Let's say we are working with the Schwarzschild metric and we have an emitter of light falling into a Schwarzschild black hole.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose we define the quantity [itex]u=t- v[/itex] where [itex]dv/dr= 1/(1-r_{s}/r)[/itex] where [itex]r_s[/itex] is the Schwarzschild radius. What is the [itex]u[/itex] as observed by the emitter? I just need a *definition of [itex]u_e[/itex]*. I have problems identifying the quantities as measured by an observer at large [itex]r[/itex] and that of the emitter. Would I be right at least to say that [itex]t_{e}=\tau[/itex] the proper time? Many thanks.

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In fact, I've been told that

$$du_o/d\tau=du_e/d\tau$$

Why is it?

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# Definitions Emitter v.s. Observer

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