Solve Einstein Field Equation without Vacuum Solution

[TimeRip496]

How to solve EFE without using the vacuum solution like how you did in schwarzschild metric?

 

[DEvens]

Do you mean, how to solve the EFE for a general situation? If that is what you mean, probably using numerical methods and a computer.

If you mean something else, please say what.

 

[TimeRip496]

Do you mean, how to solve the EFE for a general situation? If that is what you mean, probably using numerical methods and a computer.

If you mean something else, please say what.

I am not sure why can we just use the vacuum solution to solve EFE? Why can't we use a nom zero stress momentum tensor to solve?

 

[Nugatory]

I am not sure why can we just use the vacuum solution to solve EFE? Why can't we use a non zero stress momentum tensor to solve?

The space outside the surface of an object floating in space (like a star or a planet) is vacuum so the stress-energy tensor there is zero. Thus, if we want a solution to the field equations that applies there we set $T$ equal to zero.

In other problems, for example a ball of dust collapsing under its own gravitational attraction to form a star or planet (google for "Oppenheimer-Snyder"), we don't have a vacuum and the stress energy tensor is not zero. Then we have to solve the field equation for a non-zero stress-energy tensor.

 

[PeterDonis]

In other problems, for example a ball of dust collapsing under its own gravitational attraction to form a star or planet (google for "Oppenheimer-Snyder"), we don't have a vacuum and the stress energy tensor is not zero. Then we have to solve the field equation for a non-zero stress-energy tensor.

Another example is the solutions describing the universe as a whole.