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Buzz Bloom

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I understand that the coordinate system (CS) for a distant observer O

Here is the scenario I have in mind.

Questions:

1) What are the functions r

2) Are either/both of these two functions different as measured/calculated by O

I am looking forward to a discussion answering these two questions, as well as a description of how the answers were developed.

_{d}is different than that for an observer O_{f}who is falling radially toward the event horizon of a non-rotating black hole (BH). Using the Schwarzschild metric, I would like to understand the transformation equations that calculate the change in observations of time, t, and radial position, r, as seen by both O_{d}and O_{f}.Here is the scenario I have in mind.

Each observer has a one of two identical clocks, syncrhonized at time t

Starting at a given radius, r

_{0}.Starting at a given radius, r

_{0}, which is the distance from the center of the BH (in O_{d}'s CS at time t_{0}), O_{d}observes as O_{f}falls towards the BH. O_{d}is maintained stationary at r_{0}by a suitable repulsion engine. t_{0}is the time a which O_{f}begins to fall radially toward the BH.Using repulsion engines, there are stationary marker objects that can be observed by both O

O

b)

In this scenario, both O_{d}and O_{f}. As O_{f}passes the marker m_{r}at radius r (in O_{d}'s CS), both observers can measure the value of t at O_{d}'s radius r (no doubt getting different values.O

_{d}and O_{f}can communicate with each other with light speed messages. The messages they exchange enable each observer to know:*a) when*the other (using the other's clock) saw O

_{f}passing m

_{r}, and

b)

*when*a message sent by one observer was received by the other.

_{d}and O_{f}measure t(r) for the falling O_{f}and both can calculate the two respective r(t) functions: t_{d}(r) and t_{f}(r).Questions:

1) What are the functions r

_{d}(r) and r_{f}(t)?2) Are either/both of these two functions different as measured/calculated by O

_{d}and O_{f}? If so, in what way?I am looking forward to a discussion answering these two questions, as well as a description of how the answers were developed.

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