arXiv:2510.05166v1 Announce Type: new
Abstract: Extreme mass-ratio inspirals (EMRIs) are among the key targets for future space-based gravitational wave detectors. The gravitational waveforms emitted by EMRIs are highly sensitive to the orbital dynamics of the small compact object, which in turn are determined by the geometry of the underlying spacetime. In this paper, we explore the de- tectability of regular black holes with sub-Planckian curvature, which can be interpreted as regularized versions of the Schwarzschild black hole (RSBH). To do so, we begin by ana- lyzing the metric and geodesics, determining the effective potential, and investigating the marginally bound orbits and the innermost stable circular orbits for timelike particles. Our analysis reveals that orbital radius, angular momentum, and energy significantly depend on the model parameter {alpha} for both orbits. Our main aim is to focus on the influence of the model parameter on a specific kind of orbit, the periodic orbit, surrounding a supermassive RSBH. The findings show that, for a constant rational integer, {alpha} has a significant impact on the energy and angular momentum of the periodic orbit. Utilising the numerical kludge method, we further investigate the gravitational waveforms of the small celestial body over various periodic orbits. The waveforms display discrete zoom and spin phases within a complete orbital period, influenced by the RSBH parameter {alpha}. As the system evolves, the phase shift in the gravitational waveforms grows progressively more pronounced, with cumulative deviations amplifying over time. With the ongoing advancements in space- based gravitational wave detection systems, our results will aid in leveraging EMRIs to probe and characterize the RSBH properties.
Conclusions
The study shows that regular black holes with sub-Planckian curvature, as interpreted as regularized versions of Schwarzschild black holes, can have a significant impact on the orbital dynamics of small celestial objects. The model parameter α plays a crucial role in determining the energy, angular momentum, and gravitational waveforms of these objects. The findings suggest that EMRIs involving supermassive RSBHs can provide valuable insights into the properties of these unique black holes.
Roadmap for the Future
Challenges:
- Further refining the models and numerical methods to accurately simulate the behavior of EMRIs around regular black holes.
- Addressing computational constraints to handle the complexity of gravitational waveforms over various orbital periods.
- Validating theoretical predictions with observational data from space-based gravitational wave detectors.
Opportunities:
- Exploring new techniques to enhance the detectability of EMRIs and extract more information about regular black holes.
- Collaborating with the scientific community to analyze the implications of the study’s results on our understanding of astrophysical phenomena.
- Utilizing advancements in technology to improve the precision and resolution of gravitational wave measurements.
By overcoming these challenges and seizing the opportunities ahead, researchers can unlock the full potential of using extreme mass-ratio inspirals to study and characterize regularized black holes in depth.