Observational signatures of Schwarzschild-MOG black holes in scalar–tensor–vector gravity: images of the accretion disk

Abstract

Abstract The present paper contains the investigations with respect to the optical appearance, redshift distribution, and observed energy flux of the thin accretion disk described by the Novikov-Thorne model in modified gravity (MOG) proposed by Moffat. The results show that the gravity coupling parameter $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> plays an indispensable role in the size of direct and secondary images of the accretion disk, while the image profile is mainly affected by the observational angles. In addition, an increase of the parameter $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> leads to that of the redshift factor, but a decrease in the radiation energy flux of the accretion disk. These results are due to the enhancement of the parameter $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> that strengthens the black hole’s gravitational effects. By comparing the accretion disk images of the Schwarzschild-MOG black hole, the Schwarzschild black hole, and the Reissner–Nordström black hole, we point out that the Schwarzschild-MOG black hole exhibits the largest inner shadow and the lowest luminosity. This finding provides a potential way to distinguish Schwarzschild-MOG black holes from their counterparts in General Relativity.