- Letter
- Open Access
Thermodynamics of analogue black holes in a non-Hermitian tight-binding model
Phys. Rev. B 113, L081110 – Published 26 February, 2026
DOI: https://doi.org/10.1103/vdsx-r3dq
Abstract
We present a non-Hermitian model with gain/loss and nonreciprocal next-nearest-neighbor hopping that emulates black-hole physics. The model describes a one-dimensional lattice with a smooth connection between regions with distinct hopping parameters. By mapping the system to an effective Schwarzschild metric in the Painlevé-Gullstrand coordinates, we find that the interface is an analogue to a black-hole event horizon. We obtain emission rates for particles and antiparticles, the Hawking temperature, the Bekenstein-Hawking entropy, and the mass of the analogue black hole as a function of the interface sharpness and the system parameters. An experimental realization of the theoretical model is proposed, thus opening the way to the detection of elusive black-hole features.
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References (46)
- S. W. Hawking, Black hole explosions? Nature (London) 248, 30 (1974).
- S. W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43, 199 (1975).
- S. Chandrasekhar, The maximum mass of ideal white dwarfs, Astrophys. J. 74, 81 (1931).
- J. R. Oppenheimer and H. Snyder, On continued gravitational contraction, Phys. Rev. 56, 455 (1939).
- R. Abbott, T. D. Abbott, S. Abraham, F. Acernese, K. Ackley, C. Adams, R. X. Adhikari, V. B. Adya, C. Affeldt, M. Agathos, et al., GW190814: Gravitational waves from the coalescence of a 23 solar mass black hole with a 2.6 solar mass compact object, Astrophys. J. Lett. 896, L44 (2020).
- B. J. Carr and S. W. Hawking, Black holes in the early universe, Mon. Not. R. Astron. Soc. 168, 399 (1974).
- B. J. Carr, S. Clesse, J. García-Bellido, M. R. S. Hawkins, and F. Kühnel, Observational evidence for primordial black holes: A positivist perspective, Phys. Rep. 1054, 1 (2024).
- C. Barceló, S. Liberati, and M. Visser, Analogue gravity, Living Rev. Relativ. 14, 3 (2011).
- W. G. Unruh, Experimental black-hole evaporation? Phys. Rev. Lett. 46, 1351 (1981).
- S. Weinfurtner, E. W. Tedford, M. C. J. Penrice, W. G. Unruh, and G. A. Lawrence, Measurement of stimulated hawking emission in an analogue system, Phys. Rev. Lett. 106, 021302 (2011).
- V. Subramanyan, S. S. Hegde, S. Vishveshwara, and B. Bradlyn, Physics of the inverted harmonic oscillator: From the lowest Landau level to event horizons, Ann. Phys. 435, 168470 (2021).
- S. Patrick, H. Goodhew, C. Gooding, and S. Weinfurtner, Backreaction in an analogue black hole experiment, Phys. Rev. Lett. 126, 041105 (2021).
- J. Steinhauer, Observation of quantum Hawking radiation and its entanglement in an analogue black hole, Nat. Phys. 12, 959 (2016).
- S. Longhi, Non-Hermitian Dirac cones, Phys. Rev. Lett. 124, 066602 (2020).
- M. Stålhammar, J. Larana-Aragon, L. Rødland, and F. K. Kunst, symmetry-protected exceptional cones and analogue Hawking radiation, New J. Phys. 25, 043012 (2023).
- P. Painlevé, La mécanique classique et la théorie de la relativité, L'Astronomie 36, 6 (1922).
- G. E. Volovik, Simulation of a Panlevé-Gullstrand black hole in a thin film, J. Exp. Theor. Phys. Lett. 69, 705 (1999).
- M. K. Parikh and F. Wilczek, Hawking radiation as tunneling, Phys. Rev. Lett. 85, 5042 (2000).
- Y. Rosenberg, Optical analogues of black-hole horizons, Philos. Trans. R. Soc. A 378, 20190232 (2020).
- J. Drori, Y. Rosenberg, D. Bermudez, Y. Silberberg, and U. Leonhardt, Observation of stimulated hawking radiation in an optical analogue, Phys. Rev. Lett. 122, 010404 (2019).
- C. M. Bender and S. Boettcher, Real spectra in non-Hermitian Hamiltonians having symmetry, Phys. Rev. Lett. 80, 5243 (1998).
- E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Exceptional topology of non-Hermitian systems, Rev. Mod. Phys. 93, 015005 (2021).
- K. Yang, Z. Li, J. L. K. König, L. Rødland, M. Stålhammar, and E. J. Bergholtz, Homotopy, symmetry, and non-Hermitian band topology, Rep. Prog. Phys. 87, 078002 (2024).
- E. Slootman, W. Cherifi, L. Eek, R. Arouca, E. J. Bergholtz, M. Bourennane, and C. M. Smith, Breaking and resurgence of symmetry in the non-Hermitian Su-Schrieffer-Heeger model in photonic waveguides, Phys. Rev. Res. 6, 023140 (2024).
- If we expand around zero, we would obtain an extra term and the calculations lead a Dirac-like operator that gives an exceptional cone with a shift in the momentum and does not change the physics of the system.
- A. Montag and F. K. Kunst, Essential implications of similarities in non-Hermitian systems, J. Math. Phys. 65, 122101 (2024).
- A. J. S. Hamilton and J. P. Lisle, The river model of black holes, Am. J. Phys. 76, 519 (2008).
- G. E. Volovik, Topological Lifshitz transitions, Low Temp. Phys. 43, 47 (2017).
- W. Wu, Z. Shi, Y. Du, Y. Wang, F. Qin, X. Meng, B. Liu, Y. Ma, Z. Yan, M. Ozerov, C. Zhang, H.-Z. Lu, J. Chu, and X. Yuan, Topological Lifshitz transition and one-dimensional Weyl mode in , Nat. Mater. 22, 84 (2023).
- S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity (Cambridge University Press, Cambridge, UK, 2019).
- T. Ortín, Gravity and Strings, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, UK, 2004).
- G. Volovik and M. Zubkov, Emergent Weyl spinors in multi-fermion systems, Nucl. Phys. B 881, 514 (2014).
- P. Hořava, Stability of Fermi surfaces and theory, Phys. Rev. Lett. 95, 016405 (2005).
- G. Lemaitre, The expanding universe, Ann. Soc. Sci. Bruxelles, Ser. A 53, 51 (1997).
- L. Vanzo, G. Acquaviva, and R. D. Criscienzo, Tunnelling methods and Hawking's radiation: Achievements and prospects, Class. Quantum Grav. 28, 183001 (2011).
- N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, UK, 1982).
- R. M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics (University of Chicago Press, Chicago, 1994).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/vdsx-r3dq for a detailed calculation of the imaginary part of the action.
- E. Keski-Vakkuri and P. Kraus, Microcanonical D-branes and back reaction, Nucl. Phys. B 491, 249 (1997).
- S. Massar and R. Parentani, How the change in horizon area drives black hole evaporation, Nucl. Phys. B 575, 333 (2000).
- J. D. Bekenstein, Black holes and the second law, Lett. Nuovo Cimento 4, 737 (1972).
- J. D. Bekenstein, Black holes and entropy, Phys. Rev. D 7, 2333 (1973).
- M. Reisenbauer, H. Rudolph, L. Egyed, K. Hornberger, A. V. Zasedatelev, M. Abuzarli, B. A. Stickler, and U. Delić, Non-Hermitian dynamics and non-reciprocity of optically coupled nanoparticles, Nat. Phys. 20, 1629 (2024).
- C. H. Lee, S. Imhof, C. Berger, F. Bayer, J. Brehm, L. W. Molenkamp, T. Kiessling, and R. Thomale, Topolectrical Circuits, Commun. Phys. 1, 39 (2018).
- D. Halder, R. Thomale, and S. Basu, Circuit realization of a two-orbital non-Hermitian tight-binding chain, Phys. Rev. B 109, 115407 (2024).
- M. Brandenbourger, X. Locsin, E. Lerner, and C. Coulais, Non-reciprocal robotic metamaterials, Nat. Commun. 10, 4608 (2019).