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Radio pulsars in relativistic binary systems are unique tools to study the curved space-time around massive compact objects. The discovery of a pulsar closely orbiting the super-massive black hole at the centre of our Galaxy, Sgr A⋆, would provide a superb test-bed for gravitational physics. To date, the absence of any radio pulsar discoveries within a few arc minutes of Sgr A⋆ has been explained by one principal factor: extreme scattering of radio waves caused by inhomogeneities in the ionized component of the interstellar medium in the central 100 pc around Sgr A⋆. Scattering, which causes temporal broadening of pulses, can only be mitigated by observing at higher frequencies. Here we describe recent searches of the Galactic centre region performed at a frequency of 18.95 GHz with the Effelsberg radio telescope.