Is it possible to make exhaust pipes from carbon and have them last under the extreme heat cycles?

Would they eventually break down from the exhaust/gas?

What would be the best process to do something like this? I'm thinking custom shaped foam core "pipe" then wrap with carbon and dissolve after.

Has this ever been done on a diy basis or at all for that matter?

Red bull exhaust pipes are made from a resin, no CF resin only.