Chaos in general relativity
DOI: 10.1063/1.4796390
Is coordinate invariant. A new study shows that general relativity, a nonlinear theory in which observers in different reference frames measure time differently, is not incompatible with chaos, a theory for nonlinear systems in which events unfold in absolute time. A physical system–-a weather system, say–-is chaotic if a very slight change in initial conditions sends the system off on a very different course. How different? The degree to which a system is chaotic can be encapsulated in a parameter called the Lyapunov exponent: When it is positive, the system is chaotic; when negative or null, the system is nonchaotic. For many years, physicists worried that a shift in a frame of reference might also alter the time parameter in such a way as to change the Lyapunov exponent from null or negative to positive or vice versa. Adilson Motter of the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, has now laid this matter to rest by showing that a change of time parameter does not alter the sign of a well-defined Lyapunov exponent. (
