Magnetized particle motion around magnetized Schwarzschild-MOG black hole

Abstract In this paper, we have presented the studies of the motion of magnetized particles and energetic processes around Schwarzschild black holes in modified gravity (MOG). The study of circular stable orbits shows that orbits of magnetized particles can not be stable for the values of magnetic coupling parameter $$\beta \ge 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>β</mml:mi><mml:mo>≥</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> . It was also shown that the range of stable circular orbits increases with the increase of both MOG and magnetic coupling parameters, while the effects of magnetic interaction stronger than the gravity. It was obtained that the increase of the MOG parameter causes the increase of center-of-mass energy collision of magnetized particles. Moreover, we have analyzed how to mimic the magnetic interaction with the spin of Kerr and Schwarzschild-MOG black holes. We have obtained that the magnetic coupling parameter can mimic the spin parameter $$a \le 0.15$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>a</mml:mi><mml:mo>≤</mml:mo><mml:mn>0.15</mml:mn></mml:mrow></mml:math> ( $$a \le 0.28$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>a</mml:mi><mml:mo>≤</mml:mo><mml:mn>0.28</mml:mn></mml:mrow></mml:math> ) giving the same radius of innermost contour(co)-rotating orbits at the values of the parameter $$\beta \in (-1,1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>β</mml:mi><mml:mo>∈</mml:mo><mml:mo>(</mml:mo><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> and the MOG parameter in the range $$\alpha \in (-0.17,0.28)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mo>∈</mml:mo><mml:mo>(</mml:mo><mml:mo>-</mml:mo><mml:mn>0.17</mml:mn><mml:mo>,</mml:mo><mml:mn>0.28</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> while the MOG parameter $$\alpha \in (-0.7, 0.9)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mo>∈</mml:mo><mml:mo>(</mml:mo><mml:mo>-</mml:mo><mml:mn>0.7</mml:mn><mml:mo>,</mml:mo><mml:mn>0.9</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> mimics spin parameter of the black hole with the range $$|a| \in (0,1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>|</mml:mo><mml:mi>a</mml:mi><mml:mo>|</mml:mo><mml:mo>∈</mml:mo><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> .