Probing the nature of Einstein nonlinear Maxwell Yukawa black hole through gravitational wave forms from periodic orbits and quasiperiodic oscillations

TL;DR

This work analyzes test-particle dynamics around the static Einstein nonlinear Maxwell– Yukawa (ENLMY) black hole to probe deviations from general relativity via gravitational waves and quasi-periodic oscillations. It derives the geodesic equations in the ENLMY metric, maps the bound-orbit structure including ISCO/IBCO, and classifies periodic orbits by a rational triplet (z,w,v) that produce distinctive zoom–whirl GW signatures through a kludge quadrupole waveform. The study then connects fundamental frequencies to QPOs using relativistic precession and warped disc models, and constrains the ENLMY parameters (mass $M$, Yukawa parameter $\\alpha$, charge $Q$, and QPO orbit radius $r$) with four microquasars and the Galactic Center via MCMC (emcee). It finds that $\\alpha$ mainly shapes outer-disk frequencies while $Q$ dominates near the horizon, and notes that periodic orbits generally require less energy than in Schwarzschild; the resulting GW signals, via $h_+$ and $h_\times$, encode the orbital structure and modified gravity effects, highlighting the model-dependent nature of parameter inference from QPO data.

Abstract

In this work, we study gravitational wave emission from periodic orbits of test particles, analyze quasi periodic oscillations, and constrain the parameters of the static, spherically symmetric Einstein nonlinear Maxwell Yukawa black hole. Using the Hamiltonian approach, we calculate the equations of motion of the particles. We analyze the effective potential to determine the innermost stable circular orbit and innermost bound circular orbit, illustrating how the Yukawa screening parameter and electric charge Q affect orbital stability and energy requirements. Periodic orbits are classified by integer triplets and exhibit characteristic zoom whirl behavior. Based on these orbits we compute the corresponding GW signals in both the polarizations. Finally, we perform Monte Carlo Markov Chain MCMC simulations to constrain the parameters of the ENLMY BH for four microquasars and the galactic center within the relativistic precession model.

Figures (26)

• Figure 1: Plot of the metric function $f(r)$ for fixed charge $Q=0.5$ and mass $M=1$ with various values of the Yukawa screening parameter $\alpha$.
• Figure 2: Plot of the metric function $f(r)$ for fixed Yukawa screening parameter $\alpha=0.05$ and mass $M=1$ with various values of $Q$.
• Figure 3: Effective potential $V_{\text{eff}}$ for massive particle with fixed $Q=0.5$ and varing Yukawa parameter $\alpha$.
• Figure 4: Effective potential $V_{\text{eff}}$ for massive particle with fixed $\alpha=0.05$ and varing charge parameter $Q$.
• Figure 5: Variation of angular momentum $\mathcal{L}$ with radial coordinate $r$ for fixed $Q=0.5$ and varying $\alpha$.