- #1

- 212

- 4

First, here is my source: http://www.thescienceforum.com/physics/30059-solving-einstein-field-equations.html [Broken]

As you can see, this person was showing how to solve at least one basic scenario for the Einstein field equations. Now I have a couple of questions about this person's work?

1. When he proposed that ansatz, why is it that only the first two terms of the space time interval had functions of r attached to them? Here is what I mean:

ds

Notice that only the first two terms of this equation have unknown functions of r like B(r) or A(r) and the other terms don't. Why is this? Why do the unknown functions only go towards the first two terms?

2. I can tell that the space time interval for this scenario is very similar to that of spherical coordinates. Therefore, it is not too hard for me to imagine what the metric tensor for this particular scenario would look like. However, in general cases where the ansatz and the ultimate space time interval that you derive as your solution are not similar to commonly known coordinate systems, how exactly would you derive your metric tensor from your solution?

From what I have learned thus far, you are solving for the metric tensor when you solve the Einstein field equations. If you just derive the space time interval however, how do you actually get your metric tensor (and actually solve the equations) from this?

As you can see, this person was showing how to solve at least one basic scenario for the Einstein field equations. Now I have a couple of questions about this person's work?

1. When he proposed that ansatz, why is it that only the first two terms of the space time interval had functions of r attached to them? Here is what I mean:

ds

^{2}= B(r)c^{2}t^{2}- A(r)dr^{2}- r^{2}(dθ^{2}+ sin^{2}θdø^{2})Notice that only the first two terms of this equation have unknown functions of r like B(r) or A(r) and the other terms don't. Why is this? Why do the unknown functions only go towards the first two terms?

2. I can tell that the space time interval for this scenario is very similar to that of spherical coordinates. Therefore, it is not too hard for me to imagine what the metric tensor for this particular scenario would look like. However, in general cases where the ansatz and the ultimate space time interval that you derive as your solution are not similar to commonly known coordinate systems, how exactly would you derive your metric tensor from your solution?

From what I have learned thus far, you are solving for the metric tensor when you solve the Einstein field equations. If you just derive the space time interval however, how do you actually get your metric tensor (and actually solve the equations) from this?

Last edited by a moderator: