Critical gravitational collapse of a nonminimally coupled scalar field

We study the critical gravitational collapse of a massless scalar field nonminimally coupled to gravity, using a quadratic coupling function with a strength parameter xi We concentrate on critical phenomena of type II, and determine with an accuracy of at least 10(-12) the value of the critical amplitude for collapse to a black hole, as well as the values of the critical and echoing exponents. Obtaining such high accuracy in the critical amplitude requires us to do a coordinate radial transformation that effectively increases resolution near the central regions by a factor of at least 10(3). As expected, we find that for the case of small coupling the critical behavior is very similar to that of a minimally coupled scalar field. On the other hand, for high coupling the dynamics become so violent that we need to introduce a special slicing condition, known as the shock-avoiding slicing condition, in order to avoid gauge pathologies that would otherwise cause our simulations to fail. With this new gauge condition we are able to perform high-accuracy simulations even in the strong-coupling regime, where we find that the critical and echoing exponents become significantly smaller, and that the echoing behavior is richer and cannot be modeled by a single harmonic.