= Solution
Consider an ideal spherical collapse with a <vacuum> exterior of constant <mass> $M$. Once <pressure> support is insufficient, a surface can continue inward and cross the <Schwarzschild event horizon> $r_s=2GM/c^2$ in finite comoving <proper time>. An <event horizon> is a causal boundary: <light> emitted from inside cannot reach distant observers. It is not a material shell or, in the classical Schwarzschild solution, a local <curvature singularity> at $r=r_s$.
The <distant view of gravitational collapse> differs from the surface clock's history. Exterior <Schwarzschild time> has $dt/d\tau\propto(1-r_s/r)^{-1}$ for regular infall and diverges as the surface approaches the horizon. Outgoing radial <light> also takes an increasingly long coordinate time to escape: $dt/dr=[c(1-r_s/r)]^{-1}$ has a logarithmically divergent integral at the horizon. Signals received far away are progressively delayed and redshifted; both gravity and the inward emitter's <Doppler shift> contribute. <photons> carry less received <energy> and arrive at a lower rate, while the available escape directions also narrow.
Thus \b[a distant observer does not receive a <light> signal announcing the crossing; the image fades and reddens rather than remaining a permanently bright frozen surface]. A finite-band detector with finite sensitivity loses it in finite observation time. The divergence of one coordinate chart does not prevent the material crossing in finite <proper time>; horizon-regular coordinates describe that continuation. The pressureless <Oppenheimer-Snyder model> makes this distinction explicit, without representing all the <pressure>, rotation and radiation of a real stellar collapse.<On Continued Gravitational Contraction by J. Robert Oppenheimer and Hartland Snyder>[abstract and pp. 455–459, finite comoving collapse time and redshifted distant description]{ref}
\Image[/past-exam-of-the-relativity-course-of-the-university-of-cambridge/2016/paper-1-infall-signals.png]
{title=Original ideal radial-infall example separating finite proper-time crossing, delayed reception and fading frequency}
The plotted example is a test-particle <geodesic> falling from rest at infinity, used to isolate the coordinate and signal effects; it is not a fitted stellar-collapse <light> curve. No actual observer can hover on the horizon to supply a static local frame there.
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