Exact analytic relations express M, α, D (and a) of Schwarzschild-MOG and Kerr-MOG black holes directly in terms of accretion-disk frequency shift, aperture angle, and redshift rapidity (plus acceleration in the rotating case).
Herrera-Aguilar and U
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Closed-form expressions for Schwarzschild black hole mass, distance to Earth, and orbital radius are derived from photon frequency shift observables along the full orbit using redshift rapidity from symmetric emitter positions.
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Accretion Disks in Schwarzschild-MOG and Kerr-MOG Backgrounds: MOG Parameter in terms of Observational Quantities
Exact analytic relations express M, α, D (and a) of Schwarzschild-MOG and Kerr-MOG black holes directly in terms of accretion-disk frequency shift, aperture angle, and redshift rapidity (plus acceleration in the rotating case).
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Black hole mass and distance from accretion disk astrophysical observables
Closed-form expressions for Schwarzschild black hole mass, distance to Earth, and orbital radius are derived from photon frequency shift observables along the full orbit using redshift rapidity from symmetric emitter positions.