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Analogue gravity and the Hawking effect: historical perspective and literature review

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Abstract

Reasoning by analogies permeates theoretical developments in physics and astrophysics, motivated by the unreachable nature of many phenomena at play. For example, analogies have been used to understand black hole physics, leading to the development of a thermodynamic theory for these objects and the discovery of the Hawking effect. The latter, which results from quantum field theory on black hole space-times, changed the way physicists approached this subject: what had started as a mere aid to understanding becomes a possible source of evidence via the research programme of “analogue gravity” that builds on analogue models for field effects. Some of these analogue models may and can be realised in the laboratory, allowing experimental tests of field effects. Here, we present a historical perspective on the connection between the Hawking effect and analogue models. We also present a literature review of current research, bringing history and contemporary physics together. We argue that the history of analogue gravity and the Hawking effect is divided into three distinct phases based on how and why analogue models have been used to investigate fields in the vicinity of black holes. Furthermore, we find that modern research signals a transition to a new phase, where the impetus for the use of analogue models has surpassed the problem they were originally designed to solve.

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Notes

  1. For more on the use of visualisation as tools for understanding, we refer to [22].

  2. It is important to underline that this information is given through recollections. In the paper in which Unruh recalled this episode [23], his account of the analogy is more refined and poetic in a way it could not have been proposed in 1972. For example, instead of the waterfall, he used the fantasy world of Rimfall, created by author Terry Pratchett in his fantasy series Discworld. The first book in the Discworld series was published in 1983, after Unruh’s 1981 paper proposing the formal analogy. Nevertheless, it is plausible and likely that a simpler version had been proposed earlier, around the year Unruh recalled.

  3. Private communication.

  4. For a deeper analysis of the historical events that led to the development of the thermodynamical theory of black holes, see [2].

  5. A proof of this law was provided by Werner Israel in 1986 [28], over a decade after Badeen, Carter, and Hawking’s formulation.

  6. It remains unattainable, for that matter.

  7. We chose to use the notation Unruh used in his 1995 paper [44] instead of the original for simplicity, since our goal with this exposition is a better understanding of the analogy.

  8. An updated version of the proposal exists in [46].

  9. Jacobson’s original spelling was “fluid-flow analog”. In the general literature, both the British “analogue” and US “analog” spellings are used.

  10. A typical example of linearised excitations are Bogoliubov excitations in quantum fluids [65, 67].

  11. Depending on the dispersion of excitations in the fluid, negative-norm modes may come from the outside region (as in water waves [44]) or the inside region (as in quantum fluids [34, 80, 81]). This dispersion-induced kinematic feature of fluid-based analogues seems not to affect the Hawking effect [44, 68, 80].

  12. Naturally, this picture also works for vacuum fluctuations of the electromagnetic field inside the fibre [83, p. 14].

  13. There are other modes because of dispersion, but they do not play a significant role in the present discussion (for more on this issue, see, for example, [68]).

  14. Nowadays, it is well established that dispersion in all systems modifies the Hawking spectrum, which is not thermal [86].

  15. Google Scholar returns over 1500 results for the search “analogue gravity” between 1 January 2008 and 21 September 2022.

  16. Much like the early work of White [118] and Anderson and Spiegel [119].

  17. These early proposals were quickly followed by a number of more realistic calculations, notably in atomic BECs proposing operational means to measure effects like inflation and cosmological particle pair creation, see, for example, [122, 123].

  18. More on these studies may be found in the references listed in [129].

  19. The title of that paper is a misnomer, and the observed wave effect is rotational superradiance [19, 132], which is different from the Penrose effect [133] (the reflection of particles on the ergosurface that is accompanied by an increase in their momentum associated with a decrease in the momentum of the rotating black hole [134]).

  20. Similar methods to [150] applied in Josephson metamaterials allow to measure the dynamical Casimir effect, as reported in 2011 [151].

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Acknowledgements

While brainstorming this manuscript, trying to connect history and modern physics, we have benefited enormously from insightful discussions with Grace Fields. We thank her wholeheartedly for those conversations and for carefully reading this manuscript and providing feedback that certainly helped us improve our work. We also thank William Unruh for his readiness to answer a few questions that had appeared during the research process and for allowing us to use his original drawing of a fish in a waterfall in this recounting.

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  1. Grupo de Teoria e História da Ciência Contemporânea (TeHCo) of the Institute of Physics, University of São Paulo, Rua do Matão 1371, Cidade Universitária, São Paulo, 05508-090, Brazil

    Carla R. Almeida

  2. Laboratoire Kastler Brossel, CNRS, ENS-Université PSL, Collège de France, Sorbonne Université, 4 Place Jussieu, Paris, 75005, France

    Maxime J. Jacquet

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Almeida, C.R., Jacquet, M.J. Analogue gravity and the Hawking effect: historical perspective and literature review. EPJ H 48, 15 (2023). https://doi.org/10.1140/epjh/s13129-023-00063-2

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