A possible failure of determinism in general relativity

Abstract

Is the future predictable? If we know the initial state of a system exactly, then do the laws of physics determine its state arbitrarily far into the future? In Newtonian mechanics, the answer is yes. Similarly in electromagnetism: if one knows the initial state of the electric and magnetic fields exactly, then Maxwell’s equations determine their state at any later time. In quantum mechanics, if the initial wave function is known exactly, then Schrödinger’s equation can be used to predict the wave function at any later time. However, new research by Vitor Cardoso from the University of Lisbon, Portugal, and colleagues [1] suggests that this predictability of the laws of physics can fail in general relativity. The researchers find that it might be possible for a star that undergoes gravitational collapse to form a black hole containing a region in which physics cannot be predicted from the initial state of the star.