Searching for Localized Black-Hole solutions in Brane-World models

In the context of this thesis, the question that is going to occupy us, is the existence of a 5-dimensional braneworld black hole solution that is localized close to the 3-brane and has the properties of a regular 4-dimensional one. For this purpose, the 4-dimensional part of the complete 5-dimensional spacetime is considered to be a generalized Vaidya metric, in the context of which, the mass parameter $m$ is allowed to vary with respect to time, while it is also allowed to have both $y$ and $r$ dependence. The dependence on the $r$-coordinate essentially means that our black hole solution can deviate from the conventional Schwarzschild solution. Additionally, the dependence on the $y$-coordinate leads to a non-trivial profile of the black hole along the extra dimension. In order to justify physically the existence of such general mass parameter, we consider the case of two scalar fields $\phi(v,r,y)$, $\chi(v,r,y)$ which interact with each other and they are also non-minimally coupled to gravity via a general coupling function $f(\phi,\chi)$. In all the cases that were investigated in the context of this particular scenario, the result for the existence of a viable 5-dimensional localized black hole solution was negative, a result that causes concern about the compatibility of brane-world models with basic predictions of General Theory of Relativity.