Journal of Holography Applications in Physics

A Brief Review of Quantum Tunneling Computational Approaches and Experimental Evidence

Document Type : Review article

Authors

Department of Physics, College of Sciences, Yasouj University, 75918-74934, Yasouj, Iran.

Abstract

‎This paper presents a concise review of the quantum tunneling approach to Hawking radiation‎, ‎covering its theoretical foundations‎, ‎extensions‎, ‎and experimental efforts‎. ‎We begin by outlining the Hamilton-Jacobi and Parikh-Wilczek methods‎, ‎which provide a semi-classical framework for deriving Hawking radiation from stationary black holes‎. ‎The discussion is then extended to dynamical black holes‎, ‎where evolving horizons require modified treatments incorporating trapping horizons‎, ‎Kodama vectors‎, ‎and dynamical surface gravity‎. ‎We explored the possible tunneling paths for particles crossing the horizon in dynamical black holes and emphasized the crucial role of the imaginary part of the action in determining the Hawking temperature‎. ‎In the second part‎, ‎we review experimental investigations of Hawking radiation‎, ‎including analogue black hole experiments‎, ‎quantum simulations‎, ‎and astrophysical searches for primordial black hole evaporation‎. ‎While no direct detection of Hawking radiation has been achieved‎, ‎recent advances in Bose-Einstein condensates‎, ‎optical analogues‎, ‎and superconducting qubits offer indirect support for the tunneling interpretation of black hole evaporation‎.

Keywords

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Article PDF

[1] S. W. Hawking, “Gravitational Radiation from Colliding Black Holes”, Phys. Rev. Lett. 26 1344 (1971) DOI: https://doi.org/10.1103/PhysRevLett.26.1344
[2] J. D. Bekenstein, “Black Holes and Entropy”, Phys. Rev. D 7, 2333 (1973) DOI: https://doi.org/10.1142/9789811203961_0023
[3] J. M. Bardeen, B. Carter and S. W. Hawking”, The Four laws of black hole mechanics,” Commun. Math. Phys. 31, 161 (1973) DOI: 10.1007/BF01645742
[4] S. W. Hawking, “Black hole explosions”, Nature 248, 30 (1974) DOI: 10.1038/248030a0
[5] S. W. Hawking, “Particle Creation by Black Holes”, Comm. Math. Phys. 43, 199 (1975) DOI: https://doi.org/10.1007/BF02345020
[6] T. Damour and R. Ruffni, “Black Hole Evaporation in the Klein-Sauter-HeisenbergEuler Formalism”, Phys. Rev. D 14, 332 (1976) DOI: 10.1103/PhysRevD.14.332
[7] G. W. Gibbons and S. W. Hawking, “Action Integrals and Partition Functions in Quantum Gravity”, Phys. Rev. D 15, 2752 (1977) DOI: 10.1103/PhysRevD.15.2752
[8] S. M. Christensen and S. A. Fulling, “Trace Anomalies and the Hawking Effect”, Phys. Rev. D 15, 2088 (1977) DOI: 10.1103/PhysRevD.15.2088
[9] K. Srinivasan and T. Padmanabhan, “Particle production and complex path analysis”, Phys. Rev. D 60, 024007 (1999) DOI: 10.1103/PhysRevD.60.024007
[10] M. K. Parikh and F. Wilczek “Hawking radiation as tunneling”, Phys. Rev. Lett. 85, 5042 (2000) DOI: 10.1103/PhysRevLett.85.5042
[11] M. K. Parikh, “A Secret tunnel through the horizon”, Int. J. Mod. Phys. D 13, 2351 (2004) DOI: 10.1142/S0218271804006498
[12] S. P. Robinson and F. Wilczek, “A Relationship between Hawking radiation and gravitational anomalies”, Phys. Rev. Lett. 95, 011303 (2005) DOI: 10.1103/PhysRevLett.95.011303
[13] B. R. Majhi, “Quantum Tunneling in Black Holes”, (2011) [arXiv:1110.6008 [gr-qc]]
[14] L. Vanzo, G. Acquaviva and R. Di Criscienzo, “Tunnelling Methods and Hawking’s Radiation: Achievements and Prospects”, Class. Quantum Grav. 28 (2011) 10.1088/0264- 9381/28/18/183001
[15] V. P. Frolov and I. D. Novikov, “Black hole physics: Basic concepts and new developments”, Fundam. Theor. Phys. 96 (1998) DOI: 10.1007/978-94-011-5139-9
[16] P. Kraus and F. Wilczek, “Self-Interaction Correction to Black Hole Radiance”, Nucl. Phy. B 433, 403 (1995) [arXiv:gr-qc/9408003]
[17] P. Painlevé, “La Mcanique Classique et la Thorie de Relativit”, C. R. Acad. Sci. 173, 677 (1921) [1922LAstr.36.6P]
[18] J. B. Hartle and S. W. Hawking, “Path Integral Derivation of Black Hole Radiance”, Phys. Rev. D 13, 2188 (1976) DOI: 10.1103/PhysRevD.13.2188
[19] E. Gourgoulhon and J. L. Jaramillo, “New theoretical approaches to black holes”, New Astron. Rev. 51, 791 (2008), DOI: 10.1016/j.newar.2008.03.026
[20] A. Hayward, “General Laws of Black Hole Dynamics”, Phys. Rev. D 49, 6467 (1994) DOI: https://doi.org/10.1103/PhysRevD.49.6467
[21] H. Kodama, “Conserved Energy Flux for the Spherically Symmetric System and the Back Reaction Problem in the Black Hole Evaporation”, Prog. Theor. Phys. 63, 1217 (1980) DOI: 10.1143/PTP.63.1217
[22] A. Hayward, “Unified First Law of Black Hole Dynamics and Relativistic Thermodynamics”, Class. Quant. Grav. 15, 1217 (1998) [arXiv:gr-qc/9710089]
[23] J. Steinhauer, “Observation of Self-amplifying Hawking Radiation in an Analog Black Hole Laser”, Nature Phys. 10, 864 (2014) [arXiv:1409.6550 [cond-mat.quant-gas]]
[24] J. Steinhauer, “Observation of Quantum Hawking Radiation and Its Entanglement in an Analogue Black Hole”, Nature Phys. 12, 959 (2016) [arXiv:1510.00621 [gr-qc]]
[25] J. R. Muñoz de Nova et al., “Observation of Thermal Hawking Radiation and Its Temperature in an Analogue Black Hole”, Nature 569, 688 (2019) [arXiv:1809.00913 [gr-qc]]
[26] A. Recati, N. Pavloff, and I. Carusotto, “Bogoliubov Theory of acoustic Hawking radiation in Bose-Einstein Condensates”, Phys. Rev. A 80, 043603 (2009) DOI: https://doi.org/10.1103/PhysRevA.80.043603
[27] F. Belgiorno et al., “Hawking Radiation from Ultrashort Laser Pulse Filaments”, Phys. Rev. Lett. 105, 203901 (2010) DOI: https://doi.org/10.1103/PhysRevLett.105.203901
[28] W. G. Unruh and R. Schützhold, “Hawking Radiation from Ultrashort Laser Pulse Filaments”, Phys. Rev. D 86, 064006 (2012) DOI: https://doi.org/10.1103/PhysRevD.86.064006
[29] M. H. Lynch, “Experimental Observation of Hawking Radiation”, (2024) [arXiv:2404.09274v1 [gr-qc]]
[30] U. Leonhardt, “A Laboratory Analogue of the Event Horizon Using Slow Light in an Atomic Medium”, Nature 415, 406 (2002) DOI: https://doi.org/10.1038/415406a
[31] J. Steinhauer, “Confirmation of Stimulated Hawking radiation, but not of Black Hole Lasing”, Phys. Rev. D 106, 102007 (2022) DOI: 10.1103/PhysRevD.106.102007
[32] Y. H. Shi et al., “Quantum Simulation of Hawking Radiation and Curved Spacetime with a Superconducting On-Chip Black Hole”, Nat. Comm. 14, 3263 (2023) [arXiv:2111.01109 [math.DS]].
[33] A. Coogan, L. Morrison, and S. Profumo, “Direct Detection of Hawking Radiation from Asteroid-Mass Primordial Black Holes”, Phys. Rev. Lett. 126, 171101 (2021) [arXiv:2010.04797 [astro-ph.CO]].
[34] G. Cacciapaglia, S. Hohenegger, and F. Sannino, “Measuring Hawking Radiation from Black Hole Morsels in Astrophysical Black Hole Mergers”, (2024) [arXiv:2405.12880 [astro-ph.HE]]. 
Journal of Holography Applications in Physics
Volume 5, Issue 2
June 2025
Pages 44-56
  • Receive Date: 04 March 2025
  • Revise Date: 05 April 2025
  • Accept Date: 05 April 2025