# Einstein Field Equation

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

DEvens
Gold Member
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.

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 cant we use a nom zero stress momentum tensor to solve?

Nugatory
Mentor
I am not sure why can we just use the vacuum solution to solve EFE? Why cant 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.

Last edited:
TimeRip496
PeterDonis
Mentor
2020 Award
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.