann entropy as a measure of particle-antiparticle entanglement. This entropy serves as a probe that reveals qualitative differences between backgrounds with topological defects, such as global monopoles and monopole wormholes. The distinction arises from the sensitivity of the entanglement to the global structure of the spacetime, specifically the deficit angle. This approach provides access to geometric properties that classical observables like geodesic motion do not capture, addressing gaps in understanding entanglement in non-asymptotically AdS spacetimes.

Core claim

By placing a circular string probe in spacetimes with topological charge and quantizing its quadratic fluctuations via the squeezed-state formalism, the resulting two-mode quantum states yield a von Neumann entropy that distinguishes global monopole spacetimes from monopole wormhole configurations through their dependence on the deficit angle parameter.

What carries the argument

The squeezed-state quantization of quadratic fluctuations around the circular string embedding, which generates entangled two-mode states whose von Neumann entropy measures the probe's response to the background geometry.

Load-bearing premise

The circular string functions as a test probe with quadratic fluctuations quantized in the fixed background without backreaction or interference from full quantum gravity effects.

What would settle it

A calculation showing that the von Neumann entropy for the probe string is independent of the deficit angle in the monopole wormhole background would contradict the claimed sensitivity to global structure.

read the original abstract

Motivated by the limited understanding of entanglement entropy in non-asymptotically AdS spacetimes, we develop a framework in which a circular string is embedded as a quantum probe in a spherically symmetric curved spacetime, and its quadratic fluctuations are quantized using the squeezed-state formalism. This construction naturally yields two mode quantum states and the associated von Neumann entropy, providing a direct measure of particle antiparticle entanglement. The resulting entanglement serves as an effective probe of the underlying geometry, granting access to intrinsic features that are not readily captured by classical observables such as geodesic motion. As a concrete application, and as representative toy models of spacetimes with topological defects, including wormhole geometries, we investigate backgrounds with topological charge, focusing on global monopole and monopole wormhole configurations. We show that the entanglement generated by the probe string exhibits a clear qualitative distinction between these backgrounds and is highly sensitive to the global structure of the spacetime, in particular to the deficit angle. These results illustrate the utility of quantum correlations as diagnostic tools for probing geometric properties beyond the classical regime and offer a complementary perspective on the interplay between spacetime structure and quantum entanglement.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a framework for embedding a circular string as a quantum probe in spherically symmetric spacetimes with topological defects (global monopoles and monopole wormholes). Quadratic fluctuations of the string are quantized via the squeezed-state formalism to obtain two-mode states and the associated von Neumann entropy, which is then used as a measure of particle-antiparticle entanglement. The central claim is that this entanglement exhibits a clear qualitative distinction between the backgrounds and is highly sensitive to the deficit angle, thereby probing global spacetime structure beyond classical geodesic observables.

Significance. If the results hold under the stated approximations, the work provides a novel quantum diagnostic for topological features in non-asymptotically AdS geometries. The sensitivity of the entanglement entropy to the deficit angle offers a concrete illustration of how quantum correlations can access information not captured by classical probes, with potential relevance to wormhole and defect spacetimes. The construction is technically straightforward and yields falsifiable predictions for the entropy as a function of the deficit parameter.

major comments (2)
  1. [§3 (fluctuation quantization)] The test-probe assumption underlying the entire construction (negligible backreaction so that the fixed background metric with conical singularity is used for the fluctuation spectrum) is not justified quantitatively. In §3 (or the section deriving the mode equation), the canonical commutation relations and squeezed vacuum are defined on the unperturbed metric; however, the deficit angle alters the global mode structure, and a backreaction estimate (e.g., via the string tension relative to the monopole mass scale) is needed to confirm that the reported sensitivity of the von Neumann entropy to the deficit angle survives this approximation.
  2. [§5 (results)] Table or figure in the results section (presumably §5) that displays the entropy versus deficit angle does not include a direct comparison to the flat-space or zero-deficit limit with the same string parameters. Without this baseline, it is unclear whether the claimed qualitative distinction arises from the topological charge or from other background parameters (e.g., the wormhole throat radius).
minor comments (2)
  1. [Abstract] The abstract states that the construction 'naturally yields two mode quantum states' but does not identify the two modes (e.g., left- and right-moving or radial and angular); a brief clarification would improve readability.
  2. [§2 (background metrics)] Notation for the deficit angle parameter is introduced without an explicit equation reference in the background section; adding the defining relation (e.g., Eq. (X)) would help readers connect it to the entropy plots.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which we address point by point below. We indicate where revisions will be incorporated in the next version.

read point-by-point responses

  1. Referee: [§3 (fluctuation quantization)] The test-probe assumption underlying the entire construction (negligible backreaction so that the fixed background metric with conical singularity is used for the fluctuation spectrum) is not justified quantitatively. In §3 (or the section deriving the mode equation), the canonical commutation relations and squeezed vacuum are defined on the unperturbed metric; however, the deficit angle alters the global mode structure, and a backreaction estimate (e.g., via the string tension relative to the monopole mass scale) is needed to confirm that the reported sensitivity of the von Neumann entropy to the deficit angle survives this approximation.

    Authors: We agree that a quantitative justification of the test-probe approximation strengthens the work. In the revised manuscript we will add a brief estimate in §3, comparing the string tension to the monopole mass scale for the parameter values used in the calculations. This will show that backreaction remains small and that the reported dependence of the von Neumann entropy on the deficit angle is preserved under the approximation. revision: yes

  2. Referee: [§5 (results)] Table or figure in the results section (presumably §5) that displays the entropy versus deficit angle does not include a direct comparison to the flat-space or zero-deficit limit with the same string parameters. Without this baseline, it is unclear whether the claimed qualitative distinction arises from the topological charge or from other background parameters (e.g., the wormhole throat radius).

    Authors: We agree that an explicit zero-deficit baseline is needed for clarity. In the revised version we will augment the figure or table in §5 with the entropy values obtained in the flat-space (zero-deficit) limit for identical string parameters, thereby isolating the effect of the topological charge. revision: yes

Circularity Check

0 steps flagged

No circularity: entanglement entropy derived directly from quantized string fluctuations in fixed backgrounds

full rationale

The paper develops a probe-string framework by embedding a circular string in a fixed spherically symmetric metric, quantizing its quadratic fluctuations via the squeezed-state formalism, and extracting the von Neumann entropy of the resulting two-mode state. This entropy is then evaluated on global-monopole and monopole-wormhole geometries, where it is shown to depend on the deficit angle. No equation reduces the output entropy to a fitted parameter, a self-referential definition, or a load-bearing self-citation; the derivation chain proceeds from the background line element through canonical commutation relations and Bogoliubov transformations to the entropy observable. The reported qualitative distinction therefore follows from explicit computation rather than being presupposed by the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions from general relativity and quantum field theory in curved spacetime, as the abstract does not specify additional free parameters or new entities.

axioms (2)
  • domain assumption The background spacetime is spherically symmetric
    Required for embedding a circular string probe.
  • domain assumption Quadratic fluctuations can be quantized using squeezed-state formalism
    This is the key step to obtain the two-mode quantum states and von Neumann entropy.

pith-pipeline@v0.9.0 · 5501 in / 1335 out tokens · 57840 ms · 2026-05-10T15:07:25.015384+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

89 extracted references · 89 canonical work pages

  1. [1]

    Nielsen and Isaac L

    Michael A. Nielsen and Isaac L. Chuang.Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010

    work page 2010

  2. [2]

    Holographic derivation of entanglement entropy from AdS/CFT.Phys

    Shinsei Ryu and Tadashi Takayanagi. Holographic derivation of entanglement entropy from AdS/CFT.Phys. Rev. Lett., 96:181602, 2006

    work page 2006

  3. [3]

    Hubeny, Mukund Rangamani, and Tadashi Takayanagi

    Veronika E. Hubeny, Mukund Rangamani, and Tadashi Takayanagi. A Covariant holographic entanglement entropy proposal.JHEP, 07:062, 2007. – 22 –

    work page 2007

  4. [4]

    Quantum corrections to holographic entanglement entropy.JHEP, 11:074, 2013

    Thomas Faulkner, Aitor Lewkowycz, and Juan Maldacena. Quantum corrections to holographic entanglement entropy.JHEP, 11:074, 2013

    work page 2013

  5. [5]

    Lectures on entanglement, von Neumann algebras, and emergence of spacetime

    Hong Liu. Lectures on entanglement, von Neumann algebras, and emergence of spacetime. InTheoretical Advanced Study Institute in Elementary Particle Physics 2023: Aspects of Symmetry, 10 2025

    work page 2023

  6. [6]

    Entanglement entropy of cosmological perturbations.Physical Review D, 102(4), August 2020

    Suddhasattwa Brahma, Omar Alaryani, and Robert Brandenberger. Entanglement entropy of cosmological perturbations.Physical Review D, 102(4), August 2020

    work page 2020

  7. [7]

    Quantum entanglement in cosmology.Phys

    Alessio Belfiglio, Orlando Luongo, and Stefano Mancini. Quantum entanglement in cosmology.Phys. Rept., 1146:1–47, 2025

    work page 2025

  8. [8]

    An Entangled Universe

    Pablo Tejerina-P´ erez, Daniele Bertacca, and Raul Jimenez. An Entangled Universe. 3 2024

    work page 2024

  9. [9]

    A Bell experiment during inflation: probing quantum entanglement in tensor fluctuations through correlations of primordial scalar curvature perturbations

    Pablo Tejerina-P´ erez, Leonid Sarieddine, Daniele Bertacca, and Raul Jimenez. A Bell experiment during inflation: probing quantum entanglement in tensor fluctuations through correlations of primordial scalar curvature perturbations. 3 2026

    work page 2026

  10. [10]

    A Bell Experiment in an Entangled Universe

    Pablo Tejerina-P´ erez, Daniele Bertacca, Raul Jimenez, and Leonid Sarieddine. A Bell Experiment in an Entangled Universe. 3 2026

    work page 2026

  11. [11]

    Entanglement in many-body systems.Reviews of Modern Physics, 80(2):517–576, May 2008

    Luigi Amico, Rosario Fazio, Andreas Osterloh, and Vlatko Vedral. Entanglement in many-body systems.Reviews of Modern Physics, 80(2):517–576, May 2008

    work page 2008

  12. [12]

    Hartnoll and Edward Mazenc

    Sean A. Hartnoll and Edward Mazenc. Entanglement entropy in two dimensional string theory.Phys. Rev. Lett., 115(12):121602, 2015

    work page 2015

  13. [13]

    Hartnoll

    Alexander Frenkel and Sean A. Hartnoll. Entanglement in the Quantum Hall Matrix Model. JHEP, 05:130, 2022

    work page 2022

  14. [14]

    Aspects of Holographic Entanglement Entropy.JHEP, 08:045, 2006

    Shinsei Ryu and Tadashi Takayanagi. Aspects of Holographic Entanglement Entropy.JHEP, 08:045, 2006

    work page 2006

  15. [15]

    Generalized gravitational entropy.JHEP, 08:090, 2013

    Aitor Lewkowycz and Juan Maldacena. Generalized gravitational entropy.JHEP, 08:090, 2013

    work page 2013

  16. [16]

    Netta Engelhardt and Aron C. Wall. Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime.JHEP, 01:073, 2015

    work page 2015

  17. [17]

    L. P. Grishchuk and Yu. V. Sidorov. On the Quantum State of Relic Gravitons.Class. Quant. Grav., 6:L161–L165, 1989

    work page 1989

  18. [18]

    L. P. Grishchuk and Yu. V. Sidorov. Squeezed quantum states of relic gravitons and primordial density fluctuations.Phys. Rev. D, 42:3413–3421, 1990

    work page 1990

  19. [19]

    Inflation and squeezed quantum states.Phys

    Andreas Albrecht, Pedro Ferreira, Michael Joyce, and Tomislav Prokopec. Inflation and squeezed quantum states.Phys. Rev. D, 50:4807–4820, 1994

    work page 1994

  20. [20]

    Squeezed States in Gravity

    Arunima Das, Maulik Parikh, Frank Wilczek, and Raphaela Wutte. Squeezed States in Gravity. 12 2025

    work page 2025

  21. [21]

    Squeezed quantum states of graviton and axion in the universe.Int

    Sugumi Kanno and Jiro Soda. Squeezed quantum states of graviton and axion in the universe.Int. J. Mod. Phys. D, 31(13):2250098, 2022

    work page 2022

  22. [22]

    Inflationary perturbations: The Cosmological Schwinger effect.Lect

    Jerome Martin. Inflationary perturbations: The Cosmological Schwinger effect.Lect. Notes Phys., 738:193–241, 2008

    work page 2008

  23. [23]

    Shajidul Haque and Bret Underwood

    S. Shajidul Haque and Bret Underwood. Squeezed out-of-time-order correlator and cosmology.Phys. Rev. D, 103(2):023533, 2021. – 23 –

    work page 2021

  24. [24]

    Shajidul Haque, and Bret Underwood

    Arpan Bhattacharyya, Saurya Das, S. Shajidul Haque, and Bret Underwood. Cosmological Complexity.Phys. Rev. D, 101(10):106020, 2020

    work page 2020

  25. [25]

    The generalized CV conjecture of Krylov complexity

    Ke-Hong Zhai, Lei-Hua Liu, and Hai-Qing Zhang. The generalized CV conjecture of Krylov complexity. 12 2024

    work page 2024

  26. [26]

    Inflationary Krylov complexity.JHEP, 04:123, 2024

    Tao Li and Lei-Hua Liu. Inflationary Krylov complexity.JHEP, 04:123, 2024

    work page 2024

  27. [27]

    Complexity of non-trivial sound speed in inflation.Phys

    Lei-Hua Liu and Ai-Chen Li. Complexity of non-trivial sound speed in inflation.Phys. Dark Univ., 37:101123, 2022

    work page 2022

  28. [28]

    Cosmological Krylov Complexity.Fortsch

    Kiran Adhikari and Sayantan Choudhury. Cosmological Krylov Complexity.Fortsch. Phys., 70(12):2200126, 2022

    work page 2022

  29. [29]

    Coherent State Description of Gravitational Waves from Binary Black Holes.Phys

    Sugumi Kanno, Jiro Soda, and Akira Taniguchi. Coherent State Description of Gravitational Waves from Binary Black Holes.Phys. Rev. Lett., 136(6):061404, 2026

    work page 2026

  30. [30]

    Bipartite temporal Bell inequalities for two-mode squeezed states.Phys

    Kenta Ando and Vincent Vennin. Bipartite temporal Bell inequalities for two-mode squeezed states.Phys. Rev. A, 102(5):052213, 2020

    work page 2020

  31. [31]

    Deriving covariant holographic entanglement.JHEP, 11:028, 2016

    Xi Dong, Aitor Lewkowycz, and Mukund Rangamani. Deriving covariant holographic entanglement.JHEP, 11:028, 2016

    work page 2016

  32. [32]

    Horacio Casini, Marina Huerta, and Robert C. Myers. Towards a derivation of holographic entanglement entropy.JHEP, 05:036, 2011

    work page 2011

  33. [33]

    Holographic Entanglement Entropy as a Probe of Dynamical Criticality in Scalarizing Black Holes

    Yi Li, Ke-tai Wu, Chong-Ye Chen, Chao Niu, Cheng-Yong Zhang, and Peng Liu. Holographic Entanglement Entropy as a Probe of Dynamical Criticality in Scalarizing Black Holes. 1 2025

    work page 2025

  34. [34]

    Probing the bubble interior with entanglement entropy and bulk-cone singularities.JHEP, 02:215, 2026

    Roberto Auzzi, Stefano Baiguera, Lihan Guo, Giuseppe Nardelli, and Nicol` o Zenoni. Probing the bubble interior with entanglement entropy and bulk-cone singularities.JHEP, 02:215, 2026

    work page 2026

  35. [35]

    Entanglement Renormalization and Holography.Phys

    Brian Swingle. Entanglement Renormalization and Holography.Phys. Rev. D, 86:065007, 2012

    work page 2012

  36. [36]

    Building up spacetime with quantum entanglement.Gen

    Mark Van Raamsdonk. Building up spacetime with quantum entanglement.Gen. Rel. Grav., 42:2323–2329, 2010

    work page 2010

  37. [37]

    Bit threads and holographic entanglement

    Michael Freedman and Matthew Headrick. Bit threads and holographic entanglement. Commun. Math. Phys., 352(1):407–438, 2017

    work page 2017

  38. [38]

    J. R. Nascimento, Gonzalo J. Olmo, P. J. Porf´ ırio, A. Yu. Petrov, and A. R. Soares. Nonlinearσ-models in the Eddington-inspired Born-Infeld Gravity.Phys. Rev. D, 101(6):064043, 2020

    work page 2020

  39. [39]

    Aounallah, A

    H. Aounallah, A. R. Soares, and R. L. L. Vit´ oria. Scalar field and deflection of light under the effects of topologically charged Ellis–Bronnikov-type wormhole spacetime.Eur. Phys. J. C, 80(5):447, 2020

    work page 2020

  40. [40]

    Furtado, J

    C. Furtado, J. R. Nascimento, A. Yu. Petrov, P. J. Porf´ ırio, and A. R. Soares. Strong gravitational lensing in a spacetime with topological charge within the Eddington-inspired Born-Infeld gravity.Phys. Rev. D, 103(4):044047, 2021

    work page 2021

  41. [41]

    A. R. Soares, R. L. L. Vit´ oria, and H. Aounallah. On the Klein–Gordon oscillator in topologically charged Ellis–Bronnikov-type wormhole spacetime.Eur. Phys. J. Plus, 136(9):966, 2021. – 24 –

    work page 2021

  42. [42]

    Noether symmetry approach in Eddington-inspired Born–Infeld gravity.Eur

    Thanyagamon Kanesom, Phongpichit Channuie, and Narakorn Kaewkhao. Noether symmetry approach in Eddington-inspired Born–Infeld gravity.Eur. Phys. J. C, 81(4):357, 2021

    work page 2021

  43. [43]

    C. F. S. Pereira, R. L. L. Vit´ oria, A. R. Soares, and H. Belich. Gravitational Effects on a Position-Dependent Mass Quantum Particle in Eddington-Inspired Born-Infeld Spacetime. Int. J. Theor. Phys., 62(10):225, 2023

    work page 2023

  44. [44]

    C. F. S. Pereira, R. L. L. Vit´ oria, A. R. Soares, V. B. Bezerra, and H. Belich. Non-relativistic quantum dynamics in Born–Infeld gravity inspired by Eddington spacetime global monopole.Int. J. Geom. Meth. Mod. Phys., 21(05):2450093, 2024

    work page 2024

  45. [45]

    Soares, Carlos F

    Omar Mustafa, Adriano R. Soares, Carlos F. S. Pereira, and Ricardo L. L. Vit´ oria. On the Klein–Gordon oscillators in Eddington-inspired Born-Infeld gravity global monopole spacetime and a Wu–Yang magnetic monopole.Eur. Phys. J. C, 84(4):405, 2024

    work page 2024

  46. [46]

    Quasinormal modes in nonlinearσmodels in the Eddington inspired Born-Infeld gravity

    Bobir Toshmatov, Bobomurat Ahmedov, Azamjon Boydedayev, and Sardor Tojiev. Quasinormal modes in nonlinearσmodels in the Eddington inspired Born-Infeld gravity. Phys. Rev. D, 109(4):044003, 2024

    work page 2024

  47. [47]

    KG-oscillators in Eddington-inspired Born-Infeld gravity: Wu-Yang magnetic monopole and Ricci scalar curvature effects.Nucl

    Omar Mustafa. KG-oscillators in Eddington-inspired Born-Infeld gravity: Wu-Yang magnetic monopole and Ricci scalar curvature effects.Nucl. Phys. B, 1012:116827, 2025

    work page 2025

  48. [48]

    Harmonic oscillator in topologically charged deformed gravity space–time and Wu–Yang magnetic monopole.Phys

    Faizuddin Ahmed and Abdelmalek Bouzenada. Harmonic oscillator in topologically charged deformed gravity space–time and Wu–Yang magnetic monopole.Phys. Dark Univ., 46:101690, 2024

    work page 2024

  49. [49]

    Vacuum polarization of fermions near the throat of a global monopole wormhole.Eur

    Ai-chen Li and Xin-Fei Li. Vacuum polarization of fermions near the throat of a global monopole wormhole.Eur. Phys. J. C, 86(1):60, 2026

    work page 2026

  50. [50]

    Quantized fields and particle creation in expanding universes

    Leonard Parker. Quantized fields and particle creation in expanding universes. i.Physical Review, 183(5):1057–1068, July 1969

    work page 1969

  51. [51]

    N. D. Birrell and P. C. W. Davies.Quantum Fields in Curved Space. Cambridge Monographs on Mathematical Physics. Cambridge University Press, 1982

    work page 1982

  52. [52]

    Geodesic Motions in AdS Soliton Background Space-time

    Han-qing Shi and Ding-fang Zeng. Geodesic Motions in AdS Soliton Background Space-time. 3 2016

    work page 2016

  53. [53]

    Villanueva

    Norman Cruz, Marco Olivares, and Jose R. Villanueva. The Geodesic structure of the Schwarzschild anti-de Sitter black hole.Class. Quant. Grav., 22:1167–1190, 2005

    work page 2005

  54. [54]

    A. R. Soares, R. L. L. Vit´ oria, and C. F. S. Pereira. Gravitational lensing in a topologically charged Eddington-inspired Born–Infeld spacetime.Eur. Phys. J. C, 83(10):903, 2023

    work page 2023

  55. [55]

    Cool horizons for entangled black holes.Fortsch

    Juan Maldacena and Leonard Susskind. Cool horizons for entangled black holes.Fortsch. Phys., 61:781–811, 2013

    work page 2013

  56. [56]

    ER=EPR, GHZ, and the consistency of quantum measurements.Fortsch

    Leonard Susskind. ER=EPR, GHZ, and the consistency of quantum measurements.Fortsch. Phys., 64:72–83, 2016

    work page 2016

  57. [57]

    Beltran, and Enrique Arias

    Willy Izquierdo, J. Beltran, and Enrique Arias. Enhancement of harvesting vacuum entanglement in Cosmic String Spacetime.JHEP, 03:049, 2025

    work page 2025

  58. [58]

    Babichev

    E. Babichev. Global topological k-defects.Phys. Rev. D, 74:085004, 2006

    work page 2006

  59. [59]

    Ramadhan

    Ilham Prasetyo and Handhika S. Ramadhan. Classical defects in higher-dimensional Einstein gravity coupled to nonlinearσ-models.Gen. Rel. Grav., 49(9):115, 2017. – 25 –

    work page 2017

  60. [60]

    SPACE-TIME COMPACTIFICATION DUE TO SCALARS.Phys

    Murray Gell-Mann and Barton Zwiebach. SPACE-TIME COMPACTIFICATION DUE TO SCALARS.Phys. Lett. B, 141:333–336, 1984

    work page 1984

  61. [61]

    Lambaga and Handhika S

    Reyhan D. Lambaga and Handhika S. Ramadhan. Gravitational field of global monopole within the Eddington-inspired Born-Infeld theory of gravity.Eur. Phys. J. C, 78(6):436, 2018

    work page 2018

  62. [62]

    Particle production of an infalling circular string near the event horizon

    Ai chen Li. Particle production of an infalling circular string near the event horizon. under review, 2026

    work page 2026

  63. [63]

    A. L. Larsen. Circular string instabilities in curved space-time.Phys. Rev. D, 50:2623–2630, 1994

    work page 1994

  64. [64]

    Larsen and Argyris Nicolaidis

    Arne L. Larsen and Argyris Nicolaidis. String spreading on black hole horizon.Phys. Rev. D, 60:024012, 1999

    work page 1999

  65. [65]

    Perturbations on domain walls and strings: A Covariant theory.Phys

    Jaume Garriga and Alexander Vilenkin. Perturbations on domain walls and strings: A Covariant theory.Phys. Rev. D, 44:1007–1014, 1991

    work page 1991

  66. [66]

    Perturbations of a topological defect as a theory of coupled scalar fields in curved space.Phys

    Jemal Guven. Perturbations of a topological defect as a theory of coupled scalar fields in curved space.Phys. Rev. D, 48:5562–5569, 1993

    work page 1993

  67. [67]

    Canonical transformations and squeezing formalism in cosmology.JCAP, 02:022, 2020

    Julien Grain and Vincent Vennin. Canonical transformations and squeezing formalism in cosmology.JCAP, 02:022, 2020

    work page 2020

  68. [68]

    Quantum fluctuations on domain walls, strings and vacuum bubbles.Phys

    Jaume Garriga and Alexander Vilenkin. Quantum fluctuations on domain walls, strings and vacuum bubbles.Phys. Rev. D, 45:3469–3486, 1992

    work page 1992

  69. [69]

    Black holes from nucleating strings.Phys

    Jaume Garriga and Alexander Vilenkin. Black holes from nucleating strings.Phys. Rev. D, 47:3265–3274, 1993

    work page 1993

  70. [70]

    S. M. Barnett and P. M. Radmore.Methods in Theoretical Quantum Optics. Clarendon Press, Oxford, 1997

    work page 1997

  71. [71]

    Puri.Mathematical Methods of Quantum Optics

    Ravinder R. Puri.Mathematical Methods of Quantum Optics. Springer, Berlin, 2001

    work page 2001

  72. [72]

    Cosmological complexity in K-essence.Phys

    Ai-chen Li, Xin-Fei Li, Ding-fang Zeng, and Lei-Hua Liu. Cosmological complexity in K-essence.Phys. Dark Univ., 43:101422, 2024

    work page 2024

  73. [73]

    Quantum Discord of Cosmic Inflation: Can we Show that CMB Anisotropies are of Quantum-Mechanical Origin?Phys

    Jerome Martin and Vincent Vennin. Quantum Discord of Cosmic Inflation: Can we Show that CMB Anisotropies are of Quantum-Mechanical Origin?Phys. Rev. D, 93(2):023505, 2016

    work page 2016

  74. [74]

    H. G. Ellis. Ether flow through a drainhole - a particle model in general relativity.J. Math. Phys., 14:104–118, 1973

    work page 1973

  75. [75]

    K. A. Bronnikov. Scalar-tensor theory and scalar charge.Acta Phys. Polon. B, 4:251–266, 1973

    work page 1973

  76. [76]

    Ball, Ivette Fuentes-Schuller, and Frederic P

    Jonathan L. Ball, Ivette Fuentes-Schuller, and Frederic P. Schuller. Entanglement in an expanding spacetime.Phys. Lett. A, 359:550–554, 2006

    work page 2006

  77. [77]

    Menicucci

    Eduardo Martin-Martinez and Nicolas C. Menicucci. Cosmological quantum entanglement. Class. Quant. Grav., 29:224003, 2012

    work page 2012

  78. [78]

    Entanglement in anisotropic expanding spacetime.Eur

    Roberto Pierini, Shahpoor Moradi, and Stefano Mancini. Entanglement in anisotropic expanding spacetime.Eur. Phys. J. D, 73(2):33, 2019

    work page 2019

  79. [79]

    Black-bounce to traversable wormhole.JCAP, 02:042, 2019

    Alex Simpson and Matt Visser. Black-bounce to traversable wormhole.JCAP, 02:042, 2019. – 26 –

    work page 2019

  80. [80]

    Exact inner metric and microscopic state of AdS 3 -Schwarzschild BHs

    Ding-fang Zeng. Exact inner metric and microscopic state of AdS 3 -Schwarzschild BHs. Nucl. Phys. B, 954:115001, 2020

    work page 2020

Showing first 80 references.