On the mass of black holes with scalar field hair in anti-de Sitter spacetime

Since it has been proven that the no-hair conjecture has exceptions, systems of gravity coupled with matter have been of great interest. This thesis studies one of these exceptions: the case of a scalar field with nonconvex self interaction potential minimally coupled with gravity in anti-de Sitter spacetime. By considering a convex potential we prove a no-hair theorem for the four possible scalar field cases. For nonconvex potential however, stable soliton and black hole solutions are found. We focus on the stable black hole solutions. We find the explicit expressions for the mass of these spacetimes in four, five and six dimensions. To obtain a finite mass it is necessary to consider the gravitational and the scalar contribution. The scalar contribution is different for different masses of the scalar field above the Breitenlohner-Freedman bound \cite{breitenlohner82}. The last part of the thesis is concerned with providing a numerical method to calculate the mass for the different spacetimes with two different nonconvex potentials. The mass depends on three parameter $a$, $b$ and $f_{rr}$. Each parameter is found by solving a differential equation using mathematica. We present a selection of plots to illustrate our results for the masses.