# A Cylindrical Optical-Space Black Hole Induced from High-Pressure Acoustics in a Dense Fluid

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## Abstract

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## 1. Brief Review and Background

#### 1.1. Metamaterials

#### 1.2. Analog Astrophysical Models

#### 1.3. Introduction to Gordon’s Metric

## 2. Materials and Methods

## 3. Results

## 4. Discussion

#### 4.1. Snell’s Law and Bessel Beam Profile

**Figure 3.**A possible explanation of the pressure-induced analog black hole. See [42] for refractive index study as function of pressure.

**Figure 4.**A Bessel function fit of image of the analog black hole. Panel (

**a**) shows the fit to the image, and panel (

**b**) shows the 3D radius, pressure, and time plot.

#### 4.2. Refractive Index from Pressure Measurement

#### 4.3. Schwarzschild Comparison and Optical Mass

#### 4.4. Comparison of Cylindrical Black Hole with Fiber Optics

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**A plot of (8). See text for details. At 200 MPa the refractive index is 1.4784.

**Figure A2.**Data from Jae-Hyeon Ko of [42]; used with their permission. See text for discussion.

**Figure A3.**Data from Jae-Hyeon Ko of [42]; used with their permission. See text for discussion.

## References

- Joannopoulos, J.D.; Johnson, S.G.; Winn, J.N.; Meade, R.D. Photonic Crystals: Molding the Flow of Light, 2nd ed.; Princeton University Press: Princeton, NJ, USA, 2008. [Google Scholar]
- Kadic, M.; Bückmann, T.; Schittny, R.; Wegener, M. Metamaterials beyond electromagnetism. Rep. Prog. Phys.
**2013**, 76, 126501. [Google Scholar] [CrossRef] [PubMed] - Deymier, P.A. Acoustic Metamaterials and Phononic Crystals; Springer: Berlin/Heidelberg, Germany, 2013. [Google Scholar]
- Rietman, E.A.; Glynn, J.M. Band-Gap Engineering of Phononic Crystals: A Computational Survey of Two-Dimensional Systems. arXiv
**2007**, arXiv:0708.3669. [Google Scholar] [CrossRef] - Guenneau, S.; Movchan, A.; Pétursson, G.; Ramakrishna, S.A. Acoustic metamaterials for sound focusing and confinement. New J. Phys.
**2007**, 9, 399. [Google Scholar] [CrossRef] - Higginson, K.A.; Costolo, M.A.; Rietman, E.A.; Ritter, J.M.; Lipkens, B. Tunable optics derived from nonlinear acoustic effects. J. Appl. Phys.
**2004**, 95, 5896–5904. [Google Scholar] [CrossRef] - Deymier, P.; Runge, K. Sound Topology, Duality, Coherence and Wave-Mixing: An Introduction to the Emerging New Science of Sound; Springer: Berlin/Heidelberg, Germany, 2017. [Google Scholar] [CrossRef]
- Novello, M.; Visser, M.; Volovik, G. (Eds.) Artificial Black Holes; World Scientific: Singapore, 2002. [Google Scholar]
- Greenleaf, A.; Kurylev, Y.; Lassas, M.; Uhlmann, G. Electromagnetic wormholes and virtual magnetic monopoles. Phys. Rev. Lett.
**2007**, 99, 183901. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Barcelo, C.; Liberati, S.; Visser, M. Analogue gravity. Living Rev. Rel.
**2005**, 8, 12. [Google Scholar] [CrossRef] [Green Version] - Cheng, Q.; Cui, T.J. An Electromagnetic black hole made of metamaterials. arXiv
**2009**, arXiv:0910.2159. [Google Scholar] - Genov, D.A.; Zhang, S.; Zhang, X. Mimicking celestial mechanics in metamaterials. Nat. Phys.
**2009**, 5, 687–692. [Google Scholar] [CrossRef] - de Felice, F. On the Gravitational field acting as an optical medium. Gen. Rel. Grav.
**1971**, 2, 347. [Google Scholar] [CrossRef] - Philbin, T.G.; Kuklewicz, C.; Robertson, S.; Hill, S.; König, F.; Leonhardt, U. Fiber-Optical Analog of the Event Horizon. Science
**2008**, 319, 1367–1370. [Google Scholar] [CrossRef] [Green Version] - Belgiorno, F.; Cacciatori, S.L.; Ortenzi, G.; Rizzi, L.; Gorini, V.; Faccio, D. Dielectric black holes induced by a refractive index perturbation and the Hawking effect. Phys. Rev. D
**2011**, 83, 024015. [Google Scholar] [CrossRef] [Green Version] - Belgiorno, F.; Cacciatori, S.L.; Clerici, M.; Gorini, V.; Ortenzi, G.; Rizzi, L.; Rubino, E.; Sala, V.G.; Faccio, D. Hawking radiation from ultrashort laser pulse filaments. Phys. Rev. Lett.
**2010**, 105, 203901. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Belgiorno, F.; Cacciatori, S.L.; Ortenzi, G.; Sala, V.G.; Faccio, D. Quantum Radiation from Superluminal Refractive-Index Perturbations. Phys. Rev. Lett.
**2010**, 104, 140403. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Cacciatori, S.L.; Belgiorno, F.; Gorini, V.; Ortenzi, G.; Rizzi, L.; Sala, V.G.; Faccio, D. Space-time geometries and light trapping in travelling refractive index perturbations. New J. Phys.
**2010**, 12, 095021. [Google Scholar] [CrossRef] - Smolyaninov, I.I. Metamaterial-based model of the Alcubierre warp drive. Phys. Rev. B
**2011**, 84, 113103. [Google Scholar] [CrossRef] [Green Version] - Smolyaninov, A.I.; Smolyaninov, I.I. Lattice models of non-trivial “optical spaces” based on metamaterial waveguides. arXiv
**2010**, arXiv:1009.1180. [Google Scholar] [CrossRef] - Smolyaninov, I.I.; Hung, Y.J. Modeling of time with metamaterials. J. Opt. Soc. Am. B
**2011**, 28, 1591. [Google Scholar] [CrossRef] - Smolyaninov, I.I. Modeling of causality with metamaterials. J. Opt.
**2013**, 15, 025101. [Google Scholar] [CrossRef] [Green Version] - Smolyaninov, I.I.; Yost, B.; Bates, E.; Smolyaninova, V.N. Experimental demonstration of metamaterial “multiverse” in a ferrofluid. Opt. Express
**2013**, 21, 14918–14925. [Google Scholar] [CrossRef] [Green Version] - Esposito, A.; Krichevsky, R.; Nicolis, A. Gravitational Mass Carried by Sound Waves. Phys. Rev. Lett.
**2019**, 122, 084501. [Google Scholar] [CrossRef] [Green Version] - Weldon, T.P.; Smith, K.L. Gravitationally-Small Gravitational Antennas, the Chu Limit, and Exploration of Veselago-Inspired Notions of Gravitational Metamaterials. In Proceedings of the 2019 Thirteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials), Rome, Italy, 16–21 September 2019; pp. X-393–X-395. [Google Scholar] [CrossRef]
- Vita, F.D.; Lillo, F.D.; Bosia, F.; Onorato, M. Attenuating surface gravity waves with mechanical metamaterials. Phys. Fluids
**2021**, 33, 047113. [Google Scholar] [CrossRef] - Poddar, A.K.; Rohde, U.L.; Koul, S.K. MTM: Casimir effect and Gravity Wave detection. In Proceedings of the 2016 Asia-Pacific Microwave Conference (APMC), New Delhi, India, 5–9 December 2016; pp. 1–4. [Google Scholar] [CrossRef]
- Lahiri, B.; McMeekin, S.G.; Khokhar, A.Z.; Rue, R.M.D.L.; Johnson, N.P. Magnetic response of split ring resonators (SRRs) at visible frequencies. Opt. Express
**2010**, 18, 3210–3218. [Google Scholar] [CrossRef] [PubMed] - Premont-Schwarz, I. Experimenting with Quantum Fields in Curved Spacetime in the Lab. arXiv
**2011**, arXiv:1112.2311. [Google Scholar] - Chen, H.; Tao, S.; Bělín, J.; Courtial, J.; Miao, R.X. Transformation cosmology. Phys. Rev. A
**2020**, 102, 023528. [Google Scholar] [CrossRef] - Novello, M.; Bittencourt, E. Gordon Metric Revisited. Phys. Rev. D
**2012**, 86, 124024. [Google Scholar] [CrossRef] [Green Version] - Chen, B.; Kantowski, R. Cosmology With A Dark Refraction Index. Phys. Rev. D
**2008**, 78, 044040. [Google Scholar] [CrossRef] [Green Version] - Chen, B.; Kantowski, R. Distance-redshift from an optical metric that includes absorption. Phys. Rev. D
**2009**, 80, 044019. [Google Scholar] [CrossRef] [Green Version] - Chen, B.; Kantowski, R. Including Absorption in Gordon’s Optical Metric. Phys. Rev. D
**2009**, 79, 104007. [Google Scholar] [CrossRef] [Green Version] - Wang, H.W.; Chen, L.W. A cylindrical optical black hole using graded index photonic crystals. J. Appl. Phys.
**2011**, 109, 103104. [Google Scholar] [CrossRef] - Narimanov, E.E.; Kildishev, A.V. Optical black hole: Broadband omnidirectional light absorber. Appl. Phys. Lett.
**2009**, 95, 041106. [Google Scholar] [CrossRef] - McGloin, D.; Dholakia, K. Bessel beams: Diffraction in a new light. Contemp. Phys.
**2005**, 46, 15–28. [Google Scholar] [CrossRef] - Axicon. Available online: https://en.wikipedia.org/wiki/Axicon (accessed on 8 August 2022).
- Barmatz, M.; Collas, P. Acoustic radiation potential on a sphere in plane, cylindrical, and spherical standing wave fields. J. Acoust. Soc. Am.
**1985**, 77, 928–945. [Google Scholar] [CrossRef] - Ferreira, A.G.; Egas, A.P.; Fonseca, I.M.; Costa, A.C.; Abreu, D.C.; Lobo, L.Q. The viscosity of glycerol. J. Chem. Thermo. 2017, 113, pp. 162–182. Available online: https://www.google.com/search?q=viscosity+of+glycerin&oq=viscosity+of+glycerin&aqs=chrome..69i57.14152j0j7&sourceid=chrome&ie=UTF-8 (accessed on 19 August 2022).
- Engineering ToolBox. Solids and Metals—Speed of Sound. 2004. Available online: https://www.engineeringtoolbox.com/sound-speed-solids-d_713.html (accessed on 25 September 2022).
- Jeong, M.S.; Ko, J.H.; Ko, Y.H.; Kim, K.J. High-pressure acoustic properties of glycerol studied by Brillouin spectroscopy. Phys. B Condens. Matter
**2015**, 478, 27–30. [Google Scholar] [CrossRef] - Tait Equation. Available online: https://en.wikipedia.org/wiki/Tait_equation (accessed on 29 August 2022).
- Oughstun, K.E.; Cartwright, N.A. On the Lorentz-Lorenz formula and the Lorentz model of dielectric dispersion. Opt. Express
**2003**, 11, 1541–1546. [Google Scholar] [CrossRef] [PubMed] - Simpson, A.; Visser, M. The eye of the storm: A regular Kerr black hole. J. Cosmol. Astropart. Phys.
**2022**, 03, 011. [Google Scholar] [CrossRef] - Optical Fiber. Available online: https://en.wikipedia.org/wiki/Optical_fiber (accessed on 17 August 2022).
- Fauser, C.M.; Gaul, E.W.; Le Blanc, S.P.; Downer, M.C. Guiding characteristics of an acoustic standing wave in a piezoelectric tube. Appl. Phys. Lett.
**1998**, 73, 2902–2904. [Google Scholar] [CrossRef] - Jaeger, L. The Second Quantum Revolution, 1st ed.; Copernicus: Cham, Switzerland, 2018. [Google Scholar]

**Figure 1.**The laser beam passes through a beam spreader, then via a mirror through the PZT tube, another mirror, an iris, and finally either to a ruled index card or focused into the fiber collimator, where the light is analyzed by the spectrometer. The inset photo shows the PZT tube mounted between the two beam steering mirrors. The PZT tube was filled with pharmaceutical grade glycerin.

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**MDPI and ACS Style**

Rietman, E.A.; Melcher, B.; Bobrick, A.; Martire, G.
A Cylindrical Optical-Space Black Hole Induced from High-Pressure Acoustics in a Dense Fluid. *Universe* **2023**, *9*, 162.
https://doi.org/10.3390/universe9040162

**AMA Style**

Rietman EA, Melcher B, Bobrick A, Martire G.
A Cylindrical Optical-Space Black Hole Induced from High-Pressure Acoustics in a Dense Fluid. *Universe*. 2023; 9(4):162.
https://doi.org/10.3390/universe9040162

**Chicago/Turabian Style**

Rietman, Edward A., Brandon Melcher, Alexey Bobrick, and Gianni Martire.
2023. "A Cylindrical Optical-Space Black Hole Induced from High-Pressure Acoustics in a Dense Fluid" *Universe* 9, no. 4: 162.
https://doi.org/10.3390/universe9040162