Pulsars in the Galactic centre promise to enable unparalleled tests of gravity theories and black hole physics and to serve as probes of the stellar formation history and evolution and the interstellar medium in the complex central region of the Milky Way. The community has surveyed the innermost region of the galaxy for decades without detecting a population of pulsars, which is puzzling. A strong scattering of the pulsed signals in this particular direction has been argued to be a potential reason for the non-detections. Scattering has a strong inverse dependence on observing frequency, therefore an effective way to alleviate its effect is to use higher frequencies in a survey for pulsars in the Galactic centre, in particular, close to the supermassive black hole Sagittarius A*. We present the first pulsar survey at short millimetre wavelengths, using several frequency bands between 84 and 156 GHz (3.57-1.92 mm), targeted to the Galactic centre. The observations were made with the Institut de Radioastronomie Millimetrique (IRAM) 30m Telescope in 28 epochs between 2016 December and 2018 May. This survey is the first that is essentially unaffected by scattering and therefore unbiased in population coverage, including fast-spinning pulsars that might be out of reach of lower-frequency Galactic centre surveys. We discovered no new pulsars and relate this result mainly to the decreased flux density of pulsars at high frequencies, combined with our current sensitivity. However, we demonstrate that surveys at these extremely high radio frequencies are capable of discovering new pulsars, analyse their sensitivity limits with respect to a simulated Galactic centre pulsar population, and discuss the main challenges and possible improvements for similar surveys in the future.
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