Strong deflection of massive particles in spherically symmetric spacetimes

Abstract

Near a gravitating compact object, massive particles traveling along timelike geodesics are gravitationally deflected similarly to light. In this paper, we study the deflection angles of these particles in the strong deflection limit. This analytical approximation applies when particles in unbound orbits approach the compact object very closely, circle around it at a radius close to that of the unstable circular orbit, and eventually escape. While previous studies have provided results for particular metrics, we offer a general solution applicable to any static, spherically symmetric and asymptotically flat spacetime. After briefly reviewing the exact expression for the deflection angle of massive particles, we present a strong deflection limit analysis for this general case. The developed formulas are then applied to three particular metrics: Schwarzschild, Reissner-Nordström and Janis-Newman-Winicour.

16 pages, 11 figures; v2: typos corrected, version accepted for publication in Physical Review D; v3: published version; v4: further typos fixed; v5: minor edits for clarity; v6: corrected typos in Eqs. (23), (24), (43), and (58); no change to the conclusions

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• Strong deflection of massive particles via the geodesic deviation equation
• Strong field gravitational lensing of particles by a black-bounce-Schwarzschild black hole