Dynamics of charged particles and magnetic dipoles around magnetized quasi-Schwarzschild black holes
Bakhtiyor Narzilloev, Javlon Rayimbaev, Ahmadjon Abdujabbarov, Bobomurat Ahmedov, Cosimo Bambi
Abstract
Abstract In the present paper, we have investigated the motion of charged particles together with magnetic dipoles to determine how well the spacetime deviation parameter $$\epsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϵ</mml:mi> </mml:math> and external uniform magnetic field can mimic the spin of a rotating Kerr black hole. Investigation of charged particle motion has shown that the deviation parameter $$\epsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϵ</mml:mi> </mml:math> in the absence of an external magnetic fields can mimic the rotation parameter of the Kerr spacetime up to $$a/M \approx 0.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>/</mml:mo> <mml:mi>M</mml:mi> <mml:mo>≈</mml:mo> <mml:mn>0.5</mml:mn> </mml:mrow> </mml:math> . The combination of an external magnetic field and deviation parameter can do even a better job mimicking the rotation parameter up to $$a/M\simeq 0.93$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>/</mml:mo> <mml:mi>M</mml:mi> <mml:mo>≃</mml:mo> <mml:mn>0.93</mml:mn> </mml:mrow> </mml:math> , which corresponds to the rapidly rotating case. Study of the dynamics of the magnetic dipoles around quasi-Schwarzschild black holes in the external magnetic field has shown that there are degeneracy values of the ISCO radius of test particles at $$\epsilon _{cr}>\epsilon \ge 0.35$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ϵ</mml:mi> <mml:mrow> <mml:mi>cr</mml:mi> </mml:mrow> </mml:msub> <mml:mo>></mml:mo> <mml:mi>ϵ</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>0.35</mml:mn> </mml:mrow> </mml:math> which may lead to two different values of the innermost stable circular orbit (ISCO) radius. When the deviation parameter is in the range of $$\epsilon \in (-1,\ 1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ϵ</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mspace/> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , it can mimic the spin of a rotating Kerr black hole in the range $$a/M \in (0.0537, \ 0.3952)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>/</mml:mo> <mml:mi>M</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>0.0537</mml:mn> <mml:mo>,</mml:mo> <mml:mspace/> <mml:mn>0.3952</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> for magnetic dipoles with values of the magnetic coupling parameter $$\beta \in [-0.25,\ 0.25]$$ <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>0.25</mml:mn> <mml:mo>,</mml:mo> <mml:mspace/> <mml:mn>0.25</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> </mml:math> in corotating orbits.