  The noninvariance of Lyapunov exponents in general relativity has led to the
conclusion that chaos depends on the choice of the space-time coordinates.
Strikingly, we uncover the transformation laws of Lyapunov exponents under
general space-time transformations and we find that chaos, as characterized by
positive Lyapunov exponents, is coordinate invariant. As a result, the previous
conclusion regarding the noninvariance of chaos in cosmology, a major claim
about chaos in general relativity, necessarily involves the violation of
hypotheses required for a proper definition of the Lyapunov exponents.
