Regular black hole's impact on the gravitational waveforms from periodic orbits

Abstract

In this paper, we investigate periodic orbits exhibiting zoom-whirl behavior around a magnetically charged black hole (MCBH) within the framework of the regular black hole. We examine how the magnetic charge influences orbital dynamics by modifying the background spacetime geometry, thereby affecting the energy and angular momentum of particles. In particular, we calculate the radii of the marginally bound orbits (MBOs) and innermost stable circular orbits (ISCOs), demonstrating that the magnetic charge parameter reduces both radii. This provides valuable insight into the role of the charge parameter in shaping orbital behavior and altering spacetime geometry. We model the complex motion of a stellar-mass object as a timelike particle, inspiraling into a supermassive black hole (SMBH) in the MCBH background, with its trajectory described using periodic geodesic orbits. Based on this analysis of such periodic orbits, we further analyze the gravitational waveforms generated by extreme mass ratio inspirals (EMRIs), in which the SMBH's spacetime dominates the dynamics of the stellar-mass object. By combining particle trajectory analysis with waveform modeling in a semi-analytical approach, we show that the charge parameter significantly alters the zoom-whirl orbital dynamics and induces notable changes in the waveform structure. These results illustrate that future gravitational wave (GW) observations may constrain the properties of MCBHs, thereby deepening our understanding of the gravitational imprint of regular black holes.

Figures (9)

• Figure 1: The plot illustrates the radial dependence of the Kretschmann scalar for different values of the magnetic charge parameter.
• Figure 2: The plot shows the radial dependence of the effective potential for different values of the magnetic charge parameter $q$ (left panel) and the orbital angular momentum (right panel).
• Figure 3: The plot shows the allowed parameter space of the energy and orbital angular momentum for the bound orbits around the MCBH with different values of the magnetic charge parameter $q$
• Figure 4: Left panel: The plot shows the rational number as a function of the energy of the particles for different values of the magnetic charge parameter. Here, we set $L_{av}=\frac{1}{2}(L_{MBO}+L_{ISCO})$. Right panel: The plot illustrates the rational number as a function of the orbital angular momentum for different values of the magnetic charge parameter $q$. The energy of the particles is $E=0.96$ for this panel.
• Figure 5: The figure illustrates the periodic orbits characterized by different $(z,w,v)$ around the MCBH. Here, $q=0.4$ and $L_{av}=\frac{1}{2}(L_{MBO}+L_{ISCO})$.