## Radiation from Charged Particles in Circular Motion Around a Schwarzschild Black Hole

arXiv:2404.02195v1 Announce Type: new

Abstract: We study radiation from charged particles in circular motion around a Schwarzschild black hole immersed in an asymptotically uniform magnetic field. In curved space, the radiation reaction force is described by the DeWitt-Brehme equation, which includes a complicated, non-local tail term. We show that, contrary to some claims in the literature, this term cannot, in general, be neglected. We account for self-force effects directly by calculating the electromagnetic energy flux at infinity and on the horizon. The radiative field is obtained using black hole perturbation theory. We solve the relevant equations analytically, in the low-frequency and slow-motion approximation, as well as numerically in the general case. Our results show that great care must be taken when neglecting the tail term, which is often fundamental to capture the dynamics of the particle: in fact, it only seems to be negligible when the magnetic force greatly dominates the gravitational force, so that the motion is well described by the Abraham–Lorentz–Dirac equation. We also report a curious “horizon dominance effect” that occurs for a radiating particle in a circular orbit around a black hole (emitting either scalar, electromagnetic or gravitational waves): for fixed orbital radius, the fraction of energy that is absorbed by the black hole can be made arbitrarily large by decreasing the particle velocity.

In this study, the authors investigate the radiation emitted by charged particles in circular motion around a Schwarzschild black hole in the presence of an asymptotically uniform magnetic field. They specifically focus on the importance of the non-local tail term in the DeWitt-Brehme equation, which describes the radiation reaction force in curved space.

## Main Conclusions:

- The non-local tail term in the DeWitt-Brehme equation cannot be neglected in general, contrary to some claims in the literature.
- The inclusion of the tail term is necessary to accurately capture the dynamics of the particle, especially when the magnetic force dominates the gravitational force.
- An analytical solution is derived in the low-frequency and slow-motion approximation, as well as a numerical solution for the general case.
- It is found that the absorption of energy by the black hole can be significantly increased by decreasing the particle velocity for a radiating particle in a circular orbit.

## Future Roadmap:

### 1. Further Investigation of Tail Term:

Future research should delve deeper into the behavior and implications of the non-local tail term in the DeWitt-Brehme equation. Specifically, a more comprehensive understanding of the scenarios in which the term cannot be neglected is necessary. This will help refine models and calculations related to the radiation emitted by charged particles in curved space.

### 2. Experimental and Observational Validation:

Experimental or observational studies could be conducted to validate the findings of this study. By examining the radiation emitted by charged particles around black holes with magnetic fields, researchers could verify the importance of the non-local tail term and its impact on the dynamics of the particles. This could involve analyzing astrophysical data or designing specialized particle acceleration experiments.

### 3. Investigation of Other Particle Orbits:

Expanding the scope of the research to include particles in different orbital configurations, such as elliptical or inclined orbits, would provide a more comprehensive understanding of the radiation emitted in curved space. The effects of the non-local tail term on these orbits could reveal additional insights into the interplay between gravitational and magnetic forces.

### 4. Study of Radiation Effects on Black Hole Evolution:

Further exploration of the absorption of energy by black holes could shed light on their evolution and the interactions between radiation and spacetime curvature. Investigating the “horizon dominance effect” reported in this study, where increasing energy absorption occurs at lower particle velocities, could have implications for the dynamics and behavior of black holes in the presence of radiation.

## Potential Challenges:

- Theoretical Complexity: The mathematical and theoretical aspects of this research may present challenges for researchers aiming to build upon these findings. Understanding and accurately modeling the non-local tail term and its effects in more complex scenarios could require advanced mathematical techniques and computational resources.
- Limited Observational Data: Obtaining observational data directly related to the radiation emitted by charged particles around black holes with magnetic fields can be challenging. Researchers may need to rely on indirect measurements or simulations to validate and extend the conclusions of this study.
- Experimental Constraints: Designing and conducting experiments to validate these theoretical findings may present technical and logistical challenges. Precision control and measurement of charged particles in the vicinity of black holes could be difficult to achieve in a laboratory setting.

## Potential Opportunities:

- Refinement of Models: The findings of this study provide an opportunity to refine models and calculations related to the radiation emitted by charged particles in curved space. By considering the non-local tail term, researchers can improve the accuracy of their predictions and gain a deeper understanding of the underlying physics.
- Exploration of Astrophysical Phenomena: The investigation of radiation from charged particles in the vicinity of black holes with magnetic fields offers opportunities to better understand astrophysical phenomena. By studying the interplay between gravitational and magnetic forces, researchers can contribute to our knowledge of black hole evolution, radiation emissions, and the dynamics of particles in extreme environments.
- Technological Applications: The insights gained from studying radiation effects in curved space could have practical applications. Understanding the behavior of charged particles in strong gravitational and magnetic fields may influence the design of future particle accelerators or facilitate developments in fields such as astrophysics and materials science.

Overall, this study highlights the importance of considering the non-local tail term in the DeWitt-Brehme equation when studying radiation from charged particles around black holes with magnetic fields. While challenges in theoretical complexity, limited observational data, and experimental constraints may exist, the opportunities for refining models, exploring astrophysical phenomena, and discovering technological applications make this area of research promising for future advancements.