Gravitational wave signatures from periodic orbits around a Schwarzschild-Bertotti-Robinson black hole

TL;DR

This paper studies how magnetic fields around a Schwarzschild-Bertotti-Robinson black hole influence orbital dynamics and gravitational wave signals, highlighting potential observable effects for future space-based detectors.

Contribution

It introduces the analysis of gravitational wave signatures from periodic orbits in a magnetized black hole spacetime, revealing magnetic field effects on GW characteristics.

Findings

Magnetic fields alter orbital frequencies and resonance conditions.

Waveforms exhibit significant modifications due to magnetic influence.

Predicted GW signals are detectable by future space-based observatories.

Abstract

In this paper, we investigate periodic bound orbits and gravitational wave (GW) emission in the Schwarzschild-Bertotti-Robinson (Schwarzschild-BR) spacetime-an exact electrovacuum solution describing a static black hole (BH) immersed in a uniform magnetic field. We explore how the background magnetic field qualitatively alters the BH's gravitational dynamics, affecting timelike geodesics such as the marginally bound orbit (MBO) and the innermost stable circular orbit (ISCO). We then analyze periodic bound orbits using the frequency ratio ${\omega_{\varphi}}/{\omega_{r}}$, which characterizes the orbits by their azimuthal and radial motions. Based on the numerical kludge method we further compute the gravitational waveforms emitted from periodic orbits around a supermassive Schwarzschild-BR BH. We show that the background magnetic field significantly changes orbital frequencies, resonance conditions, zoom-whirl structures, and the resulting waveforms. Finally, we examine the frequency spectra in the mHz range and the detectability of these GW signals by computing the characteristic strain via a discrete Fourier transform on the time-domain waveforms, comparing the results with the sensitivity curves of space-based GW detectors such as LISA, Taiji, and TianQin. Our results show that intrinsically magnetic fields modify spacetime and leave observable imprints on extreme mass-ratio inspiral GWs, which may be tested by future observations.