Vanishing surface energy density for thin shells in generalized Vaidya spacetimes

For any generalized Vaidya spacetime with mass function [Formula: see text] matched to a standard Vaidya exterior across a timelike thin shell at fixed areal radius [Formula: see text] with [Formula: see text], the angular extrinsic curvature jump vanishes identically, [Formula: see text], and the surface energy density is [Formula: see text], in all spacetime dimensions [Formula: see text]. The proof is algebraic: the angular extrinsic curvature depends only on the boundary value of the mass function, which is shared by both sides when the exterior carries the same Misner–Sharp mass at [Formula: see text]. The result is independent of [Formula: see text] and of [Formula: see text]. The shell is a pure stress membrane carrying tangential pressure [Formula: see text] but zero proper shell mass. The theorem is verified in [Formula: see text] for Vaidya–Bonnor, regular black hole (general [Formula: see text]), and Hayward mass functions, in [Formula: see text] for Vaidya–Bonnor and Hayward, and computationally across [Formula: see text] through [Formula: see text]. For all verified cases with [Formula: see text], the null, weak, and strong energy conditions hold on the shell while the dominant energy condition is violated.