New features of black strings and branes in higher dimensional gravity due to a cosmological constant

This thesis is essentially organized in two parts: braneworlds and higher dimensional black objects with a cosmological constant. We present solitonic braneworld models where the brane are inflating and with the presence of a cosmological constant, by analyzing four particular models. These models, although slightly different exhibit common features which are pointed out. We also consider $1+1$ dimensional toy models for coupling fermionic matter fields to braneworld. In particular, we focus on a kink or kink/anti-kink solution of the Sine-Gordon model, which can be seen as modeling a brane in the dimensions transverse to our four dimensional spacetime. We also analyze the stability of three particular models admitting kink or anti-kink like solutions and show that the stability equations are Poschl-Teller equations. In the second part after quickly reviewing available analytically known solutions, we present the numerical construction of the higher dimensional charged rotating black hole with a cosmological constant. Then, we present the black string solution and review the stability problem of the latter before investigating the existence of a de Sitter black string, which turns out not to be regular. Finally, we present the AdS counterpart of the black string solution and study its stability. Then, we construct numerically non uniform black strings, first in a perturbative approach, then in the full non linear regime. Our result suggest the existence of a thermodynamically stable phase of non uniform black string and point to the presence of a phase of AdS localized black hole. Moreover, we argue that the phase transition from uniform to non uniform black strings can be of order larger than one in any number of dimensions, which is not the case without a cosmological constant.