The Schwarzschild weak-deflection angle is derived to all orders from a phase-plane amplitude cubic, giving an explicit coefficient formula with convergence radius at the photon sphere.
Gravitational lensing in metric theories of gravity
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abstract
Gravitational lensing in metric theories of gravity is discussed. I introduce a generalized approximate metric element, inclusive of both post-post-Newtonian (ppN) contributions and gravito-magnetic field. Following Fermat's principle and standard hyphoteses, I derive the time delay function and deflection angle caused by an isolated mass distribution. Several astrophysical systems are considered. In most of the cases, the gravito-magnetic correction offers the best perspectives for an observational detection. Actual measurements distinguish only marginally different metric theories one from another.
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gr-qc 1years
2026 1verdicts
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Phase-plane formulation of weak gravitational deflection in static spherical spacetimes
The Schwarzschild weak-deflection angle is derived to all orders from a phase-plane amplitude cubic, giving an explicit coefficient formula with convergence radius at the photon sphere.