@filipm hey, good morning. I would like to know if you found any solution

@Hullzie16 I'm looking for a solution that has a positive cosmological constant for an empty spacetime. Maybe this will help! Thanks for your help!

I started using Maple now for research, but I'm having a lot of difficulty because I don't know the language to work in Maple. My problem is knowing how to use maple step by step to solve the following problem: I need to find the solution to Einstein's discovery in 2+1 dimensions, for a sitter space-time under the following conditions: 1- positive cosmological constant; 2- circularly symmetrical line element; tensor energy momentum of a perfect fluid equal to the image with only rho and p nonzero; for small values ​​of r, the metric must be Minkowsk; My goal is to find the Christoffel symbols, the Ricci tensor, the Ricci scalar, substitute this into the field equations and find the line element that describes the Sitter universe.

The images below may help.

solution:

More information that may help: Immediately after calculating the nonzero components of the Ricci tensor and the Ricci scalar, substitute the results into the field equations for the following conditions:

 , , 

getting:

and 

observation:

For the Universe to be static and homogeneous, the measurements of rho and p, made by a local observer, are the same in all parts of space, that is, p and p do not must depend on r.

@Hullzie16  you are correct, it is a tensor that represents a perfect fluid. These images below may help. Images of the line element we need to find, the metric tensor associated with the problem and the components of the Riemann tensor.
My goal is to calculate the simé metric tensor, the line element and the associated components of the Riemann tensor for De Sitter spacetime with positive cosmological constant.