Holm 15A, the brightest cluster galaxy (BCG) of the galaxy cluster Abell 85, has an ultra-diffuse central region, 2 mag fainter than the faintest depleted core of any early-type galaxy (ETG) that has been dynamically modelled in detail. We use orbit-based, axisymmetric Schwarzschild models to analyse the stellar kinematics of Holm 15A from new high-resolution, wide-field spectral observations obtained with MUSE at the VLT. We find a supermassive black hole (SMBH) with a mass of (4.0 +- 0.80) x 10^10 solar masses at the center of Holm 15A. This is the most massive black hole with a direct dynamical detection in the local universe. We find that the distribution of stellar orbits is increasingly biased towards tangential motions inside the core. However, the tangential bias is less than in other cored elliptical galaxies. We compare Holm 15A with N-body simulations of mergers between galaxies with black holes and find that the observed amount of tangential anisotropy and the shape of the light profile are consistent with a formation scenario where Holm 15A is the remnant of a merger between two ETGs with pre-existing depleted cores. We find that black hole masses in cored galaxies, including Holm 15A, scale inversely with the central stellar surface brightness and mass density, respectively. These correlation are independent of a specific parameterization of the light profile.
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