Time dilation and gravitational constant

[zonde]

I have a question about gravitational constant.
Gravitational constant is dimensionfull constant but say time is is affected by gravitation causing gravitational time dilation. So the definition of second is local.
Does it means that gravitational constant is well defined locally but not globally?
How this is treated in GR?

 

[A.T.]

Gravitational constant is dimensionfull

Not in the http://en.wikipedia.org/wiki/Geometrized_unit_system" , where it is just 1.

constant but say time is is affected by gravitation causing gravitational time dilation. So the definition of second is local. Does it means that gravitational constant is well defined locally but not globally?

If you use a distant clock to measure some physical processes in a gravity well, you will come up with different values for constants, because everything is slowed down.

 

[Entropia]

Time dilation and gravitational constant are both important concepts in the theory of general relativity (GR). Time dilation refers to the phenomenon in which time appears to pass at a different rate for two observers in different gravitational fields. This is due to the curvature of spacetime caused by massive objects. Gravitational constant, on the other hand, is a fundamental constant in physics that determines the strength of the gravitational force between two objects.

To answer your question, in GR, the gravitational constant is considered to be a fundamental constant that is well-defined globally. This means that it has the same value in all regions of spacetime, regardless of the strength of the gravitational field. However, as you mentioned, time dilation does affect the measurement of time, which is why the definition of a second is considered to be local. This means that the length of a second can vary in different gravitational fields.

In GR, the effects of time dilation and the value of the gravitational constant are both taken into account when making calculations and predictions. The theory allows for the gravitational constant to be a fixed value globally, while also allowing for variations in the measurement of time due to gravitational effects. This allows for a consistent and accurate understanding of the universe at both local and global levels.

In summary, while time dilation and the gravitational constant may seem to contradict each other, they are both important concepts in GR that are accounted for in calculations and observations. The gravitational constant is considered to be a well-defined constant globally, while the measurement of time can vary locally due to the effects of gravity.