  We consider type-A higher-spin gravity in AdS_4, holographically dual to a
free U(N) vector model on the boundary. We study the linearized version of the
Didenko-Vasiliev "BPS black hole", which we view as this theory's equivalent of
the fundamental string. The Didenko-Vasiliev solution consists of gauge fields
of all spins generated by a particle-like source along a bulk geodesic, and is
holographically dual to a bilocal boundary operator at the geodesic's
endpoints. Our first main result is a new gauge for this solution, which makes
manifest its behavior under the boundary field equation. It can be viewed as an
AdS uplift of flat spacetime's de Donder gauge, but is not de Donder in AdS. To
our knowledge, this gauge is novel even in the spin-2 sector, and thus provides
a new expression for the linearized gravitational field of a massive point
particle in (A)dS_4. Our second main result is a proof of the holographic
duality between the mutual bulk action of two Didenko-Vasiliev solutions and
the CFT correlator of two boundary bilocals. As an intermediate step, we show
that in a bilocal->local limit, the Didenko-Vasiliev solution reproduces the
standard boundary-bulk propagators of all spins. We work in the "metric-like"
language of Fronsdal fields, and use the embedding-space formalism.
