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While light cannot escape an event horizon, external light should still be observable from within. Would "entering" an event horizon cause it to apparently shrink away from you as you neared the singularity?

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The event horizon will appear to do just the opposite. There is a radial distance at which a photon will in fact orbit the black hole. We can find this by working with the Schwarzschild metric $$ ds^2~=~\left(1~-~\frac{2m}{r}\right)dt^2~-~\left(1~-~\frac{2m}{r}\right)^{-1}dr^2~-~r^2d\Omega^2. $$ where $m~=~GM/c^2$ and $d\Omega^2~=~sin^2\theta d\phi^2~+~d\theta^2$. We now consider an orbit that is circular, and so $dr~=~0$, and we put the orbit on a plane with $\theta~=~\pi/2$ so that $$ ds^2~=~\left(1~-~\frac{2m}{r}\right)dt^2~-~r^2d\phi^2. $$ Before considering the orbit of a photon we can look at the circular orbit of a massive particle with the angular velocity $\omega~=~d\phi/dt$ so the metric is $$ ds^2~=~\left(1~-~\frac{2m}{r}~-~r^2\omega^2\right)dt^2. $$ This can be thought of as a Lagrangian that computes the orbit, and the inclusion of the $dr$ can generalize this for non-spherical orbits. We also have that there is a generalized Lorentz gamma factor $\Gamma~=~dt/ds$, which for $m~=~0$ reduces to the gamma factor in special relativity $\gamma~=~1/\sqrt{1~-~v^2/c^2}$.

The vanishing of $1/\Gamma$ means that we have the angular velocity $$ \omega^2~=~\left(\frac{d\phi}{dt}\right)^2~=~1~-~\frac{2m}{r}. $$ Now compute the radius for the circular orbit of a photon. For simplicity let $A~=~1~-~2m/r$ and $A'~=~dA/dr$. We now look for the radial geodesic equation with $$ \Gamma^r_{tt}~=~AA'/2,~\Gamma^r_{\phi\phi}~=~-Ar, $$ again for $\theta~=~\pi/2$ and put this in the geodesic equation to get $$ \frac{m}{r^3}~=~\left(\frac{d\phi}{dt}\right)^2~=~1~-~\frac{2m}{r} $$ and find the radius is $r~=~3m$

This means at this constant radius a photon would orbit the black hole. This is the last stable orbit. An observer able to remain stationary at this point would see a copy of them selves in front of them; in fact a sort of smeared panorama of them selves. This image would repeat endlessly a bit like a reflection of a mirror in a mirror. The optical perspective of the world in this region would be similar, and as a result the event horizon would not become smaller, but would rather roll out into a large nearly infinite black sheet.

This website gives examples of what would optically appear as one falls towards a black hole. The horizon even persists after you cross it, where the black sheet is now an apparent horizon. enter image description here

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