The lower bound on the orbital period of Kerr–Newman black holes

Abstract Based on studies of orbital periods in Kerr black hole spacetimes, Hod conjectured the existence of a universal lower bound on the orbital period for compact objects. In this work, we test this bound for Kerr–Newman black holes using both analytical and numerical methods. By choosing different charge and spin of Kerr–Newman black holes, we establish a lower bound on the orbital period for Kerr–Newman black holes expressed as $$T(r)\geqslant 4\pi M$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>(</mml:mo> <mml:mi>r</mml:mi> <mml:mo>)</mml:mo> <mml:mo>⩾</mml:mo> <mml:mn>4</mml:mn> <mml:mi>π</mml:mi> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> , where r is the orbital radius, T ( r ) is the orbital period observed from infinity and M is the black hole mass. This bound is consistent with Hod’s conjecture. Moreover, we numerically demonstrate that the lower bound is achieved at the extreme Kerr limit in the absence of charge. Our findings support Hod’s conjectured lower bound within the Kerr–Newman family. However, they do not constitute a universal proof for arbitrary black holes.