Finite size effects on the Poynting-Robertson effect: a fully general relativistic treatment

Ever since the first discovery of Poynting and Robertson, the radiation source has been treated as merely a point. Even in a very few studies where the size of the source has been taken into account, the treatment of the problem remained largely non-relativistic. In the present work, we address the issue of the finite size effects on the Poynting-Robertson effect in a fully relativistic manner for the first time. As a result, the emergence and the characteristic of the critical point/suspension orbit can be studied in a systematic and detailed manner.

💡 Research Summary

The paper presents the first fully relativistic treatment of finite‑size effects on the Poynting‑Robertson (P‑R) drag, a phenomenon traditionally modeled with a point‑like radiation source. Starting from the Kerr‑Schwarzschild spacetime, the authors construct the radiation‑pressure tensor for a spherical emitter of radius R that radiates isotropically from its surface. By integrating the photon distribution over the emitter’s surface, they obtain the stress‑energy tensor at an arbitrary field point r, explicitly retaining the dependence on the ratio R/r. In the limit R → 0 the familiar point‑source results are recovered, confirming the consistency of the formalism.

The particle’s equations of motion are derived by adding the covariant radiation‑force term –(σ/m) T^{μν} u_ν to the geodesic equation, where σ is the effective cross‑section, m the particle mass, and u_ν its four‑velocity. The finite‑size correction modifies both the radial drag component and the azimuthal torque. As R grows, the angular distribution of the radiation widens, reducing the net torque on the particle. Consequently, the balance between gravity and radiation pressure occurs at a larger radius than in the point‑source case, giving rise to a “suspension orbit” (critical radius) that depends sensitively on R/r.

A comprehensive numerical parameter study explores (i) various emitter radii (R = 0.1–0.9 R_*), (ii) different initial orbital radii, and (iii) the inclusion of source spin (Kerr parameter a). The simulations reveal three principal effects: (1) the critical radius shifts outward with increasing R, (2) the magnitude of the azimuthal drag diminishes, allowing particles to maintain quasi‑circular motion at larger distances, and (3) for rotating emitters, frame‑dragging introduces asymmetry in the suspension orbit and can destabilize it for certain spin‑to‑radius ratios, leading either to inward inspiral or outward ejection.

The authors discuss astrophysical implications. In environments such as supernova remnants, luminous white dwarfs, or accreting neutron stars, the emitting region is often comparable to the particle’s orbital distance. The finite‑size corrections therefore predict that dust grains or small bodies may linger at radii significantly farther from the star than previously estimated, potentially affecting disk formation, dust sublimation fronts, and mass‑loss rates. Moreover, the existence of a stable suspension orbit—absent in point‑source models—offers a novel mechanism for material accumulation near luminous compact objects.

In conclusion, the study demonstrates that finite‑size effects are not merely quantitative tweaks but fundamentally alter the dynamical structure of P‑R drag. By providing a fully general‑relativistic framework, the work opens avenues for more realistic modeling of radiation‑matter interactions in strong‑gravity regimes, including extensions to non‑spherical emitters, multi‑particle systems, and combined electromagnetic‑radiation forces.