Dynamics of spinning particles around static black holes in effective quantum gravity
Abstract
Abstract We investigate the dynamics of spinning test particles orbiting static black holes in effective quantum gravity (EQG) using the Mathisson–Papapetrou–Dixon (MPD) formalism with two distinct models. The purpose of using two models is to compare qualitatively different realizations of EQG corrections and assess their impact on spin-gravity coupling and orbital behavior. Through analysis of the effective potential, we demonstrate how $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> and particle spin s jointly influence orbital stability, revealing that (i) in Model-1, increasing $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> elevates the potential barrier while spin effects become dominant near the horizon, (ii) Model-2 shows weaker dependence on $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> except for high-spin configurations. The innermost stable circular orbits (ISCOs) exhibit characteristic scaling $$r_{\text {ISCO}}(\zeta ,s)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>r</mml:mi> <mml:mtext>ISCO</mml:mtext> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ζ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>s</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , with quantum corrections that increase the radius of the ISCO by up to 27% relative to Schwarzschild for $$\zeta =4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ζ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> in Model-1. We derive critical spin values $$s_{\text {max}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>s</mml:mi> <mml:mtext>max</mml:mtext> </mml:msub> </mml:math> beyond which particle trajectories become spacelike, finding $$s_{\text {max}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>s</mml:mi> <mml:mtext>max</mml:mtext> </mml:msub> </mml:math> decreases monotonically with $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> in Model-2 but shows non-monotonic behaviour in Model-1. The particle collision energetics are analyzed, showing that the center-of-mass energies $$E_{\text {cm}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mtext>cm</mml:mtext> </mml:msub> </mml:math> can be enhanced by spin-parameter tuning, reaching $$E_{\text {cm}}/2m \sim 8$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mtext>cm</mml:mtext> </mml:msub> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> <mml:mi>m</mml:mi> <mml:mo>∼</mml:mo> <mml:mn>8</mml:mn> </mml:mrow> </mml:math> for $$(\zeta ,s_1,s_2)=(4,-0.5,0.5)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ζ</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>s</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mo>-</mml:mo> <mml:mn>0.5</mml:mn> <mml:mo>,</mml:mo> <mml:mn>0.5</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> near the horizon. Trajectory simulations reveal that quantum corrections in Model-1 induce precession effects absent in Model-2, suggesting observational signatures to distinguish EQG models. Our results establish the combined influence of quantum spacetime structure and spin-curvature coupling on the test particle dynamics, with implications for EQG phenomenology and gravitational wave astronomy.