# Einstein Field Equation

1. Feb 16, 2015

### TimeRip496

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

2. Feb 16, 2015

### 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.

3. Feb 17, 2015

### TimeRip496

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?

4. Feb 17, 2015

### Staff: Mentor

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: Feb 17, 2015
5. Feb 17, 2015

### Staff: Mentor

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