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These lecture notes offer a pedagogical resource on using Bose-Einstein condensates to simulate black hole phenomena like Hawking radiation and superradiance. The material bridges theoretical descriptions of quantum fluids with practical numerical methods, supported by solved problems and Julia notebooks for hands-on exploration. This work advances analogue gravity research by providing a controlled platform to study quantum field behaviors in curved spacetime analogues.
Analogue gravity with Bose-Einstein condensates
arXiv:2512.14209v2 Announce Type: replace-cross Abstract: Analogue gravity explores how collective excitations in condensed matter systems can reproduce the behavior of fields in curved spacetimes. An important example is the acoustic black holes that can occur for sound in a moving fluid. In these lecture notes, we focus on atomic Bose-Einstein condensates (BECs), quantum fluids that provide an interesting platform for analogue gravity studies thanks to their accurate theoretical description, remarkable experimental control, and ultralow temperatures that allow the quantum nature of sound to emerge. We give a pedagogical introduction to analogue black holes and the theoretical description of BECs and their elementary excitations, which behave as quantum fields in curved spacetimes. We then apply these tools to survey the current understanding of black-hole superradiance and analogue Hawking radiation, including explicit examples and numerical methods.
Abstract:Analogue gravity explores how collective excitations in condensed matter systems can reproduce the behavior of fields in curved spacetimes. An important example is the acoustic black holes that can occur for sound in a moving fluid. In these lecture notes, we focus on atomic Bose-Einstein condensates (BECs), quantum fluids that provide an interesting platform for analogue gravity studies thanks to their accurate theoretical description, remarkable experimental control, and ultralow temperatures that allow the quantum nature of sound to emerge. We give a pedagogical introduction to analogue black holes and the theoretical description of BECs and their elementary excitations, which behave as quantum fields in curved spacetimes. We then apply these tools to survey the current understanding of black-hole superradiance and analogue Hawking radiation, including explicit examples and numerical methods.
Lecture notes based on the course given by Luca Giacomelli at "Analogue Gravity in 2023, Benasque". 71 pages, 13 figures, 10 solved problems (with 3 attached Julia notebooks)
General Relativity and Quantum Cosmology (gr-qc); Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
arXiv:2512.14209 [gr-qc]
(or arXiv:2512.14209v2 [gr-qc] for this version)
Full text under the publisher's open licence · 177 words
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