Suppose there is a radially free falling object starting at r(t=0) = r(adsbygoogle = window.adsbygoogle || []).push({}); _{0}> r_{S}with some initial velocity v. And suppose there is a radial light ray starting at R(t=0) = R_{0}> r_{0}.

Suppose that both the object and the light ray reach the singularity at the same time.

Question: is there a simple expression to calculate R_{0}in terms of r_{0}and v?

In other words: from which radius R_{0}must a radial light ray start in order to reach the singularity together with a radial free fall observer starting at r_{0}with initial velocity v?

Another equivalent question: which maximal sphere defined by R_{0}can be observed by an astronaut falling towards the singularity starting at starting at r_{0}with initial velocity v?

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# Radial Schwarzschild geodesics - again

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