Fundamental physical constants are naturally included in all laws of physics. Their numerical values should reflect the properties of the world around us, but their origin remains unexplained to this day. It has been suggested since Dirac's work of 1937, 1938 that in a dynamically evolving Universe the physical constants may also be dynamical variables corresponding to the local age of the world. However, numerous laboratory experiments with various atomic and, more recently, nuclear clocks have failed to detect changes in physical constants with time at an ever deeper level, which corresponds at present to an upper limit on the relative change in, for example, the fine structure constant α, 10^(-19)/year. Astronomical spectral measurements allow such tests to go beyond laboratory experiments and study spatial and temporal constraints on variations of physical constants. It turned out that in this case the most sensitive parameter is the dimensionless quantity - the electron-to-proton mass ratio
(μ = m_e/m_p), since it determines the structure of molecular levels in a wide spectral range. The most accurate cosmological constraints, corresponding to look-back time greater than 10 billion years, give an estimate of Δμ/µ < 5*10^(-8), which is based on the analysis of methanol (CH3OH) transitions. The same order of magnitude upper limit was obtained from observations of the methanol lines in the disk of our Galaxy at relatively large galactocentric distances, R ~ 8-12 kpc.  In our work we estimated
Δμ/µ near a massive black hole, the Galactic center, at a distance R ~ 100 pc, which showed a possible decrease of μ at the level Δμ/µ = (-3.7±0.5)*10^(-7). The detected signal requires further independent study.

J.Vorotyntseva, S.Levshakov
JETP Letters 121, issue 8 (2025)