New Physics and Hypercomputation

Does new physics give us a chance for designing computers, at least in principle, beyond the Turing barrier?

Part of what we call "new physics" is the surge of results in black hole physics in the last 15 years, which certainly changed our perspective on certain things. The two main directions in this line seem to be quantum computers and relativistic i.e. spacetime theory based ones. We will concentrate on the relativistic case.

Is there a remote possibility that relativity can give some feedback to its "founding grandmother", namely, to logic?