Self-similar collapse of a scalar field in dilaton gravity and critical behaviour

Abstract

We present new analytical self-similar solutions describing a collapse of a massless scalar field in scalar-tensor theories. The solutions exhibit a type of critical behavior. The black hole mass for the near critical evolution is analytically obtained for several scalar-tensor theories and the critical exponent is calculated. Within the framework of the analytical models we consider it is found that the black hole mass law for some scalar-tensor theories is of the form $M_{BH}=f(p-p_{cr})(p-p_{cr})^γ$ which is slightly different from the general relativistic law $M_{BH}=const (p-p_{cr})^γ$.