A continued question about GR (mainly for Greg Hansen)



Hello.

I am an applied math major with a (nonprofessional) interest in
physics. A few days ago, I posted a question in this group concerning
the force on a scenario in which there are only two objects in the
entire universe and the force on them.between them. Unforunately, my
original thread became diverted with a debate about the validity of
general relativity itself.

The best response I have so far received was one by a man named Greg
Hansen:
"If one object is small compared with the other (the "test mass") and
they are kept stationary relative to each other, and we use naturalized
units where c=G=1, the acceleration of the test mass would be given by

g = (M/r^2) / sqrt(1 - 2M/r)

Newton's theory predicts g=M/r^2. We can say the force is mg."

I have a few questions about this response:
1. The formula above seemed a bit ambiguous to me.
Was the quantity under the radical 1-(2M/r) or (1-2M)/r?
It seems like what you meant was the former, but I could be mistaken.
2. Let us not use naturalized units. Instead, if one uses some other
system, where neither c nor G would be one, what would be the resultant
expression for g?

Thank You in advance.

.


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