Dynamics of charged particles and magnetic dipoles around magnetized quasi-Schwarzschild black holes
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.