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We present the discovery of correlations between the X-ray spectral (photon)index and mass accretion rate observed in active galactic nuclei (AGNs)3C~454.3 and M87. We analyzed spectral transition episodes observed in theseAGNs using Chandra, Swift, Suzaku, BeppoSAX, ASCA and RXTE data. We applied ascaling technique for a black hole (BH) mass evaluation which uses acorrelation between the photon index (Gamma) and normalization of the seedcomponent which is proportional to a disk mass accretion rate Mdot. Wedeveloped an analytical model that shows that Gamma of the BH emergent spectrumundergoes an evolution from lower to higher values depending on Mdot. Toestimate a BH mass in 3C~454.3 we consider extra-galactic SMBHs NGC~4051 andNGC~7469 as well as Galactic BHs Cygnus X--1 and GRO~J1550--564 as referencesources for which distances, inclination angles are known and the BH masses arealready evaluated. For M87 on the other hand, we provide the BH mass scalingusing extra-galactic sources (IMBHs: ESO 243-49 HLX 1 and M 101 ULX--1) andGalactic sources (stellar mass BHs: XTE J1550-564, 4U 1630-472, GRS 1915+105and H 1743-322) as reference sources. Application of the scaling technique forthe photon index-Mdot correlation provides estimates of the BH masses in 3C454.3 and M87 to be about 3.4x10^9 and 5.6 x10^7 solar masses, respectively. Wealso compared our scaling BH mass estimates with a recent BH mass estimate ofM_{87}=6.5x 10^9 M_{\odot} made using the {Event Horizon Telescope} which givesan image at 1.3 mm and is based on the angular size of the `BH event horizon'.Our BH mass estimate in M87 is at least two orders of magnitude lower than thatmade by the EHT team.

Spectral index-mass accretion rate correlation and evaluation of black hole masses in AGNs 3C~454.3 and M87