# Astrophysical Wormholes

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## Abstract

**:**

## 1. Introduction

## 2. Formation and Stability

## 3. Search for Astrophysical Wormholes

#### 3.1. Gravitational Lensing

#### 3.2. Orbiting Stars

#### 3.3. Imaging

#### 3.4. Accretion Disk Spectra

#### 3.5. Gravitational Waves

## 4. Concluding Remarks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Emparan, R.; Grado-White, B.; Marolf, D.; Tomasevic, M. Multi-mouth Traversable Wormholes. arXiv
**2012**, arXiv:2012.07821. [Google Scholar] - Einstein, A.; Rosen, N. The Particle Problem in the General Theory of Relativity. Phys. Rev.
**1935**, 48, 73–77. [Google Scholar] [CrossRef] - Misner, C.W.; Wheeler, J.A. Classical physics as geometry: Gravitation, electromagnetism, unquantized charge, and mass as properties of curved empty space. Annals Phys.
**1957**, 2, 525–603. [Google Scholar] [CrossRef] - Bronnikov, K.A. Scalar-tensor theory and scalar charge. Acta Phys. Polon. B
**1973**, 4, 251–266. [Google Scholar] - Ellis, H.G. Ether flow through a drainhole—A particle model in general relativity. J. Math. Phys.
**1973**, 14, 104–118. [Google Scholar] [CrossRef] - Morris, M.S.; Thorne, K.S. Wormholes in space-time and their use for interstellar travel: A tool for teaching general relativity. Am. J. Phys.
**1988**, 56, 395–412. [Google Scholar] [CrossRef] [Green Version] - Morris, M.S.; Thorne, K.S.; Yurtsever, U. Wormholes, Time Machines, and the Weak Energy Condition. Phys. Rev. Lett.
**1988**, 61, 1446–1449. [Google Scholar] [CrossRef] [Green Version] - Visser, M. Traversable wormholes: Some simple examples. Phys. Rev. D
**1989**, 39, 3182–3184. [Google Scholar] [CrossRef] [Green Version] - Bronnikov, K.A.; Krechet, V.G. Potentially observable cylindrical wormholes without exotic matter in general relativity. Phys. Rev. D
**2019**, 99, 084051. [Google Scholar] [CrossRef] [Green Version] - Shinkai, H.A.; Hayward, S.A. Fate of the first traversible wormhole: Black hole collapse or inflationary expansion. Phys. Rev. D
**2002**, 66, 044005. [Google Scholar] [CrossRef] [Green Version] - Gravanis, E.; Willison, S. ‘Mass without mass’ from thin shells in Gauss–Bonnet gravity. Phys. Rev. D
**2007**, 75, 084025. [Google Scholar] [CrossRef] [Green Version] - Richarte, M.G.; Simeone, C. Thin-shell wormholes supported by ordinary matter in Einstein-Gauss-Bonnet gravity. Phys. Rev. D
**2008**, 76, 087502, Erratum in**2008**, 77, 089903. [Google Scholar] [CrossRef] [Green Version] - Eiroa, E.F.; Richarte, M.G.; Simeone, C. Thin-shell wormholes in Brans-Dicke gravity. Phys. Lett. A
**2008**, 373, 1–4, Erratum in**2009**, 373, 2399–2400. [Google Scholar] [CrossRef] [Green Version] - Richarte, M.G. Wormholes and solitonic shells in five-dimensional DGP theory. Phys. Rev. D
**2010**, 82, 044021. [Google Scholar] [CrossRef] [Green Version] - Abbott, B.P.; Abbott, R.; Abbott, T.D.; Abernathy, M.R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R.X.; et al. [LIGO Scientific and Virgo]. Observation of Gravitational Waves from a Binary Black Hole Merger. Phys. Rev. Lett.
**2016**, 116, 061102. [Google Scholar] [CrossRef] [PubMed] - The Event Horizon Telescope Collaboration; Akiyama, K.; Alberdi, A.; Alef, W.; Asada, K.; Azulay, R.; Baczko, A.-K.; Ball, D.; Baloković, M.; Barrett, J. First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole. Astrophys. J.
**2019**, 875. [Google Scholar] [CrossRef] - Friedman, J.L.; Schleich, K.; Witt, D.M. Topological censorship. Phys. Rev. Lett.
**1993**, 71, 1486–1489, Erratum in**1995**, 75, 1872. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Galloway, G.J.; Schleich, K.; Witt, D.M.; Woolgar, E. Topological censorship and higher genus black holes. Phys. Rev. D
**1999**, 60, 104039. [Google Scholar] [CrossRef] [Green Version] - Gao, P.; Jafferis, D.L.; Wall, A.C. Traversable Wormholes via a Double Trace Deformation. J. High Energy Phys.
**2017**, 12, 151. [Google Scholar] [CrossRef] [Green Version] - Maldacena, J.; Qi, X.L. Eternal traversable wormhole. arXiv
**2018**, arXiv:1804.00491. [Google Scholar] - Horowitz, G.T.; Marolf, D.; Santos, J.E.; Wang, D. Creating a Traversable Wormhole. Class Quant. Grav.
**2019**, 36, 205011. [Google Scholar] [CrossRef] [Green Version] - Maldacena, J.; Susskind, L. Cool horizons for entangled black holes. Fortsch. Phys.
**2013**, 61, 781–811. [Google Scholar] [CrossRef] [Green Version] - Visser, M.; Kar, S.; Dadhich, N. Traversable wormholes with arbitrarily small energy condition violations. Phys. Rev. Lett.
**2003**, 90, 201102. [Google Scholar] [CrossRef] [Green Version] - Deng, H.; Garriga, J.; Vilenkin, A. Primordial black hole and wormhole formation by domain walls. J. Cosmol. Astropart. Phys.
**2017**, 4, 50. [Google Scholar] [CrossRef] - Polchinski, J. Cosmic superstrings revisited. AIP Conf. Proc.
**2004**, 743, 331–340. [Google Scholar] [CrossRef] [Green Version] - Dai, D.C.; Minic, D.; Stojkovic, D. How to form a wormhole. Eur. Phys. J. C
**2020**, 80, 1103. [Google Scholar] [CrossRef] - Arkani-Hamed, N.; Dimopoulos, S.; Dvali, G.R. The Hierarchy problem and new dimensions at a millimeter. Phys. Lett. B
**1998**, 429, 263–272. [Google Scholar] [CrossRef] [Green Version] - Randall, L.; Sundrum, R. A Large mass hierarchy from a small extra dimension. Phys. Rev. Lett.
**1999**, 83, 3370–3373. [Google Scholar] [CrossRef] [Green Version] - Randall, L.; Sundrum, R. An Alternative to compactification. Phys. Rev. Lett.
**1999**, 83, 4690–4693. [Google Scholar] [CrossRef] [Green Version] - Dai, D.C.; Minic, D.; Stojkovic, D. New wormhole solution in de Sitter space. Phys. Rev. D
**2017**, 98, 124026. [Google Scholar] [CrossRef] [Green Version] - Bambi, C. Testing black hole candidates with electromagnetic radiation. Rev. Mod. Phys.
**2017**, 89, 025001. [Google Scholar] [CrossRef] [Green Version] - Yagi, K.; Stein, L.C. Black Hole Based Tests of General Relativity. Class. Quant. Grav.
**2016**, 33, 054001. [Google Scholar] [CrossRef] [Green Version] - Kim, S.W.; Cho, Y.M. Wormhole gravitational lens. In Proceedings of the 37th Yamada Conference: Evolution of the Universe and its Observational Quest, Tokyo, Japan, 8–12 June 1993; Sato, K., Ed.; Universal Academy Press: Tokyo, Japan, 1994; pp. 353–354. [Google Scholar]
- Cramer, J.G.; Forward, R.L.; Morris, M.S.; Visser, M.; Benford, G.; Landis, G.A. Natural wormholes as gravitational lenses. Phys. Rev. D
**1995**, 51, 3117–3120. [Google Scholar] [CrossRef] [Green Version] - Torres, D.F.; Romero, G.E.; Anchordoqui, L.A. Might some gamma-ray bursts be an observable signature of natural wormholes? Phys. Rev. D
**1998**, 58, 123001. [Google Scholar] [CrossRef] [Green Version] - Torres, D.F.; Eiroa, E.F.; Romero, G.E. On the possibility of an astronomical detection of chromaticity effects in microlensing by wormhole - like objects. Mod. Phys. Lett. A
**2001**, 16, 1849–1861. [Google Scholar] [CrossRef] [Green Version] - Nandi, K.K.; Zhang, Y.Z.; Zakharov, A.V. Gravitational lensing by wormholes. Phys. Rev. D
**2006**, 74, 024020. [Google Scholar] [CrossRef] [Green Version] - Rahaman, F.; Kalam, M.; Chakraborty, S. Gravitational lensing by stable C-field wormhole. Chin. J. Phys.
**2017**, 45, 518. [Google Scholar] - Dey, T.K.; Sen, S. Gravitational lensing by wormholes. Mod. Phys. Lett. A
**2008**, 23, 953–962. [Google Scholar] [CrossRef] - Bhattacharya, A.; Potapov, A.A. Bending of light in Ellis wormhole geometry. Mod. Phys. Lett. A
**2010**, 25, 2399–2409. [Google Scholar] [CrossRef] - Nakajima, K.; Asada, H. Deflection angle of light in an Ellis wormhole geometry. Phys. Rev. D
**2012**, 85, 107501. [Google Scholar] [CrossRef] [Green Version] - Tsukamoto, N.; Harada, T.; Yajima, K. Can we distinguish between black holes and wormholes by their Einstein ring systems? Phys. Rev. D
**2012**, 86, 104062. [Google Scholar] [CrossRef] [Green Version] - Kuhfittig, P.K.F. Gravitational lensing of wormholes in the galactic halo region. Eur. Phys. J. C
**2014**, 74, 2818. [Google Scholar] [CrossRef] [Green Version] - Tsukamoto, N. Strong deflection limit analysis and gravitational lensing of an Ellis wormhole. Phys. Rev. D
**2016**, 94, 124001. [Google Scholar] [CrossRef] [Green Version] - Shaikh, R.; Kar, S. Gravitational lensing by scalar-tensor wormholes and the energy conditions. Phys. Rev. D
**2017**, 96, 044037. [Google Scholar] [CrossRef] [Green Version] - Jusufi, K.; Ovgün, A.; Banerjee, A. Light deflection by charged wormholes in Einstein–Maxwell-dilaton theory. Phys. Rev. D
**2017**, 96, 084036. [Google Scholar] [CrossRef] [Green Version] - Övgün, A. Light deflection by Damour-Solodukhin wormholes and Gauss–Bonnet theorem. Phys. Rev. D
**2018**, 98, 044033. [Google Scholar] [CrossRef] [Green Version] - Övgün, A.; Gyulchev, G.; Jusufi, K. Weak Gravitational lensing by phantom black holes and phantom wormholes using the Gauss–Bonnet theorem. Ann. Phys.
**2019**, 406, 152–172. [Google Scholar] [CrossRef] [Green Version] - Ono, T.; Ishihara, A.; Asada, H. Deflection angle of light for an observer and source at finite distance from a rotating wormhole. Phys. Rev. D
**2018**, 98, 044047. [Google Scholar] [CrossRef] [Green Version] - Shaikh, R.; Banerjee, P.; Paul, S.; Sarkar, T. A novel gravitational lensing feature by wormholes. Phys. Lett. B
**2019**, 789, 270–275, Erratum in**2019**, 791, 422–423. [Google Scholar] [CrossRef] - Shaikh, R.; Banerjee, P.; Paul, S.; Sarkar, T. Strong gravitational lensing by wormholes. J. Cosmol. Astropart. Phys.
**2019**, 7, 28. [Google Scholar] [CrossRef] [Green Version] - Anchordoqui, L.A.; Romero, G.E.; Torres, D.F.; Andruchow, I. In search for natural wormholes. Mod. Phys. Lett. A
**1999**, 14, 791–798. [Google Scholar] [CrossRef] [Green Version] - Abe, F. Gravitational Microlensing by the Ellis Wormhole. Astrophys. J.
**2010**, 725, 787–793. [Google Scholar] [CrossRef] - Toki, Y.; Kitamura, T.; Asada, H.; Abe, F. Astrometric Image Centroid Displacements due to Gravitational Microlensing by the Ellis Wormhole. Astrophys. J.
**2011**, 740, 121. [Google Scholar] [CrossRef] [Green Version] - Takahashi, R.; Asada, H. Observational Upper Bound on the Cosmic Abundances of Negative-mass Compact Objects and Ellis Wormholes from the Sloan Digital Sky Survey Quasar Lens Search. Astrophys. J. Lett.
**2013**, 768, L16. [Google Scholar] [CrossRef] [Green Version] - Kitamura, T.; Nakajima, K.; Asada, H. Demagnifying gravitational lenses toward hunting a clue of exotic matter and energy. Phys. Rev. D
**2013**, 87, 027501. [Google Scholar] [CrossRef] [Green Version] - Izumi, K.; Hagiwara, C.; Nakajima, K.; Kitamura, T.; Asada, H. Gravitational lensing shear by an exotic lens object with negative convergence or negative mass. Phys. Rev. D
**2013**, 88, 024049. [Google Scholar] [CrossRef] [Green Version] - Nakajima, K.; Izumi, K.; Asada, H. Negative time delay of light by a gravitational concave lens. Phys. Rev. D
**2014**, 90, 084026. [Google Scholar] [CrossRef] [Green Version] - Dai, D.C.; Stojkovic, D. Observing a Wormhole. Phys. Rev. D
**2019**, 100, 083513. [Google Scholar] [CrossRef] [Green Version] - Dai, D.C.; Stojkovic, D. Reply to “Comment on ‘Observing a wormhole’”. Phys. Rev. D
**2020**, 101, 068302. [Google Scholar] [CrossRef] - Do, T.; Hees, A.; Ghez, A.; Martinez, G.D.; Chu, D.S.; Jia, S.; Sakai, S.; Lu, J.R.; Gautam, A.K.; O’Neil, K.K.; et al. Relativistic redshift of the star S0-2 orbiting the Galactic center supermassive black hole. Science
**2019**, 365, 664–668. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Simonetti, J.H.; Kavic, M.J.; Minic, D.; Stojkovic, D.; Dai, D.C. A sensitive search for wormholes. arXiv
**2020**, arXiv:2007.12184. [Google Scholar] - Kavic, M.; Simonetti, J.H.; Cutchin, S.E.; Ellingson, S.W.; Patterson, C.D. Transient Pulses from Exploding Primordial Black Holes as a Signature of an Extra Dimension. J. Cosmol. Astropart. Phys.
**2008**, 11, 17. [Google Scholar] [CrossRef] - Kavic, M.; Minic, D.; Simonetti, J. Transient Astrophysical Pulses and Quantum Gravity. Int. J. Mod. Phys. D
**2009**, 17, 2495–2500. [Google Scholar] [CrossRef] [Green Version] - Simonetti, J.H.; Kavic, M.; Minic, D.; Surani, U.; Vijayan, V. A Precision Test for an Extra Spatial Dimension Using Black Hole–Pulsar Binaries. Astrophys. J. Lett.
**2011**, 737, L28. [Google Scholar] [CrossRef] - Estes, J.; Kavic, M.; Lippert, M.; Simonetti, J.H. Pulsar–black hole binaries as a window on quantum gravity. Int. J. Mod. Phys. D
**2017**, 26, 1743004. [Google Scholar] [CrossRef] [Green Version] - Liebling, S.L.; Kavic, M.; Lippert, M. Probing Near-Horizon Fluctuations with Black Hole Binary Mergers. J. High Energy Phys.
**2018**, 3, 176. [Google Scholar] [CrossRef] [Green Version] - Kavic, M.J.; Minic, D.; Simonetti, J. Quantum gravity and BH-NS binaries. Int. J. Mod. Phys. D
**2018**, 27, 1847007. [Google Scholar] [CrossRef] [Green Version] - Kavic, M.; Liebling, S.L.; Lippert, M.; Simonetti, J.H. Accessing the axion via compact object binaries. J. Cosmol. Astropart. Phys.
**2020**, 8, 5. [Google Scholar] [CrossRef] - Weisberg, J.M.; Huang, Y. Relativistic Measurements from Timing the Binary Pulsar PSR B1913+16. Astrophys. J.
**2016**, 829, 55. [Google Scholar] [CrossRef] [Green Version] - Falcke, H.; Melia, F.; Agol, E. Viewing the shadow of the black hole at the galactic center. Astrophys. J. Lett.
**2000**, 528, L13. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Bambi, C.; Freese, K. Apparent shape of super-spinning black holes. Phys. Rev. D
**2009**, 79, 043002. [Google Scholar] [CrossRef] [Green Version] - Bambi, C. Can the supermassive objects at the centers of galaxies be traversable wormholes? The first test of strong gravity for mm/sub-mm very long baseline interferometry facilities. Phys. Rev. D
**2013**, 87, 107501. [Google Scholar] [CrossRef] [Green Version] - Mizuno, Y.; Younsi, Z.; Fromm, C.M.; Porth, O.; de Laurentis, M.; Olivares, H.; Falcke, H.; Kramer, M.; Rezzolla, L. The Current Ability to Test Theories of Gravity with Black Hole Shadows. Nat. Astron.
**2018**, 2, 585–590. [Google Scholar] [CrossRef] - Nedkova, P.G.; Tinchev, V.K.; Yazadjiev, S.S. Shadow of a rotating traversable wormhole. Phys. Rev. D
**2013**, 88, 124019. [Google Scholar] [CrossRef] [Green Version] - Ohgami, T.; Sakai, N. Wormhole shadows. Phys. Rev. D
**2015**, 91, 124020. [Google Scholar] [CrossRef] [Green Version] - Abdujabbarov, A.; Juraev, B.; Ahmedov, B.; Stuchlík, Z. Shadow of rotating wormhole in plasma environment. Astrophys. Space Sci.
**2016**, 361, 226. [Google Scholar] [CrossRef] - Shaikh, R. Shadows of rotating wormholes. Phys. Rev. D
**2018**, 98, 024044. [Google Scholar] [CrossRef] [Green Version] - Gyulchev, G.; Nedkova, P.; Tinchev, V.; Yazadjiev, S. On the shadow of rotating traversable wormholes. Eur. Phys. J. C
**2018**, 78, 544. [Google Scholar] [CrossRef] - Amir, M.; Banerjee, A.; Maharaj, S.D. Shadow of charged wormholes in Einstein–Maxwell–dilaton theory. Ann. Phys.
**2019**, 400, 198–207. [Google Scholar] [CrossRef] [Green Version] - Wang, X.; Li, P.C.; Zhang, C.Y.; Guo, M. Novel shadows from the asymmetric thin-shell wormhole. Phys. Lett. B
**2020**, 811, 135930. [Google Scholar] [CrossRef] - Wielgus, M.; Horak, J.; Vincent, F.; Abramowicz, M. Reflection-asymmetric wormholes and their double shadows. Phys. Rev. D
**2020**, 102, 084044. [Google Scholar] [CrossRef] - Li, Z.; Bambi, C. Distinguishing black holes and wormholes with orbiting hot spots. Phys. Rev. D
**2014**, 90, 024071. [Google Scholar] [CrossRef] [Green Version] - Shatskiy, A. Image of another universe being observed through a wormhole throat. Phys. Usp.
**2009**, 52, 811–814. [Google Scholar] [CrossRef] [Green Version] - Doroshkevich, A.; Hansen, J.; Novikov, I.; Shatskiy, A. Passage of radiation through wormholes. Int. J. Mod. Phys. D
**2009**, 18, 1665–1691. [Google Scholar] [CrossRef] [Green Version] - Novikov, I.D.; Thorne, K.S. Astrophysics of black holes. In Black Holes; De Witt, C., De Witt, B., Eds.; Gordon and Breach: New York, NY, USA, 1973; pp. 343–450. [Google Scholar]
- Page, D.N.; Thorne, K.S. Disk-Accretion onto a Black Hole. Time-Averaged Structure of Accretion Disk. Astrophys. J.
**1974**, 191, 499–506. [Google Scholar] [CrossRef] - Bambi, C. Black Holes: A Laboratory for Testing Strong Gravity; Springer: Singapore, 2017. [Google Scholar] [CrossRef]
- Bambi, C.; Brenneman, L.W.; Dauser, T.; Garcia, J.A.; Grinberg, V.; Ingram, A.; Jiang, J.; Liu, H.; Lohfink, A.M.; Marinucci, A.; et al. Towards precision measurements of accreting black holes using X-ray reflection spectroscopy. arXiv
**2020**, arXiv:2011.04792. [Google Scholar] - Bambi, C. Astrophysical Black Holes: A Compact Pedagogical Review. Ann. Phys.
**2018**, 530, 1700430. [Google Scholar] [CrossRef] [Green Version] - Harko, T.; Kovacs, Z.; Lobo, F.S.N. Electromagnetic signatures of thin accretion disks in wormhole geometries. Phys. Rev. D
**2008**, 78, 084005. [Google Scholar] [CrossRef] [Green Version] - Harko, T.; Kovacs, Z.; Lobo, F.S.N. Thin accretion disks in stationary axisymmetric wormhole spacetimes. Phys. Rev. D
**2009**, 79, 064001. [Google Scholar] [CrossRef] [Green Version] - Karimov, R.K.; Izmailov, R.N.; Nandi, K.K. Accretion disk around the rotating Damour–Solodukhin wormhole. Eur. Phys. J. C
**2019**, 79, 952. [Google Scholar] [CrossRef] [Green Version] - Paul, S.; Shaikh, R.; Banerjee, P.; Sarkar, T. Observational signatures of wormholes with thin accretion disks. J. Cosmol. Astropart. Phys.
**2020**, 3, 55. [Google Scholar] [CrossRef] [Green Version] - Tripathi, A.; Zhou, M.; Abdikamalov, A.B.; Ayzenberg, D.; Bambi, C.; Gou, L.; Grinberg, V.; Liu, H.; Steiner, J.F. Testing general relativity with the stellar-mass black hole in LMC X-1 using the continuum-fitting method. Astrophys. J.
**2020**, 897, 84. [Google Scholar] [CrossRef] - Tripathi, A.; Abdikamalov, A.B.; Ayzenberg, D.; Bambi, C.; Grinberg, V.; Zhou, M. Testing the Kerr Black Hole Hypothesis with GX 339–4 by a Combined Analysis of Its Thermal Spectrum and Reflection Features. Astrophys. J.
**2021**, 907, 31. [Google Scholar] [CrossRef] - Tripathi, A.; Zhang, Y.; Abdikamalov, A.B.; Ayzenberg, D.; Bambi, C.; Jiang, J.; Liu, H.; Zhou, M. Testing General Relativity with NuSTAR data of Galactic Black Holes. arXiv
**2020**, arXiv:2012.10669. [Google Scholar] - Bambi, C. Broad Kα iron line from accretion disks around traversable wormholes. Phys. Rev. D
**2013**, 87, 084039. [Google Scholar] [CrossRef] [Green Version] - Zhou, M.; Cardenas-Avendano, A.; Bambi, C.; Kleihaus, B.; Kunz, J. Search for astrophysical rotating Ellis wormholes with X-ray reflection spectroscopy. Phys. Rev. D
**2016**, 94, 024036. [Google Scholar] [CrossRef] [Green Version] - Bambi, C.; Cardenas-Avendano, A.; Dauser, T.; Garcia, J.A.; Nampalliwar, S. Testing the Kerr black hole hypothesis using X-ray reflection spectroscopy. Astrophys. J.
**2017**, 842, 76. [Google Scholar] [CrossRef] [Green Version] - Abdikamalov, A.B.; Ayzenberg, D.; Bambi, C.; Dauser, T.; Garcia, J.A.; Nampalliwar, S. Public Release of RELXILL_NK: A Relativistic Reflection Model for Testing Einstein’s Gravity. Astrophys. J.
**2019**, 878, 91. [Google Scholar] [CrossRef] - Tripathi, A.; Zhou, B.; Abdikamalov, A.B.; Ayzenberg, D.; Bambi, C. Search for traversable wormholes in active galactic nuclei using x-ray data. Phys. Rev. D
**2020**, 101, 064030. [Google Scholar] [CrossRef] [Green Version] - Piotrovich, M.Y.; Krasnikov, S.V.; Buliga, S.D.; Natsvlishvili, T.M. Search for wormhole candidates in active galactic nuclei: Radiation from colliding accreting flows. Mon. Not. R. Astron. Soc.
**2020**, 498, 3684–3686. [Google Scholar] [CrossRef] - Dent, J.B.; Gabella, W.E.; Holley-Bockelmann, K.; Kephart, T.W. The Sound of Clearing the Throat: Gravitational Waves from a Black Hole Orbiting in a Wormhole Geometry. arXiv
**2007**, arXiv:2007.09135. [Google Scholar] - Cardoso, V.; Pani, P. Testing the nature of dark compact objects: A status report. Living Rev. Rel.
**2019**, 22, 4. [Google Scholar] [CrossRef] [Green Version] - Cardoso, V.; Franzin, E.; Pani, P. Is the gravitational-wave ringdown a probe of the event horizon? Phys. Rev. Lett.
**2016**, 116, 171101. [Google Scholar] [CrossRef] - Konoplya, R.A.; Molina, C. The Ringing wormholes. Phys. Rev. D
**2005**, 71, 124009. [Google Scholar] [CrossRef] [Green Version] - Konoplya, R.A.; Zhidenko, A. Wormholes versus black holes: Quasinormal ringing at early and late times. J. Cosmol. Astropart. Phys.
**2016**, 12. [Google Scholar] [CrossRef] [Green Version] - Nandi, K.K.; Izmailov, R.N.; Yanbekov, A.A.; Shayakhmetov, A.A. Ring-down gravitational waves and lensing observables: How far can a wormhole mimic those of a black hole? Phys. Rev. D
**2017**, 95, 104011. [Google Scholar] [CrossRef] [Green Version] - Bueno, P.; Cano, P.A.; Goelen, F.; Hertog, T.; Vercnocke, B. Echoes of Kerr-like wormholes. Phys. Rev. D
**2018**, 97, 024040. [Google Scholar] [CrossRef] [Green Version] - Aneesh, S.; Bose, S.; Kar, S. Gravitational waves from quasinormal modes of a class of Lorentzian wormholes. Phys. Rev. D
**2018**, 97, 124004. [Google Scholar] [CrossRef] [Green Version] - Blázquez-Salcedo, J.L.; Chew, X.Y.; Kunz, J. Scalar and axial quasinormal modes of massive static phantom wormholes. Phys. Rev. D
**2018**, 98, 044035. [Google Scholar] [CrossRef] [Green Version] - Churilova, M.S.; Konoplya, R.A.; Zhidenko, A. Arbitrarily long-lived quasinormal modes in a wormhole background. Phys. Lett. B
**2020**, 802, 135207. [Google Scholar] [CrossRef]

**Figure 1.**If we visualize our 3D space as a 2D surface, a wormhole can be represented as a cylindrical surface connecting two regions in the same universe or two different universes. The entrances are the mouths of the wormhole. The mouths are connected by the throat of the wormhole.

**Figure 2.**Penrose diagram of the non-traversable Einstein–Rosen wormhole. The wormhole throat, which is a horizon, is represented by the two dashed lines: every point on the wormhole throat corresponds to the two points at the same height on the two dashed lines.

**Figure 3.**Evolution of the intensity of a background source at the passage of a wormhole with effective negative mass (

**left**panel) and a normal compact object (

**right**panel). Different curves correspond to different values of the impact parameters (from the smallest value of the impact parameter producing larger effects to the largest value of the impact parameter producing less pronounced modulation of the intensity of the source: green-orange-red-magenta-violet-blue-green-orange-red). Figure from Ref. [34].

**Figure 4.**Upper bounds at the 68% and 95% confidence levels on the number density of Ellis wormholes in the Universe from the Sloan Digital Sky Survey Quasar Lens Search. The horizontal axis is for the throat radius a (in units pc/h, where h is the scaling factor for the present-day Hubble expansion rate). Figure from Ref. [55].

**Figure 5.**Penrose diagram of the traversable wormhole discussed in Section 3.2. The wormhole throat is the horizontal dashed line and connects the two universes.

**Figure 6.**We plot the constraints on the mass $\mu $ (y-axis) and the periapsis radius ${r}_{p}$ (x-axis) of a hypothetical star that orbits Sgr A* on the other side and perturbs the orbit of the S2 star on our side. The solid, doted, and dashed lines represent the constraints with acceleration precision of the star S2 of $4\times {10}^{-4}$ m/s${}^{2}$, $2\times {10}^{-5}$ m/s${}^{2}$, and ${10}^{-6}$ m/s${}^{2}$, respectively. The regions above the lines rule out a wormhole explanation. The x-axis has units of ${r}_{g}=2GM$. The y-axis has units of the solar mass ${M}_{\odot}$. The bottom line probes the most reasonable parameter space—a few solar masses star orbiting around Sgr A* at the distance of a few gravitational radii.

**Figure 7.**Simulated image of an optically thin emission region surrounding a Schwarzschild black hole (

**left**panel) and a traversable spherically-symmetric wormhole (

**right**panel). The coordinates X and Y are in units of the gravitational radius of the system. Figure from Ref. [73].

**Figure 8.**A compact object accreting from a geometrically thin and optically thick disk. We highlight the multi-temperature blackbody spectrum of the disk (

**red**), the Comptonized photons (

**blue**), and the reflection spectrum (

**green**). Figure adapted from Ref. [90].

**Figure 9.**Temporal evolution of the strain, the black hole separation, and the black hole relative velocity in the event GW150914. From Ref. [15] under the terms of the Creative Commons Attribution 3.0 License.

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Bambi, C.; Stojkovic, D.
Astrophysical Wormholes. *Universe* **2021**, *7*, 136.
https://doi.org/10.3390/universe7050136

**AMA Style**

Bambi C, Stojkovic D.
Astrophysical Wormholes. *Universe*. 2021; 7(5):136.
https://doi.org/10.3390/universe7050136

**Chicago/Turabian Style**

Bambi, Cosimo, and Dejan Stojkovic.
2021. "Astrophysical Wormholes" *Universe* 7, no. 5: 136.
https://doi.org/10.3390/universe7050136