On the Localisation of 4-Dimensional Brane-World Black Holes II: the
  general case
  We perform a comprehensive analysis of a number of scalar field theories in a
attempt to find analytically 5-dimensional, localised-on-the-brane, black-hole
solutions. Extending a previous analysis, we assume a generalised Vaidya ansatz
for the 5-dimensional metric tensor that allows for time-dependence,
non-trivial profile of the mass function in terms of the bulk coordinate and a
deviation from the over-restricting Schwarzschild-type solution on the brane.
In order to support such a solution, we study a variety of theories including
single or multiple scalar fields, with canonical or non-canonical kinetic
terms, minimally or non-minimally coupled to gravity. We demonstrate that for
such a metric ansatz and for a carefully chosen, non-isotropic in 5 dimensions,
energy-momentum tensor, solutions that have the form of a
Schwarzschild-(Anti)de Sitter or Reissner-Nordstrom type of solution do emerge,
however, the resulting profile of the mass-function along the bulk coordinate,
when allowed, is not the correct one to eliminate the bulk singularities.
