Gravitational wave radiation from periodic orbits and quasi-periodic oscillations in Einstein non-linear Maxwell-Yukawa black hole

TL;DR

This paper evaluates test-particle dynamics around an Einstein-nonlinear Maxwell-Yukawa (ENLMY) black hole, a modified-gravity solution with a Yukawa-like potential, to explore strong-field effects. By employing a Hamiltonian formulation, it derives the equations of motion, effective potential, and circular-orbit conditions, revealing how the Yukawa parameters $\delta$ and $\lambda$ shift ISCO/IBCO radii and circular-orbit energetics. It then classifies bound periodic orbits using Levin’s framework, analyzes the resulting gravitational-wave (GW) signals via a kludge EMRI approach, and computes fundamental frequencies, including QPO relations under RP, WD, and TD models. An extensive MCMC analysis constrains the ENLMY BH mass and Yukawa parameters using QPO data from stellar-, intermediate-, and supermassive BHs, illustrating how $\lambda$ governs the GR-like mimic region and the potential to distinguish ENLMY gravity from GR with precise observations. Overall, the study demonstrates that ENLMY gravity can imprint measurable signatures on both GW and QPO phenomenology, providing a framework to test intermediate-scale deviations from GR and constrain the underlying Yukawa-type corrections.

Abstract

In this article, we investigate the orbital dynamics and quasi-periodic oscillations (QPOs) surrounding a static, spherically symmetric geometry of an Einstein-nonlinear Maxwell-Yukawa (ENMY) black hole (BH). Using the Hamiltonian formalism, we derive equations of motion and analyze the effective potential. We determine the innermost stable circular orbits (ISCO) and innermost bound circular orbits (IBCO) radii for different values of the Yukawa parameters $λ$ and $δ$, and classify periodic orbits via rational frequency analysis, highlighting deviations from Schwarzschild geometry. We also study gravitational wave (GW) emission from periodic orbits and show how Yukawa terms affect GW signals. Fundamental frequencies are computed, and QPOs are analyzed using relativistic precession, warped disk, and tidal disruption models. By increasing $λ$, the ENLMY spacetime effectively mimics the behavior of a Schwarzschild spacetime. Constraints on the BH mass and Yukawa parameters are derived using QPO data from stellar-mass (XTE J1550-564, GRO J1655-40, GRS 1915+105), intermediate-mass (M82 X-1), and supermassive (Sgr A*) BHs within the relativistic precession model by employing a Markov Chain Monte Carlo analysis.

Figures (17)

• Figure 1: Ricci scalar as a function of the radial coordinate $r$, plotted for two values of $\delta$, with fixed $M = 1$ and $\lambda = 10$. Vertical red dotted lines mark the corresponding event horizons.
• Figure 2: Effective potential for radial motion of test particles around the ENLMY BH for various values of parameter $\lambda$ and $\delta$.
• Figure 3: The radial dependence of the specific energy of a particle in circular orbits around the ENLMY BH for different values of $\lambda$ and $\delta$.
• Figure 4: The radial dependence of the specific angular momentum of a particle in circular orbits around the ENLMY BH for different values of $\lambda$ and $\delta$.
• Figure 5: Behavior of the effective potential for various angular momenta, plotted for $\lambda = 10$ and $\delta = -0.5$ (top), $0.5$ (bottom).