To give you a sense of the range of possibility, let me mention that some researchers have proposed algorithms for computation that involve falling into a black hole and taking advantage of relativistic time foreshortening so that parts of the machine undergo an infinite time history while remaining in the light cone of another part of the machine that experiences only a finite time. In this way, the machine as a whole seems able to simulate an infinite unbounded search and thereby come to know in a finite amount time the answer to a question that a Turing machine could not.
