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Numerical Relativity by Tomas Baumagrte and Stuart Shapiro page 10.

By adapting $h=c=1$, so in schwarzchild solution the areal radius $r=2M$ is the event horizon, and $r=3M$ is the photon orbit. But what happened between $2M<r<3M$ then? is that the distance where mass must falls in?

Also $E/\mu=\frac{(r-2M)^2}{r(r-3M)}$ where $\mu$ is the rest mass for particle.(Also one conservation for the angular momentum.) How could any matter pass through the photon orbit then?

ShoutOutAndCalculate
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1 Answers1

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$r=3M$ is where there is an (unstable) lightlike orbit around the black hole. for $2M < r < 3M$, the light ray will spiral into the black hole. In this range, nonaccelerating timelike paths can fall in, but they still can escape (i.e., by "firing their rockets).

This is different than paths that pass into the region $r \leq 2M$, where there are no timelike or null paths that escape back to infinity.

Zo the Relativist
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