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?

To my knowledge, nobody makes headers out of CF. It may be technically possible, yet not realistic. In high HP operations with high rpms, steel headers can glow red hot without much trouble. The headers are usually steel, titanium or some other alloy. Further down the exhaust pipe, carbon could be used I suppose.

cheers