Gravitational Constant in GR: How & Why?

[Zak]

(precursor: I have not formally studied GR)

I have noticed that the gravitational constant found in classical gravitation is also used in GR. Why is this the case? Am I correct in thinking that the constant was determined by Cavendish and was for the classical theory of gravitation? So, my question: how do we know that the same gravitational constant is suitable for GR and why did we not have to, say, measure a new constant?

 

[JorisL]

(precursor: I have not formally studied GR)

I have noticed that the gravitational constant found in classical gravitation is also used in GR. Why is this the case? Am I correct in thinking that the constant was determined by Cavendish and was for the classical theory of gravitation? So, my question: how do we know that the same gravitational constant is suitable for GR and why did we not have to, say, measure a new constant?

We get $G$ into the Einstein equations by requiring that they reduce to the classical gravitation law in the limit of slow (test-)particles in low gravitational fields.

Essentially the reason is that we want GR to supersede Newtonian gravity.

 

[Dale]

I have noticed that the gravitational constant found in classical gravitation is also used in GR. Why is this the case?

As JorisL mentioned, you can look at is as a requirement so that GR can reduce to Newtonian gravity in the appropriate limit.

Another way to look at it is that G is just a universal conversion factor between different units, so any time that you will convert between the same units you will get a the same conversion factor.

 

[Dale]

I have noticed that the gravitational constant found in classical gravitation is also used in GR. Why is this the case?

You can think of it in terms of reducing to Newtonian gravitation in the appropriate limit. You can also look at it as a conversion factor between different units. So then it is the same in both theories as long as you use the same units.