Gravitational waveforms from periodic orbits around a dyonic ModMax black hole

TL;DR

The study investigates gravitational-wave signals from periodic equatorial orbits (zoom-whirl) of a massive particle around a static dyonic ModMax black hole, highlighting how the ModMax screening parameter $\gamma$ and charge $Q$ alter orbital dynamics and EMRI waveforms. By deriving the spacetime with $f(r) = 1 - 2M/r + Q^2 e^{-\gamma}/r^2$ and using an effective potential $V_{eff} = f(r)\left(1 + L^2/r^2\right)$, the authors compute marginally bound and ISCO thresholds, showing that these quantities generally increase with the parameters and depend on $Q$ and $\gamma$. Periodic orbits are classified by $(z,w,v)$ and labeled by the rational ratio $q = w + v/z$, with energies tabulated for specific configurations. Gravitational waveforms for EMRIs are generated via a numerical kludge, projected into a detector frame, and demonstrated to exhibit characteristic zoom-whirl signatures that shift with $Q$, indicating the potential to constrain BH charge and ModMax screening with future space-based GW observations.

Abstract

In this work, we study the gravitational waveforms from the periodic orbits of a massive particle around a dyonic ModMax black hole. We begin with a brief analysis of the spacetime and then examine how its parameters influence the dynamics of a massive neutral particle using the Lagrangian formalism. In particular, we compute the characteristics of marginally bound orbits and innermost stable circular orbits. Our results show that the values of these quantities increase with the black hole charge $Q$ and the screening parameter $γ$. We then plot various periodic orbits, characterized by the integers ($z$,$w$,$v$). Finally, we present the gravitational waveforms associated with extreme mass ratio inspirals, consisting of a stellar-mass compact object orbiting a supermassive black hole.

Figures (11)

• Figure 1: The left panel shows the radial dependence of the metric function $f(r)$ for different values of the BH charge. The screening parameter is fixed as $\gamma=-0.5$. The right panel illustrates the radial dependence of the metric function $f(r)$ for different values of the screening parameter $\gamma$. The BH charge is fixed as $Q=0.5$.
• Figure 2: The phase diagram demonstrates the existence of the ModMax BH in the $(Q,r)$ plane. The blue region corresponds to the slice of the parameter space where $f(r,Q)\leq0$, indicating the presence of the ModMax BH. The different opacities of the blue refer to the different values of the screening parameter $\gamma$.
• Figure 3: The top-left panel shows the radial dependence of the effective potential of the test particles around the ModMax BH for different values of the BH charge $Q$. Here, we set the screening factor as $\gamma=0.5$. The top-right panel illustrates the radial dependence of the effective potential for different values of the screening factor $\gamma$. Here, the BH charge is equal to $0.5$. Bottom panel: The plot demonstrates the radial dependence of the effective potential for different values of the orbital angular momentum. The other parameters are fixed as $Q=0.5$ and $\gamma=0.5$.
• Figure 4: The plot shows the dependence of the orbital angular momentum (left panel) and the radius of the MBO (right panel) on the BH charge for the different values of the $\gamma$ parameter.
• Figure 5: The plot shows the dependence of the orbital angular momentum (top-left panel) and the radius of the ISCO (top-right panel) on the BH charge for the different values of the $\gamma$ parameter. Bottom panel illustrates the dependence of the ISCO energy on the BH charge $Q$ for different values of the $\gamma$ parameter.