Expression of Gravitational Potential in GR

[neelakash]

Hello everyone...can anyone tell me what is the modified expression for the gravitational potential in GR which takes into account the fact that the speed of gravity is finite (c, to be precise)...In fact, it may be a non-sense question as I haven't started to read GR yet...Is there any correction factor that involves c and the relative velocity of the two bodies?

--Neel

 

[pervect]

There isn't any such thing as "gravitational potential" in full GR, though you'll see the Newtonian potential used in various places, such as weak-field GR, or in the PPN approximation to GR. One of the reasons for this is that gravity isn't a force in GR as it is in Newtonian theory, it's a curvature of space-time. You can't explain "gravitational time dilation" - i.e. that a clock at a higher altitude will seem to tick more rapidly than a clock at a lower altitude - using just the idea that gravity is a force, for instance. However, the curvature of space-time does explain why the clocks appear to tick at different rates.

While it's true that the speed of gravity in Newtonian gravity is infinite and it's finite in GR, this is not the most fundamental difference between the theories.

 

[bcrowell]

Static spacetimes can be described by a scalar potential, but the OP seems to have non-static spacetimes explicitly in mind. See http://www.lightandmatter.com/html_books/genrel/ch07/ch07.html#Section7.3 , subsection 7.3.7.

There is also a sense in which the metric can be considered to be the gravitational potential -- but it's not a scalar.