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PSR B1820$-$30A is located in the globular cluster NGC 6624 and is theclosest known pulsar to the centre of any globular cluster. We present morethan 25 years of high-precision timing observations of this millisecond pulsarand obtain four rotational frequency time derivative measurements. Modellingthese higher-order derivatives as being due to orbital motion, we findsolutions which indicate that the pulsar is in either a low-eccentricity($0.33\lesssim e\lesssim0.4$) smaller orbit with a low mass companion (such asa main sequence star, white dwarf, neutron star, or stellar mass black hole) ora high-eccentricity ($e\gtrsim0.9$) larger orbit with a massive companion. Thecluster mass properties and the observed properties of 4U 1820$-$30 and theother pulsars in the cluster argue against the low-eccentricity possibility.The high-eccentricity solution reveals that the pulsar is most likely orbitingaround an intermediate-mass black hole (IMBH) of mass $> 7,500$~M$_\odot$located at the cluster centre. A gravitational model for the globular cluster,which includes such a central black hole (BH), predicts an acceleration that iscommensurate with that measured for the pulsar. It further predicts that themodel-dependent minimum mass of the IMBH is $\sim60,000$~M$_\odot$. Accountingfor the associated contribution to the observed period derivative indicatesthat the $\gamma$-ray efficiency of the pulsar should be between 0.08 and 0.2.Our results suggest that other globular clusters may also contain central blackholes and they may be revealed by the study of new pulsars found sufficientlyclose to their centres.  Note that we found an erratum in Section 5 and thus, the$\sim$60,000~M$_\odot$ mass mentioned above has to be replaced by the correctmodel-dependent mass limit of $\sim$20,000~M$_\odot$. See the erratum appended.

Evidence for an intermediate-mass black hole in the globular cluster NGC 6624