Boundary‐Only Weak Deflection by Regular Black Holes, Black‐Bounces, Wormholes, and Static Quadrupolar Spacetimes

ABSTRACT

We apply the boundary‐only isothermal formulation of finite‐distance weak gravitational deflection to regular black holes, black‐bounces, traversable wormholes, non‐asymptotically flat backgrounds, and static quadrupolar spacetimes. The methodological advance is not a new value for a known bending angle. It is a metric‐level reduction that removes the Gaussian‐curvature area integral before any particular spacetime is chosen. Local conformal flatness converts the bulk term in the Gauss–Bonnet construction into boundary information from the isothermal conformal factor, while the logarithmic conformal derivative provides a normalization‐invariant input that does not require a photon sphere, a circular null orbit, or an auxiliary calibration radius. At leading weak‐field order, the source and receiver dependence is carried by a reusable set of endpoint functions, whereas the spacetime dependence is carried by the radial expansion of a single boundary datum. This separation is useful when the relevant circular orbit is absent, nonunique, or unrelated to the observed ray, and when asymptotic scattering is unavailable. We demonstrate this scope using Bardeen, Hayward, and Ayón‐Beato–García regular black holes, the Simpson–Visser family, Ellis–Bronnikov and Morris–Thorne wormholes, Schwarzschild–global‐monopole and Mannheim–Kazanas backgrounds, and the equatorial sectors of Zipoy–Voorhees and Erez–Rosen geometries. These applications serve as stress tests and expose a common classification of mass, charge, throat, regular‐core, conical‐background, cosmological‐background, and quadrupolar terms. The present formulation is restricted to static regions with a Riemannian equatorial optical metric and a suitable isothermal covering. The explicit model corrections reported here are leading straight‐ray boundary contributions, not complete higher‐order post‐Minkowskian deflection angles.