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In this work we make use of a general relativistic method to estimate themass-to-distance ratio M/D = 3.54^{+0.2}_{-0.2} X 10^4 M_{sun}/Mpc of the blackhole hosted at the core of the active galactic nucleus of TXS 2226-184, alongwith its Right Ascension offset and the recession redshift (velocity) of thegalaxy. Our statistical fit is based on the frequency shift of photons emittedby water masers and their orbital positions when circularly revolving aroundthe black hole center within the accretion disk of the active galactic nucleus.By taking into account a previously reported distance to the galaxy, we comparethe result of the black hole mass fit to an estimate based on a mass-luminositycorrelation. We find that the black hole mass at the core of TXS 2226-184obtained with the aid of the statistical fit using the general relativisticmethod, M = 3.67 ^{+0.2}_{-0.2} X 10^6 M_{sun}, is approximately 0.6 times theblack hole mass, M_{BH} = 6.24^{+3.6}_{-2.3} X 10^6 M_{sun}, computed with themass-luminosity correlation.

A general relativistic estimation of the black hole mass-to-distance ratio at the core of TXS 2226-184