Mathematical modelling of scalar field gravitational collapse by means of covariant series in normal coordinates

A new method for solving the Cauchy problem for the spherically symmetric Einstein equations is developed. The method is based on analytical continuation of initial data along geodesics by means of covariant series in normal coordinates. We use this method to study the spherically symmetric collapse of real, minimally coupled gravitating scalar fields in an asymptotically flat spacetime. The obtained results are in good agreement with the theory of critical phenomena in gravitational collapse. In addition it is shown that there are two horizons at an early stage of collapse.