Quasi-Periodic Oscillations and Parameter Constraints in ModMax Black Holes

TL;DR

This study investigates test-particle dynamics and quasi-periodic oscillations around ModMax black holes, a nonlinear electrodynamics extension of GR. By deriving the equations of motion, analyzing the effective potential, and computing Keplerian and epicyclic frequencies, the work shows how the ModMax parameter $η$ transitions the spacetime behavior from RN toward Schwarzschild, producing outward shifts of the ISCO and reduced orbital frequencies at fixed radius. It then examines six QPO models (PR, RP, WD, ER2–ER4) to map resonance radii and demonstrates that QPO-generating regions move outward as $η$ increases. Finally, an MCMC analysis across stellar-, intermediate-, and supermassive-black-hole data constrains $M,η,Q/M,r/M$, finding $η$ typically order unity, suggesting detectable nonlinear electrodynamics signatures in QPO spectra that could help test deviations from standard electrodynamics in strong-field gravity.

Abstract

We analyze the impact of ModMax parameter on the dynamics of test particles around black holes and its effect on the characteristics of Quasi-Periodic Oscillations (QPOs). The effect of the ModMax parameter $η$ is studied using the effective potential, angular momentum and the energy of the circular orbits of the test particles. Our analysis shows that increasing $η$ brings about a continuous transition from the RN regime toward the Schwarzschild limit, accompanied by noticeable modifications in the Innermost Stable Circular Orbit (ISCO) and the corresponding Keplerian frequencies. We also explore the dependence of QPO radii on the ModMax parameter $η$ within the framework of the PR, RP, WD, and ER models. Finally, to place observational constraints, we perform a Markov Chain Monte Carlo (MCMC) analysis using QPO data from a range of black hole sources spanning stellar-mass, intermediate-mass, and supermassive scales.

Figures (8)

• Figure 1: Dependence of the effective potential $V_\text{eff}$ on the radial coordinate $r$ for different values of ModMax parameter $\eta$. Here $Q=0.5$
• Figure 2: The radial dependence of specific angular momentum and energy for circular orbits for different values of NED parameter b. Here, we have considered $Q = 0.5$.
• Figure 3: Dependence of the ISCO radius on the ModMax parameter $\eta$
• Figure 4: Variation of angular frequency $\Omega_\phi$ with respect to $r$
• Figure 5: The correlations between the upper ($\nu_U$) and lower ($\nu_L$) twin-peak QPO frequencies as analyzed under the PR, RP, WD, and ER2–ER4 models for Schwarzschild, RN, and ModMax black hole backgrounds.