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Observation of thermal Hawking radiation and its temperature in an analogue black hole


The entropy of a black hole1 and Hawking radiation2 should have the same temperature given by the surface gravity, within a numerical factor of the order of unity. In addition, Hawking radiation should have a thermal spectrum, which creates an information paradox3,4. However, the thermality should be limited by greybody factors5, at the very least6. It has been proposed that the physics of Hawking radiation could be verified in an analogue system7, an idea that has been carefully studied and developed theoretically8,9,10,11,12,13,14,15,16,17,18. Classical white-hole analogues have been investigated experimentally19,20,21, and other analogue systems have been presented22,23. The theoretical works and our long-term study of this subject15,24,25,26,27 enabled us to observe spontaneous Hawking radiation in an analogue black hole28. The observed correlation spectrum showed thermality at the lowest and highest energies, but the overall spectrum was not of the thermal form, and no temperature could be ascribed to it. Theoretical studies of our observation made predictions about the thermality and Hawking temperature29,30,31,32,33. Here we construct an analogue black hole with improvements compared with our previous setup, such as reduced magnetic field noise, enhanced mechanical and thermal stability and redesigned optics. We find that the correlation spectrum of Hawking radiation agrees well with a thermal spectrum, and its temperature is given by the surface gravity, confirming the predictions of Hawking’s theory. The Hawking radiation observed is in the regime of linear dispersion, in analogy with a real black hole, and the radiation inside the black hole is composed of negative-energy partner modes only, as predicted.

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Fig. 1: Hawking and partner modes.
Fig. 2: Profile of the analogue black hole.
Fig. 3: Measured Hawking radiation.
Fig. 4: Spectrum of the Hawking radiation.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. Bekenstein, J. D. Black holes and entropy. Phys. Rev. D 7, 2333–2346 (1973).

    Article  ADS  MathSciNet  Google Scholar 

  2. Hawking, S. W. Black hole explosions? Nature 248, 30–31 (1974).

    Article  ADS  Google Scholar 

  3. Hawking, S. W. Breakdown of predictability in gravitational collapse. Phys. Rev. D 14, 2460–2473 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  4. Wald, R. M. On particle creation by black holes. Commun. Math. Phys. 45, 9–34 (1975).

    Article  ADS  MathSciNet  Google Scholar 

  5. Page, D. N. Particle emission rates from a black hole: massless particles from an uncharged, nonrotating hole. Phys. Rev. D 13, 198–206 (1976).

    Article  ADS  CAS  Google Scholar 

  6. Visser, M. Thermality of the Hawking flux. J. High Energy Phys. (2015).

  7. Unruh, W. G. Experimental black-hole evaporation? Phys. Rev. Lett. 46, 1351–1353 (1981).

    Article  ADS  Google Scholar 

  8. Garay, L. J., Anglin, J. R., Cirac, J. I. & Zoller, P. Sonic analog of gravitational black holes in Bose–Einstein condensates. Phys. Rev. Lett. 85, 4643–4647 (2000).

    Article  ADS  CAS  Google Scholar 

  9. Visser, M. Acoustic black holes: horizons, ergospheres and Hawking radiation. Class. Quantum Gravity 15, 1767–1791 (1998).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  10. Balbinot, R., Fabbri, A., Fagnocchi, S., Recati, A. & Carusotto, I. Nonlocal density correlations as a signature of Hawking radiation from acoustic black holes. Phys. Rev. A 78, 021603 (2008).

    Article  ADS  Google Scholar 

  11. Carusotto, I., Fagnocchi, S., Recati, A., Balbinot, R. & Fabbri, A. Numerical observation of Hawking radiation from acoustic black holes in atomic Bose–Einstein condensates. New J. Phys. 10, 103001 (2008).

    Article  ADS  Google Scholar 

  12. Macher, J. & Parentani, R. Black-hole radiation in Bose–Einstein condensates. Phys. Rev. A 80, 043601 (2009).

    Article  ADS  Google Scholar 

  13. Larré, P.-É., Recati, A., Carusotto, I. & Pavloff, N. Quantum fluctuations around black hole horizons in Bose–Einstein condensates. Phys. Rev. A 85, 013621 (2012).

    Article  ADS  Google Scholar 

  14. Recati, A., Pavloff, N. & Carusotto, I. Bogoliubov theory of acoustic Hawking radiation in Bose–Einstein condensates. Phys. Rev. A 80, 043603 (2009).

    Article  ADS  Google Scholar 

  15. Steinhauer, J. Measuring the entanglement of analogue Hawking radiation by the density–density correlation function. Phys. Rev. D 92, 024043 (2015).

    Article  ADS  Google Scholar 

  16. Jacobson, T. A. & Volovik, G. E. Event horizons and ergoregions in 3He. Phys. Rev. D 58, 064021 (1998).

    Article  ADS  Google Scholar 

  17. Schützhold, R. & Unruh, W. G. Hawking radiation in an electromagnetic waveguide? Phys. Rev. Lett. 95, 031301 (2005).

    Article  ADS  Google Scholar 

  18. de Nova, J. R. M., Guéry-Odelin, D., Sols, F. & Zapata, I. Birth of a quasi-stationary black hole in an outcoupled Bose–Einstein condensate. New J. Phys. 16, 123033 (2014).

    Article  Google Scholar 

  19. Weinfurtner, S., Tedford, E. W., Penrice, M. C. J., Unruh, W. G. & Lawrence, G. A. Measurement of stimulated Hawking emission in an analogue system. Phys. Rev. Lett. 106, 021302 (2011).

    Article  ADS  Google Scholar 

  20. Rousseaux, G., Mathis, C., Maïssa, P., Philbin, T. G. & Leonhardt, U. Observation of negative-frequency waves in a water tank: a classical analogue to the Hawking effect? New J. Phys. 10, 053015 (2008).

    Article  ADS  Google Scholar 

  21. Euvé, L.-P., Michel, F., Parentani, R., Philbin, T. G. & Rousseaux, G. Observation of noise correlated by the Hawking effect in a water tank. Phys. Rev. Lett. 117, 121301 (2016).

    Article  ADS  Google Scholar 

  22. Philbin, T. G. et al. Fiber-optical analog of the event horizon. Science 319, 1367–1370 (2008).

    Article  ADS  CAS  Google Scholar 

  23. Nguyen, H. S. et al. Acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons. Phys. Rev. Lett. 114, 036402 (2015).

    Article  ADS  CAS  Google Scholar 

  24. Lahav, O. et al. Realization of a sonic black hole analog in a Bose–Einstein condensate. Phys. Rev. Lett. 105, 240401 (2010).

    Article  ADS  Google Scholar 

  25. Shammass, I., Rinott, S., Berkovitz, A., Schley, R. & Steinhauer, J. Phonon dispersion relation of an atomic Bose–Einstein condensate. Phys. Rev. Lett. 109, 195301 (2012).

    Article  ADS  CAS  Google Scholar 

  26. Schley, R. et al. Planck distribution of phonons in a Bose–Einstein condensate. Phys. Rev. Lett. 111, 055301 (2013).

    Article  ADS  CAS  Google Scholar 

  27. Steinhauer, J. Observation of self-amplifying Hawking radiation in an analogue black-hole laser. Nat. Phys. 10, 864–869 (2014).

    Article  CAS  Google Scholar 

  28. Steinhauer, J. Observation of quantum Hawking radiation and its entanglement in an analogue black hole. Nat. Phys. 12, 959–965 (2016).

    Article  Google Scholar 

  29. Michel, F., Coupechoux, J.-F. & Parentani, R. Phonon spectrum and correlations in a transonic flow of an atomic Bose gas. Phys. Rev. D 94, 084027 (2016).

    Article  ADS  Google Scholar 

  30. Coutant, A. & Weinfurtner, S. Low-frequency analogue Hawking radiation: the Bogoliubov–de Gennes model. Phys. Rev. D 97, 025006 (2018).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  31. Fabbri, A. & Pavloff, N. Momentum correlations as signature of sonic Hawking radiation in Bose–Einstein condensates. SciPost Phys. 4, 019 (2018).

    Article  ADS  Google Scholar 

  32. Carusotto, I. & Balbinot, R. Acoustic Hawking radiation. Nat. Phys. 12, 897–898 (2016).

    Article  CAS  Google Scholar 

  33. Robertson, S., Michel, F. & Parentani, R. Assessing degrees of entanglement of phonon states in atomic Bose gases through the measurement of commuting observables. Phys. Rev. D 96, 045012 (2017).

    Article  ADS  Google Scholar 

  34. Salasnich, L., Parola, A. & Reatto, L. Dimensional reduction in Bose–Einstein-condensed alkali-metal vapors. Phys. Rev. A 69, 045601 (2004).

    Article  ADS  Google Scholar 

  35. Steinhauer, J. et al. Bragg spectroscopy of the multibranch Bogoliubov spectrum of elongated Bose–Einstein condensates. Phys. Rev. Lett. 90, 060404 (2003).

    Article  ADS  CAS  Google Scholar 

  36. Tozzo, C. & Dalfovo, F. Bogoliubov spectrum and Bragg spectroscopy of elongated Bose–Einstein condensates. New J. Phys. 5, 54 (2003).

    Article  ADS  Google Scholar 

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We thank the participants of the LITP Analogue Gravity Workshop for their conversations. We thank I. Carusotto, R. Parentani, D. Marolf and F. Michel for comments. This work was supported by the Israel Science Foundation.

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Authors and Affiliations



J.R.M.d.N. and J.S. designed and built the experimental apparatus. J.R.M.d.N., K.G. and V.I.K. performed theoretical calculations. J.S. acquired the data. K.G., V.I.K. and J.S. analysed the data. J.R.M.d.N. performed the numerical simulations. J.R.M.d.N. and J.S. wrote the manuscript with input from all authors.

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Correspondence to Jeff Steinhauer.

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Muñoz de Nova, J.R., Golubkov, K., Kolobov, V.I. et al. Observation of thermal Hawking radiation and its temperature in an analogue black hole. Nature 569, 688–691 (2019).

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